IMT Institutional Repository: No conditions. Results ordered -Date Deposited. 2020-02-25T07:33:36ZEPrintshttp://eprints.imtlucca.it/images/logowhite.pnghttp://eprints.imtlucca.it/2017-09-26T07:55:57Z2017-09-26T07:55:57Zhttp://eprints.imtlucca.it/id/eprint/3800This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/38002017-09-26T07:55:57ZStrength prediction of notched thin ply laminates using finite fracture mechanics and the phase field approachThin ply laminates are a new class of composite materials with great potential for application in the design of thinner and highly optimized components, resulting in potential weight savings and improved mechanical performance. These new composites can stir the development of lighter structures, overcoming current design limitations as well as notably reducing the onset and development of matrix cracking and delamination events. This paper presents the application of two recent modeling methods for the failure analysis and strength prediction of open-hole thin ply laminates under tensile loading,
which exhibit a brittle response upon failure: (i) the analytical coupled energy-stress Finite Fracture Mechanics (FFMs) technique, and (ii) the FE-based Phase Field (PF) approach for fracture that is incorporated into an enhanced assumed solid shell element. The predictions obtained using both strategies are compared with experimental data. These correlations exhibit a very satisfactory level of agreement, proving the robustness and reliability of both methods under consideration.José ReinosoA. ArterioMarco Paggimarco.paggi@imtlucca.itP.P. Camanho2017-09-26T07:53:06Z2017-09-26T07:53:06Zhttp://eprints.imtlucca.it/id/eprint/3801This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/38012017-09-26T07:53:06ZA new analytical critical thrust force model for delamination analysis of laminated composites during drilling operationFibre reinforced polymer (FRP) composite laminates are employed in many industrial applications due to
their attractive mechanical and structural properties. Machining operation, such as drilling of FRP
laminates, plays a significant role in the assembly of parts in aircraft and spacecraft production. Among
other production bottlenecks, drilling-induced delamination remains a major defect which adversely
affects the quality of assembly parts. An efficient strategy in preventing this problem is the calculation of
the critical thrust force above which delamination is initiated. Therefore, in this study, a new analytical
model is proposed to predict the critical thrust force for delamination. Unlike the general models in the
literature which derived only mode I strain energy release rate based on the assumption of classical
laminate plate theory (CLPT) combined with linear elastic fracture mechanics (LEFM) mode I considerations
in the elliptic delamination zone, the proposed analytical model is derived based on first-order
shear deformation theory (FSDT) and accounts for mode I and mode II strain energy release rates in
the delamination zone. This strategy allows to activate mixed mode criteria for delamination initiation
which is a valid assumption for laminates with layers of different orientations. The present model is
partly derived for general laminates subject to distributed loading and further extended to cross-ply
laminate sequence subject to a mixed load condition. The results show that the effect of shear deformation
in the prediction of the critical thrust force is influential with increasing ply thickness and the
effect of chisel edge on shear deformation is more profound in the distributed load regime.Saheed Olalekan Ojosaheed.ojo@imtlucca.itS.O. IsmailMarco Paggimarco.paggi@imtlucca.itH.N. Dhakal2017-03-21T14:13:22Z2017-03-21T14:13:22Zhttp://eprints.imtlucca.it/id/eprint/3680This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36802017-03-21T14:13:22ZA nonlinear finite thickness cohesive interface element for modeling delamination in fibre-reinforced composite laminatesAbstract Delamination events are major issues which notably affect the integrity of composite structures. To minimize the experimental efforts, there is an increasing demand for developing reliable numerical tools that can accurately simulate delamination initiation and propagation under mixed-mode loading conditions. The current investigation is concerned with the formulation and the finite element (FE) implementation of a new nonlinear finite thickness cohesive interface model for delamination analysis of fibre-reinforced composite laminates relying on the solid shell concept. The incorporation of geometrically nonlinear effects into the proposed interface formulation is motivated by the recent trend of producing composite structures that can experience large displacements prior to failure, as is the case of postbuckling in stiffened panels. The inelastic material behavior of the interface is modeled using two standard nonlinear decohesion laws: (i) an exponential-based, and (ii) a polynomial-based interface laws. Finally, the performance of the proposed interface element is demonstrated by means of several examples focusing on double cantilever beam (DCB) and rib-stiffened specimens. A excellent level of accuracy is achieved when comparing the numerical predictions and the available experimental data.José ReinosoMarco Paggimarco.paggi@imtlucca.itA. Blázquez2017-03-21T14:01:17Z2017-03-21T14:01:17Zhttp://eprints.imtlucca.it/id/eprint/3679This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36792017-03-21T14:01:17ZRevisiting the problem of a crack impinging on an interface: a modeling framework for the interaction between the phase field approach for brittle fracture and the interface cohesive zone modelThe problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In this investigation, this problem is revisited in view of the recent progresses on the phase field approach to brittle fracture. In this concern, a novel formulation combining the phase field approach for modeling brittle fracture in the bulk and a cohesive zone model for pre-existing adhesive interfaces is herein proposed to investigate the competition between crack penetration and deflection at an interface. The model, implemented within the finite element method framework using a monolithic fully implicit solution strategy, is applied to provide a further insight into the understanding of the role of model parameters on the above competition. In particular, in this study, the role of the fracture toughness ratio between the interface and the adjoining bulks and the characteristic fracture-length scales of the dissipative models are analyzed. In the case of a brittle interface, the asymptotic predictions based on linear elastic fracture mechanics criteria for crack penetration, single deflection or double deflection are fully captured by the present method. Moreover, by increasing the size of the process zone along the interface, or by varying the internal length scale of the phase field model, new complex phenomena are emerging, such as simultaneous crack penetration and deflection and the transition from single crack penetration to deflection and penetration with subsequent branching into the bulk.Marco Paggimarco.paggi@imtlucca.itJosé Reinoso2017-03-21T12:24:42Z2017-09-18T09:30:16Zhttp://eprints.imtlucca.it/id/eprint/3675This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36752017-03-21T12:24:42ZAuxetic behavior and acoustic properties of microstructured piezoelectric strain sensorsThe use of multifunctional composite materials adopting piezo-electric periodic cellular lattice structures with auxetic elastic behavior is a recent and promising solution in the design of piezoelectric sensors. In the present work, periodic anti-tetrachiral auxetic lattice structures, characterized by different geometries, are taken into account and the mechanical and piezoelectrical response are investigated. The equivalent piezoelectric properties are obtained adopting a first order computational homogenization approach, generalized to the case of electro-mechanical coupling, and various polarization directions are adopted. Two examples of in-plane and out-of-plane strain sensors are proposed as design concepts. Moreover, a piezo-elasto-dynamic dispersion analysis adopting the Floquet–Bloch decomposition is performed. The acoustic behavior of the periodic piezoelectric material with auxetic topology is studied and possible band gaps are detected.Maria Laura De BellisAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2017-03-21T12:19:26Z2017-03-21T12:19:26Zhttp://eprints.imtlucca.it/id/eprint/3674This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36742017-03-21T12:19:26ZMulti-field asymptotic homogenization of thermo-piezoelectric materials with periodic microstructureThis study proposes a multi-field asymptotic homogenization for the analysis of thermo-piezoelectric materials with periodic microstructures. The effect of the microstructural heterogeneity is taken into account by means of periodic perturbation functions, which derive from the solution of non homogeneous recursive cell problems defined over the unit periodic cell. A strong coupling is present between the micro displacement field and the micro electric potential field, since the mechanical and the electric problems are fully coupled in the asymptotically expanded microscale field equations. The micro displacement, the electric potential, and the relative temperature fields have been related to the macroscopic quantities and to their gradients in the derived down-scaling relations. Average field equations of infinite order have been obtained and the closed form of the overall constitutive tensors has been determined for the equivalent first-order homogenized continuum. A formal solution of such equations has been derived by means of an asymptotic expansion of the macro fields. The accuracy of the proposed formulation is assessed in relation to illustrative examples of a bi-material periodic microstructure subjected to harmonic body forces, free charge densities, and heat sources, whose periodicity is much greater than the characteristic microstructural size. The good agreement obtained between the solution of the homogenized model and the finite element solution of the original heterogeneous material problem confirms the validity of the proposed formulation.Francesca FantoniAndrea Bacigalupoandrea.bacigalupo@imtlucca.itMarco Paggimarco.paggi@imtlucca.it2017-03-21T12:16:36Z2017-03-21T12:16:36Zhttp://eprints.imtlucca.it/id/eprint/3673This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36732017-03-21T12:16:36ZParametric design of the band structure for lattice materialsLattice materials are often investigated to determine how small parameter variations in the periodic microstructrure can influence the elastic wave propagation. A general hierarchical scheme, based on asymptotic perturbation techniques, is outlined to analytically assess the parametric sensitivity of the material band structure to a generic multi-parametric perturbation (direct problem). Modeling refinements, parameters updates, microstructural damages and manufacturing irregularities can be treated indifferently and simultaneously. According to a converse strategy, based on the inversion of the sensitivity problem, a hierarchical scheme is sketched to identify the parameter combinations which realize a design band structure (inverse problem). The direct and inverse problem are applied to the sensitivity analysis and band structure design of the anti-tetrachiral lattice material. Despite the high spectral density and the high-dimensional parameter space, the multi-parameter perturbation technique demonstrates its suitability in, first, analytically---although asymptotically---describe the material spectrum and, second, designing the material microstructure to obtain the desired spectral components. The inverse problem solution is discussed in terms of existence, uniqueness, asymptotic consistency and physical admissibility.Marco LepidiAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2017-03-21T12:12:26Z2017-03-21T12:12:26Zhttp://eprints.imtlucca.it/id/eprint/3672This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36722017-03-21T12:12:26ZOverall thermomechanical properties of layered materials for energy devices applicationsThis paper is concerned with the analysis of effective thermomechanical properties of multi-layered materials of interest for solid oxide fuel cells (SOFC) and lithium ions batteries fabrication. The recently developed asymptotic homogenization procedure is applied in order to express the overall thermoelastic constants of the first order equivalent continuum in terms of microfluctuations functions, and these functions are obtained by the solution of the corresponding recursive cell problems. The effects of thermal stresses on periodic multi-layered thermoelastic composite reproducing the characteristics of solid oxide fuel cells (SOFC-like) are studied assuming periodic body forces and heat sources, and the solution derived by means of the asymptotic homogenization approach is compared with the results obtained by finite elements analysis of the associate heterogeneous material.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLorenzo MoriniAmdrea Piccolroaz2017-03-21T12:04:34Z2017-09-21T14:58:45Zhttp://eprints.imtlucca.it/id/eprint/3670This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36702017-03-21T12:04:34ZWave propagation in non-centrosymmetric beam-lattices with lumped masses: discrete and micropolar modellingThe in-plane acoustic behavior of non-centrosymmetric lattices having nodes endowed with mass and rotational inertia and connected by massless ligaments with asymmetric elastic properties has been analyzed through a discrete model and a continuum micropolar model. In the first case the propagation of harmonic waves and the dispersion functions have been obtained by the discrete Floquet–Bloch approach. It is shown that the optical branch departs from a critical point with vanishing group velocity and is decreasing for increasing the norm of the wave vector. A micropolar continuum model has been derived through a continualization method based on a down-scaling law from a second-order Taylor expansion of the generalized macro-displacement field. It is worth noting that the second order elasticity tensor coupling curvatures and micro-couples turns out to be negative-definite also in the general case of non-centrosymmetric lattice. The eigenvalue problem governing the harmonic propagation in the micropolar non-centrosymmetric continuum results in general characterized by a hermitian full matrix that is exact up to the second order in the wave vector.
Examples concerning square and equilateral triangular lattices have been analyzed and their acoustic properties have been derived with the discrete and continuum models. The dependence of the Floquet–Bloch spectra on the lattice non-centrosymmetry is shown together with validity limits of the micropolar model. Finally, in consideration of the negative definiteness of the second order elastic tensor of the micropolar model, the loss of strong hyperbolicity of the equation of motion has been investigated.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2017-01-30T11:29:16Z2017-09-21T14:32:15Zhttp://eprints.imtlucca.it/id/eprint/3648This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36482017-01-30T11:29:16ZConcurrently coupled solid shell based adaptive multiscale method for fractureA solid shell-based adaptive atomistic–continuum numerical method is herein proposed to simulate complex crack growth patterns in thin-walled structures. A hybrid solid shell formulation relying on the combined use of the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods has been considered to efficiently model the material in thin structures at the continuum level. The phantom node method (PNM) is employed to model the discontinuities in the bulk. The discontinuous solid shell element is then concurrently coupled with a molecular statics model placed around the crack tip. The coupling between the coarse scale and the fine scale is realized through the use of ghost atoms, whose positions are interpolated from the coarse scale solution and enforced as boundary conditions to the fine scale model. In the proposed numerical scheme, the fine scale region is adaptively enlarged as the crack propagates and the region behind the crack tip is adaptively coarsened in order to reduce the computation costs. An energy criterion is used to detect the crack tip location. All the atomistic simulations are carried out using the LAMMPS software. A computational framework has been developed in MATLAB to trigger LAMMPS through system command. This allows a two way interaction between the coarse and fine scales in MATLAB platform, where the boundary conditions to the fine region are extracted from the coarse scale, and the crack tip location from the atomistic model is transferred back to the continuum scale. The developed framework has been applied to study crack growth in the energy minimization problems. Inspired by the influence of fracture on current–voltage characteristics of thin Silicon photovoltaic cells, the cubic diamond lattice structure of Silicon is used to model the material in the fine scale region, whilst the Tersoff potential function is employed to model the atom–atom interactions. The versatility and robustness of the proposed methodology is demonstrated by means of several fracture applications.Pattabhi R. Budarapupattabhi.budarapu@imtlucca.itJosé ReinosoMarco Paggimarco.paggi@imtlucca.it2017-01-30T10:33:52Z2017-01-30T11:33:18Zhttp://eprints.imtlucca.it/id/eprint/3647This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/36472017-01-30T10:33:52ZLattice orientation and crack size effect on the mechanical properties of GrapheneThe effect of lattice orientation and crack length on the mechanical properties of Graphene are studied based on molecular dynamics simulations. Bond breaking and crack initiation in an initial edge crack model with 13 different crack lengths, in 10 different lattice orientations of Graphene are examined. In all the lattice orientations, three recurrent fracture patterns are reported. The influence of the lattice orientation and crack length on yield stress and yield strain of Graphene is also investigated. The arm-chair fracture pattern is observed to possess the lowest yield properties. A sudden decrease in yield stress and yield strain can be noticed for crack sizes <10 nm. However, for larger crack sizes, a linear decrease in yield stress is observed, whereas a constant yield strain of ≈≈0.05 is noticed. Therefore, the yield strain of ≈≈0.05 can be considered as a critical strain value below which Graphene does not show failure. This information can be utilized as a lower bound for the design of nano-devices for various strain sensor applications. Furthermore, the yield data will be useful while developing the Graphene coating on Silicon surface in order to enhance the mechanical and electrical characteristics of solar cells and to arrest the growth of micro-cracks in Silicon cells.Pattabhi R. Budarapupattabhi.budarapu@imtlucca.itB. JavvajiV. K. SutrakarD. Roy MahapatraMarco Paggimarco.paggi@imtlucca.itG. ZiT. Rabczuk2016-06-30T13:06:19Z2016-06-30T13:06:19Zhttp://eprints.imtlucca.it/id/eprint/2512This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25122016-06-30T13:06:19ZA micropolar model for the analysis of dispersive waves in hexachiral mass-in-mass latticesAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2016-04-19T08:06:52Z2016-04-19T08:06:52Zhttp://eprints.imtlucca.it/id/eprint/3456This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/34562016-04-19T08:06:52ZFrom NASGRO to fractals: Representing crack growth in metalsThis paper presents the results of an extensive experimental analysis of the fractal properties of fatigue crack rough surfaces. The analysis of the power-spectral density functions of profilometric traces shows a predominance of the box fractal dimension D = 1.2. This result leads to a particularization of the fatigue crack growth equation based on fractality proposed by the last two authors which is very close to the generalized Frost–Dugdale equation proposed by the first three authors. The two approaches, albeit based
on different initial modelling assumptions, are both very effective in predicting the crack growth rate of short cracks.R. JonesF. ChenS. PittMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2016-03-15T10:30:26Z2016-03-15T10:30:26Zhttp://eprints.imtlucca.it/id/eprint/3238This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/32382016-03-15T10:30:26ZInterfacial cracks in bi-materials solids: Stroh
formalism and skew-symmetric weight functionsLorenzo Morinilorenzo.morini@imtlucca.itEnrico RadiAlexander MovchanNatalia Movchan2016-03-15T10:15:54Z2016-03-15T10:15:54Zhttp://eprints.imtlucca.it/id/eprint/3237This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/32372016-03-15T10:15:54ZLoading profile effects on dynamic crack
propagation in couple stress elastic materialsAmdrea PiccolroazLorenzo Morinilorenzo.morini@imtlucca.itGennady MishurisP.A. Gourgiotis2015-10-08T08:06:56Z2017-03-27T14:23:19Zhttp://eprints.imtlucca.it/id/eprint/2764This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27642015-10-08T08:06:56ZEvolution of the free volume between rough surfaces in contactThe free volume comprised between rough surfaces in contact governs the fluid/gas transport properties across networks of cracks and the leakage/percolation phenomena in seals. In this study, a fundamental insight into the evolution of the free volume depending on the mean plane separation, on the real contact area and on the applied pressure is gained in reference to fractal surfaces whose contact response is solved using the boundary element method. Particular attention is paid to the effect of the surface fractal dimension and of the surface resolution on the predicted results. The free volume domains corresponding to different threshold levels are found to display fractal spatial distributions whose bounds to their fractal dimensions are theoretically derived. A synthetic formula based on the probability distribution function of the free volumes is proposed to synthetically interpret the numerically observed trends.Marco Paggimarco.paggi@imtlucca.itQi-Chang He2015-10-08T08:03:17Z2015-10-08T08:04:30Zhttp://eprints.imtlucca.it/id/eprint/2763This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/27632015-10-08T08:03:17ZOptimization algorithms for the solution of the frictionless normal contact between rough surfacesThis paper revisits the fundamental equations for the solution of the frictionless unilateral normal contact problem between a rough rigid surface and a linear elastic half-plane using the boundary element method (BEM). After recasting the resulting Linear Complementarity Problem (LCP) as a convex quadratic program (QP) with nonnegative constraints, different optimization algorithms are compared for its solution: (i) a Greedy method, based on different solvers for the unconstrained linear system (Conjugate Gradient CG, Gauss–Seidel, Cholesky factorization), (ii) a constrained CG algorithm, (iii) the Alternating Direction Method of Multipliers (ADMM), and (iv) the Non-Negative Least Squares (NNLS) algorithm, possibly warm-started by accelerated gradient projection steps or taking advantage of a loading history. The latter method is two orders of magnitude faster than the Greedy CG method and one order of magnitude faster than the constrained CG algorithm. Finally, we propose another type of warm start based on a refined criterion for the identification of the initial trial contact domain that can be used in conjunction with all the previous optimization algorithms. This method, called cascade multi-resolution (CMR), takes advantage of physical considerations regarding the scaling of the contact predictions by changing the surface resolution. The method is very efficient and accurate when applied to real or numerically generated rough surfaces, provided that their power spectral density function is of power-law type, as in case of self-affine fractal surfaces.Alberto Bemporadalberto.bemporad@imtlucca.itMarco Paggimarco.paggi@imtlucca.it2015-04-07T14:00:07Z2015-04-07T14:00:07Zhttp://eprints.imtlucca.it/id/eprint/2657This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26572015-04-07T14:00:07ZA dual gradient-projection algorithm for model predictive control in fixed-point arithmetic Although linear Model Predictive Control has gained increasing popularity for controlling dynamical systems subject to constraints, the main barrier that prevents its widespread use in embedded applications is the need to solve a Quadratic Program (QP) in real-time. This paper proposes a dual gradient projection (DGP) algorithm specifically tailored for implementation on fixed-point hardware. A detailed convergence rate analysis is presented in the presence of round-off errors due to fixed-point arithmetic. Based on these results, concrete guidelines are provided for selecting the minimum number of fractional and integer bits that guarantee convergence to a suboptimal solution within a pre-specified tolerance, therefore reducing the cost and power consumption of the hardware device. Panagiotis Patrinospanagiotis.patrinos@imtlucca.itAlberto Guiggianialberto.guiggiani@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2015-04-07T13:53:35Z2015-10-28T14:49:34Zhttp://eprints.imtlucca.it/id/eprint/2656This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26562015-04-07T13:53:35ZA multiparametric quadratic programming algorithm with polyhedral computations based on nonnegative least squaresModel Predictive Control (MPC) is one of the most successful techniques adopted in industry to control multivariable systems under constraints on input and output variables. To circumvent the main drawback of MPC, i.e., the need to solve a Quadratic Program (QP) on line to compute the control action, explicit MPC was proposed in the past to precompute the control law off line using multiparametric QP (mpQP). The resulting form of the MPC law is piecewise affine, which is extremely easy to code, can be computed online by simple arithmetic operations, and requires a maximum number of iterations that can be exactly determined a priori. On the other hand, the offline computations to solve the mpQP problem require detecting emptiness, full-dimensionality, and minimal hyperplane representations of polyhedra, and other computational geometric operations. While most of the existing methods solve such operations via linear programming, the approach proposed in this paper relies on a nonnegative least squares (NNLS) solver that is very simple to code, fast to execute, and provides solutions up to machine precision. In addition, the new approach exploits QP duality to identify and construct critical regions and to handle degeneracy issues.Alberto Bemporadalberto.bemporad@imtlucca.it2015-03-02T09:41:51Z2015-03-02T09:41:51Zhttp://eprints.imtlucca.it/id/eprint/2624This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/26242015-03-02T09:41:51ZA convex feasibility approach to anytime model predictive controlThis paper proposes to decouple performance optimization and enforcement of asymptotic convergence in Model Predictive Control (MPC) so that convergence to a given terminal set is achieved independently of how much performance is optimized at each sampling step. By embedding an explicit decreasing condition in the MPC constraints and thanks to a novel and very easy-to-implement convex feasibility solver proposed in the paper, it is possible to run an outer performance optimization algorithm on top of the feasibility solver and optimize for an amount of time that depends on the available CPU resources within the current sampling step (possibly going open-loop at a given sampling step in the extreme case no resources are available) and still guarantee convergence to the terminal set. While the MPC setup and the solver proposed in the paper can deal with quite general classes of functions, we highlight the synthesis method and show numerical results in case of linear MPC and ellipsoidal and polyhedral terminal sets. Alberto Bemporadalberto.bemporad@imtlucca.itDaniele Bernardinidaniele.bernardini@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.it2015-01-21T09:53:35Z2016-03-11T12:17:52Zhttp://eprints.imtlucca.it/id/eprint/2544This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25442015-01-21T09:53:35ZEffective elastic properties of planar SOFCs: a non-local dynamic homogenization approachAbstract The focus of the article is on the analysis of effective elastic properties of planar Solid Oxide Fuel Cell (SOFC) devices. An ideal periodic multi-layered composite (SOFC-like) reproducing the overall properties of multi-layer {SOFC} devices is defined. Adopting a non-local dynamic homogenization method, explicit expressions for overall elastic moduli and inertial terms of this material are derived in terms of micro-fluctuation functions. These micro-fluctuation functions are then obtained solving the cell problems by means of finite element techniques. The effects of the temperature variation on overall elastic and inertial properties of the fuel cells are studied. Dispersion relations for acoustic waves in SOFC-like multilayered materials are derived as functions of the overall constants, and the results obtained by the proposed computational homogenization approach are compared with those provided by rigorous Floquet–Bloch theory. Finally, the influence of the temperature and of the elastic properties variation on the Bloch spectrum is investigated.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLorenzo Morinilorenzo.morini@imtlucca.itAmdrea Piccolroaz2015-01-21T09:29:47Z2015-01-21T09:29:47Zhttp://eprints.imtlucca.it/id/eprint/2543This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25432015-01-21T09:29:47ZHomogenization of periodic hexa- and tetrachiral cellular solids Abstract The homogenization of periodic hexachiral and tetrachiral honeycombs is dealt with two different techniques. The first is based on a micropolar homogenization. The second approach, developed to analyse two-dimensional periodic cells consisting of deformable portions such as the ring, the ligaments and possibly a filling material, is based on a second gradient homogenization developed by the authors. The obtained elastic moduli depend on the parameter of chirality, namely the angle of inclination of the ligaments with respect to the grid of lines connecting the centers of the rings. For hexachiral cells the auxetic property of the lattice together with the elastic coupling modulus between the normal and the asymmetric strains is obtained; a property that has been confirmed here for the tetrachiral lattice. Unlike the hexagonal lattice, the classical constitutive equations of the tetragonal lattice turns out to be characterized by the coupling between the normal and shear strains through an elastic modulus that is an odd function of the parameter of chirality. Moreover, this lattice is found to exhibit a remarkable variability of the Young’s modulus and of the Poisson’s ratio with the direction of the applied uniaxial stress. Finally, a simulation of experimental results is carried out. Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-21T09:25:51Z2015-01-21T09:25:51Zhttp://eprints.imtlucca.it/id/eprint/2542This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25422015-01-21T09:25:51ZA micropolar model for the analysis of dispersive waves in chiral mass-in-mass latticesThe possibility of obtaining band gap structures in chiral auxetic lattices is here considered and applied to the case of inertial locally resonant structures. These periodic materials are modelled as beam-lattices made up of a periodic array of rigid rings, each one connected to the others through elastic slender ligaments. To obtain low-frequency stop bands, elastic circular resonating inclusions made up of masses located inside the rings and connected to them through an elastic surrounding interface are considered and modeled. The equations of motion are obtained for an equivalent homogenized micropolar continuum and the overall elastic moduli and the inertia terms are given for both the hexachiral and the tetrachiral lattice. The constitutive equation of the beam lattice given by the Authors [15] are then applied and a system of six equations of motion is obtained. The propagation of plane waves travelling along the direction of the lines connecting the ring centres of the lattice is analysed and the secular equation is derived, from which the dispersive functions may be obtained.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-21T09:18:34Z2015-01-21T09:18:34Zhttp://eprints.imtlucca.it/id/eprint/2541This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25412015-01-21T09:18:34ZSecond-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limitsIn this paper a second-order homogenization approach for periodic material is derived from an appropriate representation of the down-scaling that correlates the micro-displacement field to the macro-displacement field and the macro-strain tensors involving unknown perturbation functions. These functions take into account of the effects of the heterogeneities and are obtained by the solution of properly defined recursive cell problems. Moreover, the perturbation functions and therefore the micro-displacement fields result to be sufficiently regular to guarantee the anti-periodicity of the traction on the periodic unit cell. A generalization of the macro-homogeneity condition is obtained through an asymptotic expansion of the mean strain energy at the micro-scale in terms of the microstructural characteristic size ɛ; the obtained overall elastic moduli result to be not affected by the choice of periodic cell. The coupling between the macro- and micro-stress tensor in the periodic cell is deduced from an application of the generalised macro-homogeneity condition applied to a representative portion of the heterogeneous material (cluster of periodic cell). The correlation between the proposed asymptotic homogenization approach and the computational second-order homogenization methods (which are based on the so called quadratic ansätze) is obtained through an approximation of the macro-displacement field based on a second-order Taylor expansion. The form of the overall elastic moduli obtained through the two homogenization approaches, here proposed, is analyzed and the differences are highlighted. An evaluation of the developed method in comparison with other recently proposed in literature is carried out in the example where a three-phase orthotropic material is considered. The characteristic lengths of the second-order equivalent continuum are obtained by both the asymptotic and the computational procedures here analyzed. The reliability of the proposed approach is evaluated for the case of shear and extensional deformation of the considered two-dimensional infinite elastic medium subjected to periodic body forces; the results from the second-order model are compared with those of the heterogeneous continuum.Andrea Bacigalupoandrea.bacigalupo@imtlucca.it2015-01-21T09:14:57Z2015-01-21T09:14:57Zhttp://eprints.imtlucca.it/id/eprint/2540This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25402015-01-21T09:14:57ZComputational dynamic homogenization for the analysis of dispersive waves in layered rock masses with periodic fractures Abstract The analysis of the wave propagation in layered rocks masses with periodic fractures is tackled via a two-scale approach in order to consider shape and size of the rock inhomogeneities. To match the displacement fields at the two scales, an approximation of the micro-displacement field is assumed that depends on the first and second gradients of the macro-displacement through micro-fluctuation displacement functions obtained by the finite element solution of cell problems derived by the classical asymptotic homogenization. The resulting equations of motion of the equivalent continuum at the macro-scale result to be not local in space, thus a dispersive wave propagation is obtained from the model. The simplifying hypotheses assumed in the multi-scale kinematics limit the validity of the model to the first dispersive branch in the frequency spectrum corresponding to the lowest modes. Although the homogenization procedure is developed to study the macro-scale wave propagation in rock masses with bounded domain, the reliability of the proposed method has been evaluated in the examples by considering unbounded rock masses and by comparing the dispersion curves provided by the rigorous process of Floquet–Bloch with those obtained by the method presented. The accuracy of the method is analyzed for compressional and shear waves propagating in the intact-layered rocks along the orthotropic axes. Therefore, the influence of crack density in the layered rock mass has been analyzed. Vertical cracks have been considered, periodically located in the stiffer layer, and two different crack densities have been analyzed, which are differentiated in the crack spacing. A good agreement is obtained in case of compressional waves travelling along the layering direction and in case of both shear and compressional waves normal to the layering. The comparison between two crack systems with different spacing has shown this aspect to have a remarkable effect on waves travelling along the direction of layering, and limited in the case of waves propagating normal to the layers. The equivalent continuous model obtained through the dynamic homogenization technique here presented may be applied to the computational analysis of non-stationary wave propagation in rock masses of finite size, also consisting of sub-domains with different macro-mechanical characteristics. This avoids the use of computational models represented at the scale of the heterogeneities, which may be too burdensome or even unfeasible. Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-21T09:02:27Z2015-01-21T09:02:27Zhttp://eprints.imtlucca.it/id/eprint/2539This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25392015-01-21T09:02:27ZSecond-gradient homogenized model for wave propagation in heterogeneous periodic media Abstract The paper is focused on a homogenization procedure for the analysis of wave propagation in materials with periodic microstructure. By a reformulation of the variational-asymptotic homogenization technique recently proposed by Bacigalupo and Gambarotta (2012a), a second-gradient continuum model is derived, which provides a sufficiently accurate approximation of the lowest (acoustic) branch of the dispersion curves obtained by the Floquet–Bloch theory and may be a useful tool for the wave propagation analysis in bounded domains. The multi-scale kinematics is described through micro-fluctuation functions of the displacement field, which are derived by the solution of a recurrent sequence of cell {BVPs} and obtained as the superposition of a static and dynamic contribution. The latters are proportional to the even powers of the phase velocity and consequently the micro-fluctuation functions also depend on the direction of propagation. Therefore, both the higher order elastic moduli and the inertial terms result to depend by the dynamic correctors. This approach is applied to the study of wave propagation in layered bi-materials with orthotropic phases, having an axis of orthotropy parallel to the direction of layering, in which case, the overall elastic and inertial constants can be determined analytically. The reliability of the proposed procedure is analysed by comparing the obtained dispersion functions with those derived by the Floquet–Bloch theory. Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-21T08:59:32Z2015-01-21T08:59:32Zhttp://eprints.imtlucca.it/id/eprint/2538This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25382015-01-21T08:59:32ZA simplified assessment of the dome and drum of the Basilica of S. Maria Assunta in Carignano in Genoa Abstract As many masonry domes, the dome of the Basilica of S. Maria Assunta in Carignano in Genoa, designed by Galeazzo Alessi and built in the {XVIth} century, exhibits a relevant crack pattern, consisting mainly of meridian cracks, which puts forward the issue of its safety. Based on Static and Kinematic Theorems of Limit Analysis, a simplified procedure for the assessment of the dome, useful to understand the overall structural behavior, is discussed first looking to kinematically admissible mechanisms and to equilibrated stress fields; the obtained equilibrium states are compared to those from a non-linear {FEM} analysis showing a good agreement. Due to the high redundancy of the structure, this latter issue is dealt with reducing the unknowns to the internal forces in key sections of the dome so that the mechanical response of the dome can be easily described and discussed. The procedure allows the assessment of the dome outlining that: (i) the drum takes part in the collapse mechanism, so that kinematical analysis of the dome only may be not conservative; (ii) hoop ties in the drum, close to the base of the dome shells, plays a crucial stabilizing role; (iii) some parts of the structure, among which the ones prone to environmental degradation, may be crucial for the safety of the dome. Andrea Bacigalupoandrea.bacigalupo@imtlucca.itAntonio BrencichLuigi Gambarotta2015-01-21T08:50:48Z2015-01-21T08:50:48Zhttp://eprints.imtlucca.it/id/eprint/2537This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25372015-01-21T08:50:48ZA multi-scale strain-localization analysis of a layered strip with debonding interfaces The paper is focused on the multi-scale modeling of shear banding in a two-phase linear elastic periodically layered strip with damaging interfaces. A two-dimensional layered strip is considered subjected to transverse shear and is assumed to have a finite thickness along the direction of the layers and an infinite extension along the direction perpendicular to layering. The strip is analyzed as a second-gradient continuum resulting from a second-order homogenization procedure developed by the Authors, here specialized to the case of layered materials. This analysis is also aimed to understand the influence on the strain localization and post-peak structural response of the displacement boundary conditions prescribed at the strip edges. To this end, a first model representative of the strip with warping allowed at the edges is analyzed in which the strain localization process is obtained as a results of a bifurcation in analogy to the approach by Chambon et al. (1998). A second model is analyzed in which the warping of the edge is inhibited and the damage propagates from the center of the specimen without exhibiting bifurcation phenomena. For this latter case the effects of a possible interaction between the shear band and the boundary shear layer are considered, which are influenced mainly by the characteristic lengths of the model and the strip length. For realistic values of the relevant parameters it is shown that the boundary conditions have a small effects on the elastic response and on the overall strength of the model. Conversely, the boundary conditions have a significant effect on the shear band location, the post-peak response and the structural brittleness. Since the model parameters directly depend on the material microstructure as a result of the homogenization process, both the extension of the shear band and the occurrence of snap-back in the post-peak phase may be controlled in terms of the constitutive parameters and of the geometry of the phases. Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-21T08:37:39Z2015-01-21T08:37:39Zhttp://eprints.imtlucca.it/id/eprint/2536This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25362015-01-21T08:37:39ZEffects of layered accretion on the mechanics of masonry structuresMasonry constructions are built up in successive layers of bricks or blocks that may have considerable effect on the deformation and equilibrium of these structures when they are statically indeterminate and when gravity loads are predominant. This problem is analyzed by referring to a thick arch that reaches its final shape by means of a continuous deposition of heavy brick layers in stress free condition. The brick/block units of the accreting layer are assumed to have a negligible size in comparison to the structural size and the resulting continuous deposition is described taking into account their possible sliding on the current extrados at the instant of deposition. The kinematics of the growing body is described by the superposition of the displacement resulting from the continuing addition of heavy layers to the initial displacement at the considered point when it is attached to the current extrados, i.e., on the accreting layer. The two corresponding strain tensor fields do not satisfy the equations of compatibility, while the total strain field results to be compatible. The stress field is the cumulative effect of the incremental stress induced by the weight of the added layers during the growing process with residual stresses, which are shown to be independent of the initial strain field.
Two examples are analyzed to show the effects of the growing process on the stress field and the properties of the strain field are discussed. The first example concerns a masonry wall supported at periodic points while the second example concerns a segmental multileaf thick arch in which the growing process begins from a thin arch resting on its own weight. In both cases a remarkable increase of the stress field is observed in comparison to the solution where the gravity loads are applied on the final domain.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-21T08:29:54Z2015-01-21T08:29:54Zhttp://eprints.imtlucca.it/id/eprint/2535This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25352015-01-21T08:29:54ZA simplified evaluation of the influence of the bond pattern on the brickwork limit strengthThe influence of the bond pattern on the in-plane limit strength of masonry is analyzed through a simplified procedure based on the application of the safe theorem of limit analysis to the unit cell that generates the whole masonry by periodic repetition. The limit strength domains of running bond, English bond and herringbone bond masonry are obtained with different orientations of the mortar bed joints with respect to the principal directions of the average stress. The effects of different brick geometries are analyzed and comparisons between strength properties of different masonry patterns are made.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itAndrea CavicchiLuigi Gambarotta2015-01-20T15:37:29Z2015-01-20T15:37:29Zhttp://eprints.imtlucca.it/id/eprint/2533This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25332015-01-20T15:37:29ZComputational two-scale homogenization of periodic masonry: Characteristic lengths and dispersive waves The equations of motion of a second-order continuum equivalent to the periodic masonry made of deformable bricks and mortar are obtained and the overall elastic moduli and the inertial properties are evaluated through a homogenization technique derived from the variational-asymptotic approach proposed by Smyshlyaev and Cherednichenko 23. The computational method consists in solving two sequences of cell problems in the standard format of vanishing body forces and prescribed boundary displacements. In the first step the classical first-order homogenization is carried out by solving four cell problems; the second step concerns the second-order homogenization and involves the solution of six additional cell problems. The equations of motion and the wave equation are specialized to the case of centro-symmetric periodic cells and orthotropic material at the macro-scale, conditions that are common in brick masonry. The characteristic lengths and dispersive elastic waves are obtained. The special cases of characteristic lengths and wave propagation along the orthotropy axes are studied. In the examples running bond and English bond masonry are analyzed by varying the stiffness mismatch between the brick and the mortar. In all cases, the obtained characteristic lengths associated to the shear and extensional strains result to be a fraction of the periodic cell size and become zero for vanishing stiffness mismatch between the brick and the mortar. For both the masonry bonds here considered, the characteristic lengths associated to the shear strain are higher by about an order of magnitude than those associated to the extensional strain. The characteristic lengths along the direction parallel to the mortar joints are prevailing on those along the normal direction. In particular, small characteristic lengths are obtained along the direction normal to the bed mortar joints for both the running bond and the English bond masonry. The wave propagation along the orthotropy axes in both the running bond and English bond masonry is analyzed by considering wave-lengths multiple of periodic cell size. Dispersive waves propagating along the orthotropy direction parallel to the mortar joints are characterized by velocities that differ quite markedly from the corresponding ones in the classical continuum and this difference increases with the increase of the stiffness mismatch between the brick and mortar. Conversely, along the direction perpendicular to the mortar joints the velocity of the shear waves is approximately equal to that in the classical equivalent continuum. These findings show the qualitative similarity of the mechanical behavior of masonry with layered materials. Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T15:18:55Z2015-01-20T15:18:55Zhttp://eprints.imtlucca.it/id/eprint/2532This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25322015-01-20T15:18:55ZNon-local computational homogenization of periodic masonryMicro-polar and second-order homogenization procedures for periodic elastic masonry have been implemented to include geometric and material length scales in the constitutive equation. From the evaluation of the numerical response of the unit cell representative of the masonry to properly prescribed displacement boundary conditions related to homogeneous macro-strain fields, the elastic moduli of the higher-order continua are obtained on the basis of an extended Hill-Mandel macro-homogeneity condition. Elastic moduli and internal lengths for the running bond masonry are obtained in the case of Cosserat and second-order homogenization. To evaluate these results, a shear layer problem representative of a masonry wall subjected to a uniform horizontal displacement at points on the top is analyzed as a micro-polar and a second-order continuum and the results are compared to those corresponding with the reference heterogeneous model. From this analysis the second-order homogenization appears to provide better results in comparison with the micro-polar homogenization.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T15:10:55Z2015-01-20T15:10:55Zhttp://eprints.imtlucca.it/id/eprint/2531This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25312015-01-20T15:10:55ZMicro-polar and second order homogenization of periodic masonryMicro-polar and second order homogenization periodic elastic masonry are implemented for include geometric and material length scales in the constitutive equation. By the solution of the RVE equilibrium problems with properly prescribed boundary conditions the orthotropic elastic moduli of the higher order continua are obtained on the basis on the enhanced Hill-Mandel condition. A shear layer problem is analysed and the results from heterogeneous models are compared with those ones by the homogenization procedures; the second-order homogenization appears to provide better results in comparison to the micro-polar homogenization.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T14:44:16Z2015-01-20T14:44:16Zhttp://eprints.imtlucca.it/id/eprint/2530This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25302015-01-20T14:44:16ZSecond-order computational homogenization of heterogeneous materials with periodic microstructureA procedure for second-order computational homogenization of heterogeneous materials is derived from the unit cell homogenization, in which an appropriate representation of the micro-displacement field is assumed as the superposition of a local macroscopic displacement field, expressed in a polynomial form related to the macro-displacement field, and an unknown micro-fluctuation field accounting for the effects of the heterogeneities. This second contribution is represented as the superposition of two unknown functions each of which related to the first-order and to the second-order strain, respectively. This kinematical micro-macro framework guarantees that the micro-displacement field is continuous across the interfaces between adjacent unit cells and implies a computationally efficient procedure that applies in two steps. The first step corresponds to the standard homogenization, while the second step is based on the results of the first step and completes the second-order homogenization. Two multi-phase composites, a three-phase and a laminated composite, are analysed in the examples to assess the reliability of the homogenization techniques. The computational homogenization is carried out by a FE analysis of the unit cell; the overall elastic moduli and the characteristic lengths of the second-order equivalent continuum model are obtained. Finally, the simple shear of a constrained heterogeneous two-dimensional strip made up of the composites considered is analysed by considering a heterogeneous continuum and a homogenized second-order continuum; the corresponding results are compared and discussed in order to identify the validity limits of the proposed technique.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T14:27:07Z2015-01-20T14:27:07Zhttp://eprints.imtlucca.it/id/eprint/2529This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25292015-01-20T14:27:07ZAcoustic velocity in layered rock masses with periodic fracturesFractures and layering in rock masses have a large impact on both the
mechanical and hydraulic properties of the rock mass. When considering seismic elastic
waves, fractures can also trap and guide waves and the behavior of such waves may prove
useful for probing the geometrical and mechanical properties of the fractures. In the longwavelength
limit, when the size of the seismic wavelength is much larger than the layer
and/or fracture spacing, the propagation velocity is obtained by the effective medium theory.
However, when the wavelength becomes smaller, a dispersive behavior is obtained that may
be significantly affected by the layer and fracture spacing.
In the proposed paper a dynamic homogenization technique proposed by the Authors to
analyze dispersive waves in periodic elastic materials (Bacigalupo & Gambarotta, 2012) is
revised and extended to the analysis of dispersive waves in periodically layered fractured
rock masses. The obtained results for some material meso-structures by means of the
proposed approach are compared to those ones by the rigorous Floquet-Bloch theory.
Finally, some examples representative of rock masses are presented and discussed.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T14:16:03Z2015-01-20T14:17:13Zhttp://eprints.imtlucca.it/id/eprint/2528This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25282015-01-20T14:16:03ZHigh-continuity multi-scale static and dynamic modelling of periodic materialsThe equations of motion of a second-order continuum representative of a classical
heterogeneous periodic material are derived through a variational-asymptotic homogenization
technique and the overall elastic moduli and the inertial properties are evaluated. The
proposed approach is an extension of a dynamic homogenization method developed by the
Authors [9] and [10] which has the aim to improve the accuracy of description of the overall
inertial terms and of the dispersive functions. This procedure is applied to the case of elastic
layered materials with two orthotropic phases having an orthotropy axis parallel to the layers.
To evaluate the reliability of the model the dispersion functions here obtained are compared
with those from the analytical model applied to heterogeneous material [1, 2], and with those
obtained by the Authors in the previous approach [9].Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T14:00:32Z2015-01-20T14:15:24Zhttp://eprints.imtlucca.it/id/eprint/2527This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25272015-01-20T14:00:32ZStrain localization analysis of layered materials with debonding interfaces by a second-order homogenization approachThe paper is focused on the multiscale modeling of shear banding in a two-phase
linear elastic periodically layered material with damaging interfaces. A layered twodimensional
strip is considered under transverse shear and is assumed to have a finite length
along the direction of the layers and an infinite extension along the direction perpendicular to
layering. The structural system has been analysed as a second-gradient continuum in order to
incorporate size effects due to the material inhomogeneities and to regularize the softening
response due to the interface debonding. The multi-scale approach is based on a secondorder
homogenization procedure proposed by the Authors, here specialized to the simple case
of layered materials. Two problems are analysed differing on the boundary conditions at the
strip edges. The first case considers free warping of the edges with classical homogeneous
response in the elastic regime followed by a localization process as a results of a bifurcation
in analogy to Chambon’s approach. In the second model warping is inhibited at the edges
and the damage propagation is obtained from the center of the specimen. In both cases the
model parameters directly depend on the material microstructure so that both the extension of
the shear band and the occurrence of snap-back in the post-peak phase are given in terms of
the constitutive parameters and geometry of the phasesAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T13:43:46Z2015-01-20T13:43:46Zhttp://eprints.imtlucca.it/id/eprint/2526This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25262015-01-20T13:43:46ZSecond grade modeling for the strain localization analysis of layered materials with damaging interfacesA second-order computational homogenization procedure for heterogeneous materials with
periodic microstructure is applied to the analysis of a layered strip with damaging interface
subjected to simple shear. The second gradient model is applied in a strain localization
analysis and localization limiters depending on the geometry and mechanical parameters of
the layered material are obtained.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T11:31:59Z2015-01-20T11:31:59Zhttp://eprints.imtlucca.it/id/eprint/2525This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25252015-01-20T11:31:59ZHigh continuity second-order homogenization of in-plane loaded periodic masonryIn this paper the second-order homogenization of periodic masonry based on a
computational analysis of the unit cell representative of the masonry wall is derived. The
multi-scale approach is based on an appropriate representation of the micro-displacement
field as the superposition of a local macroscopic displacement field, represented in a polynomial
form related to the macro-displacement field, and an unknown micro-fluctuation field
accounting for the effects of the heterogeneities. By this approach a continuous microdisplacement
field is obtained, i.e. in each unit cell and across the interfaces between adjacent
unit cells. The computational procedure is applied in two steps: the first one corresponds
to the standard homogenization, while the second step is a second-order homogenization
based on the results of the first step. Two numerical examples are presented concerning running
bond and English bond masonry. For both the masonry patterns the overall elastic
moduli of the second-order model and the corresponding characteristic lengths are obtained;
the effects on the characteristic lengths of the stiffness mismatch between the brick phase and
the mortar phase are considered. Moreover, the wave propagation in the homogenized medium
is considered and dispersive waves are obtained. It is shown that remarkable differences
in the phase and group velocities between the first-order and the second-order homogenized
models are obtained for wavelengths shorter than ten times the average brick unit size.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T10:55:09Z2015-01-20T10:55:09Zhttp://eprints.imtlucca.it/id/eprint/2524This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25242015-01-20T10:55:09ZNon-local modelling of blocky rock masses with periodic jointed structureAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T10:38:01Z2015-01-20T10:38:01Zhttp://eprints.imtlucca.it/id/eprint/2523This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25232015-01-20T10:38:01ZA simplified evalutation of the influence of the bond pattern on the brickwork limit strengthAndrea Bacigalupoandrea.bacigalupo@imtlucca.itAndrea CavicchiLuigi Gambarotta2015-01-20T10:31:38Z2015-01-20T10:31:38Zhttp://eprints.imtlucca.it/id/eprint/2522This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25222015-01-20T10:31:38ZHomogenization of Periodic MasonryAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T10:12:08Z2015-01-20T10:12:08Zhttp://eprints.imtlucca.it/id/eprint/2521This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25212015-01-20T10:12:08ZNon-local computational homogenization of periodic masonry for the in-plane analysis of shear wallsAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T09:49:30Z2015-01-20T09:49:30Zhttp://eprints.imtlucca.it/id/eprint/2520This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25202015-01-20T09:49:30ZHomogenization of periodic chiral latticesAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T09:32:24Z2015-01-20T09:33:38Zhttp://eprints.imtlucca.it/id/eprint/2519This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25192015-01-20T09:32:24ZMultiscale modeling of periodic chiral cellular materialsAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T09:21:05Z2015-01-20T09:21:05Zhttp://eprints.imtlucca.it/id/eprint/2518This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25182015-01-20T09:21:05ZDispersive wave propagation in anisotropic materials with periodic microstructureAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T09:13:57Z2015-01-20T09:13:57Zhttp://eprints.imtlucca.it/id/eprint/2517This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25172015-01-20T09:13:57ZSecond-gradient computational homogenization of periodic materialsAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T09:00:41Z2015-01-20T09:00:41Zhttp://eprints.imtlucca.it/id/eprint/2516This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25162015-01-20T09:00:41ZStrain localization analysis of layered materials with soft interfaces based on a second-order homogenization approachAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T08:54:59Z2015-01-20T09:01:03Zhttp://eprints.imtlucca.it/id/eprint/2515This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25152015-01-20T08:54:59ZA computational high-continuity approach to the multi-scale static and dynamic modeling of materials with periodic microsrtuctureAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T08:49:48Z2015-01-20T08:49:48Zhttp://eprints.imtlucca.it/id/eprint/2514This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25142015-01-20T08:49:48ZCosserat homogenization of elastic periodic blocky masonryIn continuum modelling masonry structures the current consensus is that a higher-order theory is necessary to include geometric and material length scales to appreciate the influence of block size and high stress and strain gradients and to prevent pathological localizations arising from the assumption of strain-softening constitutive equations due to the quasi brittle components of the masonry. Elastic micropolar continuum models for 2D periodic masonry have been derived through an integral equivalence procedure starting from the description of a Lagrangian system of rigid bodies interacting through linear elastic interfaces (see for reference [1-
2]). From this approach the validity limits of the Cauchy models can be quantitatively obtained, and turn out to be remarkable in cases of load or geometrical discontinuities
and when the block size is not small with respect to the structure size. However, an evaluation of the Cosserat continuum model would require to consider the block
deformability, which in some cases is comparable to the mortar one’s. General approaches to the micropolar homogenisation of periodic heterogeneous materials have been proposed in [3,4]. A micropolar homogenization of 2D periodic masonry with elastic brick/blocks and mortar joints has been proposed in [5], where the rotational dof of the homogenised continuum has been assumed through a heuristic evaluation of the mean local rotation of the block. In this work a two-dimensional Cosserat homogenization is developed for periodic masonry made up of elastic brick/block units and mortar joints. According to [3], the homogenization of the representative periodic masonry element is obtained by prescribing the macroscopic dofs and generalized strain measures through a
corresponding displacement field including a periodic perturbation. The orthotropic moduli of the homogenized micropolar continuum are obtained for realistic values of
the elastic moduli of the components and compared to the corresponding orthotropic moduli of the Cauchy continuum. Finally, a sensitivity analysis is carried out for
varying geometric and constitutive parameters.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-20T08:34:00Z2015-01-20T08:34:00Zhttp://eprints.imtlucca.it/id/eprint/2513This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25132015-01-20T08:34:00ZModelling of deformation and damage of heterogeneous-engineering structures: Masonry MechanicsAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T14:45:48Z2015-01-19T14:45:48Zhttp://eprints.imtlucca.it/id/eprint/2511This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25112015-01-19T14:45:48ZDispersive acoustic waves in elastic periodic media: a non-local dynamic homogenization approachThe paper is addressed to the analysis of low-frequency wave propagation in
materials with periodic microstructure. A second-gradient continuum model is derived, which
provides a sufficiently accurate simulation of for a wide range of wavelengths and a useful tool for
the wave propagation analysis in bounded domains. The multi-scale kinematics is described
through micro-fluctuation functions of the displacement field, which are derived by the solution of
a recurrent sequence of cell BVPs and obtained as the superposition of a static and dynamic
contribution. The latters are proportional to the even powers of the phase velocity and
consequently the micro-fluctuation functions also depend on the direction of propagation.
Therefore, both the higher order elastic moduli and the inertial terms results to depend on
dynamic correctors. This approach is applied to the study of wave propagation in layered bimaterials
with orthotropic phases, having an axis of orthotropy parallel to the direction of layering,
in which case, the overall elastic and inertial constants can be determined analytically. The
reliability of the proposed procedure is analysed by comparing the obtained dispersion functions
with those derived by the Floquet-Bloch theory.Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T14:43:56Z2015-01-19T14:46:14Zhttp://eprints.imtlucca.it/id/eprint/2510This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25102015-01-19T14:43:56ZModellazione multi-scala di materiali auxetici a microstruttura periodica chiraleIl controllo delle proprietà elastiche globali di compositi a microstruttura periodica
può risultare un argomento di interesse per la progettazione di materiali auxetici caratterizzati da
coefficiente di Poisson negativo e da elevate prestazioni meccaniche tra cui l’ultra-resistenza e
l’ultra-rigidezza. La caratterizzazione di continui omogenei non locali equivalenti energeticamente
a materiali complessi eterogenei motiva pertanto l’uso degli approcci multi-scala.
Nel presente lavoro vengono formulate equazioni costitutive per materiali che presentano una
geometria esachirale e tetrachirale attraverso diverse tecniche di omogeneizzazione. Da un lato si è
considerato un modello di omogeneizzazione cellulare a gradi di libertà concentrati che permette
la caratterizzazione di un continuo omogeneo al primo ordine ovvero micro-polare e dall’altro si è
adottata una tecnica di omogeneizzazione computazionale non locale proposta recentemente dagli
Autori in [6] attraverso la quale è possibile determinare le costanti globali di un continuo del
secondo ordine ovvero di un continuo a gradiente di deformazioneAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2015-01-19T14:35:56Z2015-01-19T14:35:56Zhttp://eprints.imtlucca.it/id/eprint/2509This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25092015-01-19T14:35:56ZOmogeneizzazione multi-scala di materiali a microstruttura periodica mediante sviluppi asintotici dell'energia di deformazioneAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2015-01-19T14:32:46Z2015-01-19T14:32:46Zhttp://eprints.imtlucca.it/id/eprint/2508This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25082015-01-19T14:32:46ZMulti-scale modelling of periodic masonry: size effects, characteristic lengths and dispersive wavesAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T14:27:53Z2015-01-19T14:27:53Zhttp://eprints.imtlucca.it/id/eprint/2507This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25072015-01-19T14:27:53ZMicro-polar and second order homogenization of periodic masonryMicro-polar and second order homogenization procedures for periodic elastic
masonry are implemented to include geometric and material length scales in the constitutive
equation. By the solution of the RVE equilibrium problems with properly prescribed boundary
conditions the orthotropic elastic moduli of the higher order continua are obtained on the basis of
an enhanced Hill–Mandel condition. A shear layer problem is analysed and the results from the
heterogeneous models are compared with those ones obtained by the homogenization procedures;
the second-order homogenization appears to provide better results in comparison to the micropolar
homogenizationAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T13:59:20Z2015-01-19T13:59:20Zhttp://eprints.imtlucca.it/id/eprint/2506This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25062015-01-19T13:59:20ZCostruire in muratura: un processo continuo di crescita strutturaleAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T13:45:44Z2015-01-19T13:45:44Zhttp://eprints.imtlucca.it/id/eprint/2505This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25052015-01-19T13:45:44ZEffetti della crescita strutturale sull’equilibrio e deformazione di elementi murari pianiAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T13:36:35Z2015-01-19T13:37:35Zhttp://eprints.imtlucca.it/id/eprint/2504This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25042015-01-19T13:36:35ZSicurezza statica del sistema cupola-tamburo: il caso della Basilica di S. Maria Assunta di Carignano a GenovaAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T13:25:17Z2015-01-19T13:25:17Zhttp://eprints.imtlucca.it/id/eprint/2503This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25032015-01-19T13:25:17ZUn approccio multi-scala per la determinazione delle proprietà meccaniche di materiali eterogenei a micro-struttura periodicameccanico dei materiali eterogenei basandosi su opportune tecniche di omogeneizzazione (asintotiche
[1] e computazionali [2]). Al mezzo eterogeneo, modellato alla micro-scala come un continuo di
Cauchy, se ne associa uno omogeneo il cui comportamento alla macro-scala può essere sinteticamente
descritto da continui non-locali. È noto che negli approcci computazionali il campo di spostamento
locale ottenuto per localizzazione imponendo sulla cella elementare macro-deformazioni di ordine
superiore non risulta, in generale, né continuo all’interfaccia di celle elementari adiacenti, né
sufficientemente regolare per garantire l’antiperiodicità delle trazioni sul contorno [3].
Nell’intento di risolvere questo problema è elaborata una semplice tecnica di omogeneizzazione nonlocale
(multipolare ovvero al secondo ordine) che si sviluppa per passi e basata su un’opportuna
definizione del down-scaling dove una particolare struttura della perturbazione del micro-spostamento,
espressa in termine delle macro-deformazioni, è sovrapposta al macro-spostamento. Le funzioni di
perturbazione, che dipendono dalle proprietà della microstruttura, sono determinate attraverso la
successiva soluzione di problemi di cella. La struttura dello spostamento locale, direttamente
riconducibile a quella utilizzata nelle tecniche asintotiche, consente di ottenere nella localizzazione
campi di spostamento e tensione opportunamente regolari sul contorno di celle adiacenti e periodici alla
micro-scala. Le costanti elastiche del continuo omogeneo equivalente sono determinate attraverso una
uguaglianza energetica alle due scale di una porzione rappresentativa di materiale eterogeneo. Nel caso
di una omogeneizzazione in un continuo al secondo ordine (ovvero in uno micropolare alla Koiter), lo
sviluppo asintotico dell’energia di deformazione alla micro-scala in termini della dimensione
caratteristica della cella elementare è arrestato al secondo ordine. In particolare, le costanti elastiche
così ottenute sono invarianti ad ogni possibile traslazione della cella elementare fissata e qualora la
microstruttura diventi evanescente le lunghezze interne restituite risultano identicamente nulle
evidenziando l’assenza di effetti non locali a scala macroscopica. La definizione dell’up-scaling è
ottenuta attraverso la soluzione di un opportuno problema di minimizzazione approssimando il macrospostamento
e le macro-deformazioni attraverso una forma polinomiale completa di ordine fissato. Una
semplificazione a livello computazionale del modello di omogeneizzazione elaborato si ottiene
esprimendo direttamente nel down-scaling il macro-spostamento come un polinomio di Taylor al
secondo ordine e risolvendo i problemi di cella in termini dello spostamento locale [3].Andrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T13:21:07Z2015-01-19T13:21:07Zhttp://eprints.imtlucca.it/id/eprint/2502This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25022015-01-19T13:21:07ZSecond-order-enhanced computational homogenization for heterogeneous materials with periodic-microstructuresAndrea Bacigalupoandrea.bacigalupo@imtlucca.itLuigi Gambarotta2015-01-19T13:06:58Z2015-01-19T13:21:40Zhttp://eprints.imtlucca.it/id/eprint/2501This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/25012015-01-19T13:06:58ZOmogeneizzazione non locale di mezzi eterogenei a microstruttura periodicaAndrea Bacigalupoandrea.bacigalupo@imtlucca.it2014-10-10T08:18:48Z2014-10-10T08:18:48Zhttp://eprints.imtlucca.it/id/eprint/2309This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23092014-10-10T08:18:48ZCalcolo delle strutture isostaticheI numerosi esercizi sulle strutture isostatiche proposti nel presente volume sono stati risolti completamente, riportando, oltre ai diagrammi delle caratteristiche della sollecitazione interna, la curva delle pressioni e il poligono delle forze attive e reattive. Inoltre, nel caso di diversi esercizi, si è verificata una reazione vincolare interna, applicando il Principio dei Lavori Virtuali per i sistemi di corpi rigidi, così come i due Teoremi delle Catene Cinematiche riguardanti i centri di rotazione assoluta e relativa. In altri casi si è calcolato invece uno spostamento elastico o una rotazione elastica, applicando il Principio dei Lavori Virtuali per i sistemi di travi elastiche. La teoria su cui si basano i metodi di risoluzione proposti, così come la stessa simbologia utilizzata, si riferiscono ai Volumi 1 e 2 della presente Collana di Ingegneria Strutturale ("Scienza delle Costruzioni 1 e 2", autore: Alberto Carpinteri, Pitagora Editrice Bologna, 1992). L'opera si sviluppa in quattro diversi capitoli, in ordine crescente di difficoltà concettuale, così come viene usualmente fatto dalla maggior parte delle Scuole Italiane: (1) Strutture reticolari; (2) Travi Gerber; (3) Archi a tre cerniere; (4) Strutture chiuse. Pur presentando geometrie strutturali e condizioni di vincolamento assai varie, le tipologie studiate risultano essere in tutti i casi analoghe a quelle che si possono incontrare nella pratica professionale (strutture di grande luce, ponti, coperture, apparecchi di sollevamento, etc.).
Alberto CarpinteriGiuseppe LacidognaMarco Paggimarco.paggi@imtlucca.it2014-10-09T09:35:03Z2014-10-09T09:35:03Zhttp://eprints.imtlucca.it/id/eprint/2308This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23082014-10-09T09:35:03ZA coupled cohesive zone model for transient analysis of thermoelastic interface debondingA coupled cohesive zone model based on an analogy between fracture and contact mechanics is proposed to investigate debonding phenomena at imperfect interfaces due to thermomechanical loading and thermal fields in bodies with cohesive cracks. Traction-displacement and heat flux–temperature relations are theoretically derived and numerically implemented in the finite element method. In the proposed formulation, the interface conductivity is a function of the normal gap, generalizing the Kapitza constant resistance model to partial decohesion effects. The case of a centered interface in a bimaterial component subjected to thermal loads is used as a test problem. The analysis focuses on the time evolution of the displacement and temperature fields during the transient regime before debonding, an issue not yet investigated in the literature. The solution of the nonlinear numerical problem is gained via an implicit scheme both in space and in time. The proposed model is finally applied to a case study in photovoltaics where the evolution of the thermoelastic fields inside a defective solar cell is predicted.Alberto Saporaalberto.sapora@polito.itMarco Paggimarco.paggi@imtlucca.it2014-10-09T09:32:08Z2014-10-09T09:32:08Zhttp://eprints.imtlucca.it/id/eprint/2306This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23062014-10-09T09:32:08ZA multi-scale numerical method for the study of size-Scale effects in ductile fractureThe use of a stress-strain constitutive relation for the undamaged material and a traction-separation cohesive crack model with softening for cracking has been demonstrated to be an effective strategy to predict and explain the size-scale effects on the mechanical response of quasi-brittle materials. In metals, where ductile fracture takes place, the situation is more complex due to the interplay between plasticity and fracture. In the present study, we propose a multi-scale numerical method where the shape of a global constitutive relation used at the macro-scale, the so-called hardening cohesive zone model, can be deduced from meso-scale numerical simulations of polycrystalline metals in tension. The shape of this constitutive relation, characterized by an almost linear initial branch followed by a plastic plateau with hardening and finally by softening, is in fact the result of the interplay between two basic forms of nonlinearities: elasto-plasticity inside the grains and classic cohesive cracking for the grain boundaries. Mauro Corradomauro.corrado@polito.itMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2014-10-09T09:30:40Z2014-10-09T09:30:40Zhttp://eprints.imtlucca.it/id/eprint/2304This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23042014-10-09T09:30:40ZThe effect of crack size and specimen size on the relation between the Paris and Wöhler curvesParis and Wöhler’s fatigue curves are intimately connected by the physics of the process of fatigue crack growth. However, their connections are not obvious due to the appearance of anomalous specimen-size and crack-size effects. In this study, considering the equations for a notched specimen (or for a specimen where failure is the result of the propagation of a main crack) and the assumption of incomplete self-similarity on the specimen size, the relations between the size-scale effects observed in the Paris and Wöhler’s diagrams are explained. In the second part of the work, the behaviour of physically short cracks is addressed and, considering a fractal model for fatigue crack growth, the crack-size effects on the Paris and Wöhler’s curves are discussed.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2014-10-09T09:28:43Z2014-10-09T09:28:43Zhttp://eprints.imtlucca.it/id/eprint/2307This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23072014-10-09T09:28:43ZFiber-size effects on the onset of fiber–matrix debonding under transverse tension: A comparison between cohesive zone and finite fracture mechanics modelsThe problem of fiber–matrix debonding due to transverse loading is revisited. Predictions of the critical load for the debond onset obtained by a Cohesive Zone Model combined with contact mechanics and by a Finite Fracture Mechanics model based on a coupled stress and energy criterion are compared. Both models predict a strong nonlinear dependence of the critical load on the fiber size. A good agreement between the predictions provided by these models is found for large and medium fiber radii. However, different scaling laws for small fiber radii are noticed. A discussion of the asymptotic trends for very small and very large fiber radii is presented. Limitations of both models are also discussed. For very small fibers, it is shown that matrix plasticity can prevail over fiber–matrix debonding, leading to an upper bound for the critical load. When fiber–matrix debonding prevails over plasticity for large enough fibers, the predictions provided by the two models are still in fair good agreement.Israel GarciaMarco Paggimarco.paggi@imtlucca.itVladislav Mantic2014-10-09T08:59:38Z2014-10-09T08:59:38Zhttp://eprints.imtlucca.it/id/eprint/2301This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/23012014-10-09T08:59:38ZOn the dependency of the parameters of fatigue crack growth from the fractal dimension of rough crack profilesA theoretical study based on dimensional analysis and fractal geometry of crack profiles is proposed to establish the relation between their fractal dimension D (1<D<2) and the parameters defining the fatigue crack propagation rate. The exponent m of the Paris' law is found to be an increasing function of the fractal dimension of the crack profile, m=2D/(2-D). This trend is confirmed by a quantitative analysis of fractographic images of Titanium alloys with different grain sizes (different roughness of crack profiles), by a new experimental test and by an indirect estimation of D from crack growth equations accounting from crack-size effects in Steel and Aluminum. The present study can be considered as the first quantitative analysis of fractographic images aiming at relating the morphological features of cracks to their kinetics in fatigue.Marco Paggimarco.paggi@imtlucca.itOleg Plekhovpoa@icmm.ru2014-09-19T07:24:07Z2014-11-17T13:01:55Zhttp://eprints.imtlucca.it/id/eprint/2283This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22832014-09-19T07:24:07ZStochastic model predictive control for constrained discrete-time Markovian switching systems In this paper we study constrained stochastic optimal control problems for Markovian switching systems, an extension of Markovian jump linear systems (MJLS), where the subsystems are allowed to be nonlinear. We develop appropriate notions of invariance and stability for such systems and provide terminal conditions for stochastic model predictive control (SMPC) that guarantee mean-square stability and robust constraint fulfillment of the Markovian switching system in closed-loop with the {SMPC} law under very weak assumptions. In the special but important case of constrained {MJLS} we present an algorithm for computing explicitly the {SMPC} control law off-line, that combines dynamic programming with parametric piecewise quadratic optimization. Panagiotis Patrinospanagiotis.patrinos@imtlucca.itPantelis Sopasakispantelis.sopasakis@imtlucca.itHaralambos SarimveisAlberto Bemporadalberto.bemporad@imtlucca.it2014-07-01T14:48:34Z2014-07-01T14:48:34Zhttp://eprints.imtlucca.it/id/eprint/2229This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22292014-07-01T14:48:34ZOptimization-based automatic flatness control in cold tandem rollingFor the problem of automatic flatness control (AFC) in cold tandem mills this paper proposes control techniques based on quadratic optimization and delay compensation. Three different strategies are presented and compared: a centralized solution based on a global quadratic programming (QP) problem that decides the commands to all the actuators, and two decentralized solutions where each actuator command is optimized locally. All schemes are based on a global exchange of information about the commands generated at the previous time step at each stand to compensate for the numerous delays present in the mill. Control algorithms are tested in simulation considering a tandem mill with five stands as a benchmark, and results are shown to demonstrate the performance of the proposed schemes. Alberto Bemporadalberto.bemporad@imtlucca.itDaniele Bernardinidaniele.bernardini@imtlucca.itFrancesco Alessandro CuzzolaAndrea Spinelli2014-07-01T12:35:16Z2014-07-01T12:35:16Zhttp://eprints.imtlucca.it/id/eprint/2228This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22282014-07-01T12:35:16ZHybrid control lyapunov functions for the stabilization of hybridsystems
The design of stabilizing controllers for hybrid systems is
particularly challenging due to the heterogeneity present
within the system itself. In this paper we propose a constructive
procedure to design stabilizing dynamic controllers for
a fairly general class of hybrid systems. The proposed technique
is based on the concept of a hybrid control Lyapunov
function (hybrid CLF) that was previously introduced by the
authors. In this paper we generalize the concept of hybrid
control Lyapunov function, and we show that the existence
of a hybrid CLF guarantees the existence of a standard control
Lyapunov function (CLF) for the hybrid system. We
provide a constructive procedure to design a hybrid CLF
and the corresponding dynamic control law, which is stabilizing
because of the established connection to a standard
CLF that becomes a Lyapunov function for the closed-loop
system. The obtained control law can be conveniently implemented
by constrained predictive control in the form of
a receding horizon control strategy. A numerical example
highlighting the features of the proposed approach is presented.Stefano Di CairanoW.P.M.H. HeemelsMircea LazarAlberto Bemporadalberto.bemporad@imtlucca.it2014-07-01T10:26:51Z2015-01-13T12:21:40Zhttp://eprints.imtlucca.it/id/eprint/2224This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22242014-07-01T10:26:51ZRobust explicit model predictive control via regular piecewise-affine approximationThis paper proposes an explicit model predictive control design approach for regulation of linear time-invariant systems subject to both state and control constraints, in the presence of additive disturbances. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. Firstly, the regularity of the simplicial partition allows one to efficiently implement the control law on digital circuits, thus achieving extremely fast computation times. Moreover, the asymptotic stability (or the convergence to a set including the origin) of the closed-loop system can be enforced a-priori, rather than checked a-posteriori via Lyapunov analysis.Matteo RubagottiDavide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.it2014-06-19T08:09:43Z2014-09-02T09:28:54Zhttp://eprints.imtlucca.it/id/eprint/2208This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/22082014-06-19T08:09:43ZRobust Model Predictive Control for optimal continuous drug administrationIn this paper the Model Predictive Control (MPC) technology is used for tackling the optimal drug administration problem. The important advantage of MPC compared to other control technologies is that it explicitly takes into account the constraints of the system. In particular,
for drug treatments of living organisms, MPC can guarantee satisfaction of the minimum toxic concentration (MTC) constraints. A whole-body physiologically-based pharmacokinetic (PBPK) model serves as the dynamic prediction model of the system after it is formulated as a
discrete-time state-space model. Only plasma measurements are assumed to be measured online. The rest of the states (drug concentrations in other organs and tissues) are estimated in real time by designing an artificial observer. The complete system (observer and MPC controller) is able to drive the drug concentration to the desired levels at the organs of interest, while satisfying the imposed constraints, even in the presence of modeling errors, disturbances and noise. A case study on a PBPK model with 7 compartments, constraints on 5 tissues and a variable drug concentration set-point illustrates the efficiency of the methodology in drug dosing control applications. The proposed methodology is also tested in an uncertain setting
and proves successful in presence of modelling errors and inaccurate measurements. Pantelis Sopasakispantelis.sopasakis@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2014-03-31T08:30:37Z2014-09-17T12:30:38Zhttp://eprints.imtlucca.it/id/eprint/2187This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/21872014-03-31T08:30:37ZFatigue degradation and electric recovery in Silicon solar cells embedded in photovoltaic modulesCracking in Silicon solar cells is an important factor for the electrical power-loss of photovoltaic modules. Simple geometrical criteria identifying the amount of inactive cell areas depending on the position of cracks with respect to the main electric conductors have been proposed in the literature to predict worst case scenarios. Here we present an experimental study based on the electroluminescence (EL) technique showing that crack propagation in monocrystalline Silicon cells embedded in photovoltaic (PV) modules is a much more complex phenomenon. In spite of the very brittle nature of Silicon, due to the action of the encapsulating polymer and residual thermo-elastic stresses, cracked regions can recover the electric conductivity during mechanical unloading due to crack closure. During cyclic bending, fatigue degradation is reported. This pinpoints the importance of reducing cyclic stresses caused by vibrations due to transportation and use, in order to limit the effect of cracking in Silicon cells.Marco Paggimarco.paggi@imtlucca.itIrene Berardoneirene.berardone@polito.itAndrea Infusoandrea.infuso@polito.it2014-03-05T14:12:53Z2014-03-05T14:12:53Zhttp://eprints.imtlucca.it/id/eprint/2176This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/21762014-03-05T14:12:53ZStabilizing embedded MPC with computational complexity guaranteesThis paper describes a model predictive control (MPC) approach for discrete-time linear systems with hard constraints on control and state variables. The finite-horizon optimal control problem is formulated as a quadratic program (QP), and solved using a recently proposed dual fast gradient-projection method. More precisely, in a finite number of iterations of the mentioned optimization algorithm, a solution with bounded levels of infeasibility and suboptimality is determined for an alternative problem. This solution is shown to be a feasible suboptimal solution for the original problem, leading to exponential stability of the closed-loop system. The proposed strategy is particularly useful in embedded control applications, for which real-time constraints and limited computing resources can impose tight bounds on the possible number of iterations that can be performed within the scheduled sampling time.Matteo RubagottiPanagiotis Patrinospanagiotis.patrinos@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2014-03-05T14:06:27Z2015-04-07T14:04:44Zhttp://eprints.imtlucca.it/id/eprint/2175This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/21752014-03-05T14:06:27ZFixed-point dual gradient projection for embedded model predictive controlAlthough linear Model Predictive Control has gained increasing popularity for controlling dynamical systems subject to constraints, the main barrier that prevents its widespread use in embedded applications is the need to solve a Quadratic Program (QP) in real-time. This paper proposes a dual gradient projection (DGP) algorithm specifically tailored for implementation on fixed-point hardware. A detailed convergence rate analysis is presented in the presence of round-off errors due to fixed-point arithmetic. Based on these results, concrete guidelines are provided for selecting the minimum number of fractional and integer bits that guarantee convergence to a suboptimal solution within a prespecified tolerance, therefore reducing the cost and power consumption of the hardware device.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itAlberto Guiggianialberto.guiggiani@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2014-03-05T13:42:53Z2014-11-19T11:15:43Zhttp://eprints.imtlucca.it/id/eprint/2174This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/21742014-03-05T13:42:53ZEvent-driven model predictive control of timed hybrid Petri netsHybrid Petri nets represent a powerful modeling formalism that offers the possibility of integrating, in a natural way, continuous and discrete dynamics in a single net model. Usual control approaches for hybrid nets can be divided into discrete-time and continuous-time approaches. Continuous-time approaches are usually more precise, but can be computationally prohibitive. Discrete-time approaches are less complex, but can entail mode-mismatch errors due to fixed time discretization. This work proposes an optimization-based event-driven control approach that applies on continuous time models and where the control actions change when discrete events occur. Such an approach is computationally feasible for systems of interest in practice and avoids mode-mismatch errors. In order to handle modelling errors and exogenous disturbances, the proposed approach is implemented in a closed-loop strategy based on event-driven model predictive controlJorge JúlvezStefano Di CairanoAlberto Bemporadalberto.bemporad@imtlucca.itCristian Mahulea2014-03-05T13:21:13Z2014-03-05T14:06:56Zhttp://eprints.imtlucca.it/id/eprint/2173This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/21732014-03-05T13:21:13ZAn accelerated dual gradient-projection algorithm for embedded linear model predictive controlThis paper proposes a dual fast gradient-projection method for solving quadratic programming problems that arise in model predictive control of linear systems subject to general polyhedral constraints on inputs and states. The proposed algorithm is well suited for embedded control applications in that: 1) it is extremely simple and easy to code; 2) the number of iterations to reach a given accuracy in terms of optimality and feasibility of the primal solution can be tightly estimated; and 3) the computational cost per iteration increases only linearly with the prediction horizon.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2013-12-20T10:48:18Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2082This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20822013-12-20T10:48:18ZContact of microscopically rough surfaces with graded elasticityMarco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-12-20T10:17:03Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2081This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20812013-12-20T10:17:03ZNonlinear interface crack propagation in concrete gravity dams under seismic loadingIn this paper, the phenomenon of interface crack propagation in concrete gravity dams under seismic
loading is addressed. This problem is particularly important from the engineering point of view. In fact,
besides Mixed-Mode crack growth in concrete, dam failure is often the result of crack propagation along
the rock-concrete interface at the dam foundation. To analyze such a problem, the generalized interface
constitutive law recently proposed by the first author is used to proper modelling the phenomenon of
crack closing and reopening at the interface. A damage variable is also introduced in the cohesive zone
formulation in order to predict crack propagation under repeated loadings. Numerical examples will
show the capabilities of the proposed approach applied to concrete gravity dams.Marco Paggimarco.paggi@imtlucca.itGiuseppe Ferro2013-12-20T10:13:04Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2080This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20802013-12-20T10:13:04ZSingular harmonic problems at multi-material wedges: mathematical analogies between elasticity, diffusion and electromagnetismMulti-material wedges are frequently observed in composite materials. They consist of two or more
sectors of dissimilar materials joined together, whose interfaces converge to the same vertex. Due to the
mismatch in the material properties, such as Young’s modulus, thermal conductivity, dielectric permittivity,
or magnetic permeability, these geometrical configurations may lead to singular fields at the junction
vertex. In this paper, focusing the attention on singular harmonic problems, the mathematical analogies
intercurring between antiplane shear problem in elasticity due to Mode III loading or torsion, the
steady-state heat transfer problem, and the diffraction of waves in electromagnetism are presented. The
proposed unified mathematical formulation is particularly convenient for the identification of common
types of singularities (power-law or logarithmic type), for the use of a standardized method for solving
the nonlinear eigenvalue problems, and for the determination of common geometrical and material
configurations permitting to relieve or remove the singularities.Marco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-20T08:53:58Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2079This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20792013-12-20T08:53:58ZA computational homogenization approach for a three-level hierarchical composite materialMarco Paggimarco.paggi@imtlucca.itPeter Wriggers2013-12-19T13:33:57Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/2078This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20782013-12-19T13:33:57ZModelli micromeccanici di contatto: analisi critica comparativaMarco Paggimarco.paggi@imtlucca.it2013-12-19T12:37:19Z2014-10-09T09:20:23Zhttp://eprints.imtlucca.it/id/eprint/2077This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20772013-12-19T12:37:19ZMetodo degli spostamenti. Fondamenti teorici e applicazioni strutturaliIl Metodo degli Spostamenti è un approccio particolarmente efficace per risolvere strutture iperstatiche e comprendere le prescrizioni tecniche della recente normativa italiana delle costruzioni.
Si espongono nei Capitoli 1 e 2 i fondamenti teorici del metodo corredati da esempi applicativi risolvibili analiticamente e illustranti le potenzialità tecniche del metodo.
Nel Capitolo 3 si propone un inquadramento e generalizzazione dell'approccio nell'ambito del metodo degli elementi finiti, e nell'ultimo Capitolo si illustra come applicare il metodo per risolvere problemi numerici più avanzati riguardanti il comportamento statico e dinamico e lo studio dell'instabilità dell'equilibrio elastico di strutture bidimensionali intelaiate.Mauro CorradoMarco Paggimarco.paggi@imtlucca.it2013-12-16T15:13:30Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2076This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20762013-12-16T15:13:30ZSpecial issue on fracture and contact mechanics for interface problems Marco Paggimarco.paggi@imtlucca.itPeter WriggersAlberto Carpinteri2013-12-16T15:00:04Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2074This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20742013-12-16T15:00:04ZSpecial issue on computational methods for interface mechanical problemsMarco Paggimarco.paggi@imtlucca.itAlberto CarpinteriPeter Wriggers2013-12-16T14:00:01Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2072This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20722013-12-16T14:00:01ZStiffness and strength of hierarchical polycrystalline materials with imperfect interfacesIn this paper, considering a cohesive zone model (CZM) for finite thickness
interfaces recently proposed by the authors, the stiffness of polycrystalline materials with
imperfect interfaces is characterized. Generalized expressions for the Voigt and Reuss
estimates of the effective elastic modulus of the composite are derived to interpret the
numerical results. Considering a polycrystalline material with a hierarchical microstructure,
the interaction between interfaces at the different hierarchical levels is numerically
investigated. A condition for scale separation, which suggests how to design the optimal
microstructure to maximize the material tensile strength is determined. An original interpretation
of this phenomenon based on the concept of flaw tolerance is finally proposed.Marco Paggimarco.paggi@imtlucca.itPeter Wriggers2013-12-16T13:43:56Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2071This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20712013-12-16T13:43:56ZA nonlocal cohesive zone model for studying crack propagation in mechanical systems with finite thickness interfacesFinite thickness regions between heterogeneous material constituents are often simplified as zerothickness
interfaces. Then, the cohesive zone model (CZM) is employed, establishing a constitutive relation between tractions and displacement discontinuities. The shape of the CZM is usually chosen as simple as possible for numerical reasons, rather than being physically meaningful. Therefore, the reliability and the predictive capabilities of these models are a serious concern. In this contribution, the complex nonlinear damage phenomena occurring in finite thickness interface regions are modeled using damage mechanics. The derived nonlinear relation between cohesive
tractions and anelastic displacements is then reinterpreted as a new nonlocal CZM. Depending on
the ductility of the material, different shapes of the CZM can be recovered, from linear and bilinear
softening curves, typical of brittle materials, to bell-shaped curves typical of ductile materials. It is
also shown that the parameters of the damage law can be tuned according to molecular dynamics simulations.
The implementation of the proposed nonlocal CZM in the finite element method is then presented. Special attention is given to the numerical treatment of the related nonlocality and to the computation of the tangent stiffness matrix to be used in the Newton-Raphson method for the solution of the nonlinear boundary value problem.
The numerical model is applied to polycrystalline materials and it is shown that the nonlocal CZM is able to reproduce realistic statistical distributions of Mode I fracture energies, as a consequence of the interface thickness distribution. Finally, we demonstrate that the relation between interface thickness and grain size can also be used to explain the grain size effects on the material
tensile strength, namely the Hall-Petch law and its inversion at the nanoscale.Marco Paggimarco.paggi@imtlucca.itPeter Wriggers2013-12-16T11:59:08Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2070This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20702013-12-16T11:59:08ZCohesive-Overlapping Crack Model describing the size-scale effects on the rotational capacity of RC beams in bendingA numerical algorithm is proposed for the prediction of the mechanical behavior of the plastic hinges taking place in RC beams at the ultimate loading conditions. The main novelty of such an approach is the introduction of the Overlapping Crack Model, based on nonlinear fracture mechanics concepts, to describe concrete crushing, along with the well-known Cohesive Crack Model for concrete in tension and a stress versus crack opening displacement relationship for steel reinforcement. As a result of a systematic application of the proposed algorithm, new practical design diagrams are proposed for the improvement of the current codes of practice, which completely disregard the size-scale effects. In this context, Dimensional Analysis is also applied in order to obtain further simplifications in the description of the overall response. It is in fact demonstrated that only two nondimensional numbers, NP and NC, are responsible for the available ductility. A new interpretation of the experimental results on the plastic rotations in terms of NP and NC is also proposed.Mauro CorradoMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-16T11:48:50Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2069This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20692013-12-16T11:48:50ZLimits to plastic analysis design due to size-scale effects on the rotational capacity of plastic hingesMauro CorradoMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-13T10:29:04Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2067This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20672013-12-13T10:29:04ZIntroduzione alla termomeccanica dei continuiNei primi cinque capitoli vengono presentate le nozioni fondamentali relative agli sforzi ed alle
deformazioni, la cinematica e la dinamica dei mezzi continui, le equazioni costitutive, i principi
della termodinamica e le equazioni fondamentali della termomeccanica con relative applicazioni,
sia per i solidi che per i fluidi.
Un ultimo capitolo è dedicato alla conduzione del calore nei solidi, con alcune soluzioni in forma
chiusa di problemi monodimensionali.
In appendice si illustrano infine alcuni importanti legami costitutivi non lineari, facendo riferimento
alla plasticità ed alla viscoelasticità.
Marco Paggimarco.paggi@imtlucca.itAlberto Rossani2013-12-12T14:15:48Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2066This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20662013-12-12T14:15:48ZA generalized dimensional analysis approach to fatigue crack growthAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-12T14:13:09Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2065This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20652013-12-12T14:13:09ZThe mitigation of stress-singularities in Linear ElasticityAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-12T14:10:00Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2064This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20642013-12-12T14:10:00ZSize-scale effects on the ductility of reinforced concrete structural elementsMauro CorradoMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-12T14:04:43Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2063This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20632013-12-12T14:04:43ZGeneralized representations of fatigue and size-scale effects on the Paris and Wöhler regimesMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-12T14:00:21Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2062This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20622013-12-12T14:00:21ZDelamination vs. shear failure in retrofitted concrete beams and related size-scale effectsAlberto CarpinteriGiuseppe LacidognaMarco Paggimarco.paggi@imtlucca.it2013-12-12T13:43:38Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2061This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20612013-12-12T13:43:38ZApplicazioni di meccanica della frattura all’analisi di stabilitá delle fessure nelle dighe in calcestruzzoRIASSUNTO. Nel presente lavoro si propone una disamina delle applicazioni di meccanica della frattura
all’analisi del processo fessurativo nelle dighe in calcestruzzo. In tale contesto, ripercorrendo gli studi
pionieristici e i casi di studio affrontati negli anni 1980 e 1990, si illustra nel dettaglio come applicare le
metodologie proprie della meccanica della frattura elastica lineare alla valutazione della stabilità delle fessure e
della loro lunghezza critica. Tale disamina riguarderà sia sollecitazioni quasi-statiche, quali il peso proprio e la
pressione idrostatica esercitata dall’acqua, che sollecitazioni sismiche, tema di particolare complessità ed
attualità. Infine, si illustreranno le problematiche relative alla corretta valutazione dei parametri meccanici per
strutture ciclopiche quali le dighe, tenendo propriamente in conto i forti effetti di scala osservati
sperimentalmente.
ABSTRACT. In the present study, a detailed analysis of the applications of fracture mechanics to the
phenomenon of fracture taking place in concrete dams is proposed. In this context, recalling the pioneering
approaches and the case studies proposed in the 1980s and in the 1990s, it will be shown how to apply the
methodologies of linear elastic fracture mechanics to the assessment of crack stability and to the determination
of the corresponding critical crack length. Such an analysis will concern both quasi-static loads, such as the
weight load and the hydraulic pressure, as well as seismic actions, a topic of high complexity and actuality.
Finally, the problems related to the proper evaluation of the mechanical parameters of huge structures such as
dams will be analyzed, taking into account the strong size-scale effects observed in experimental tests.Marco Paggimarco.paggi@imtlucca.itGiuseppe Ferro2013-12-12T13:19:24Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2060This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20602013-12-12T13:19:24ZFatigue of quasi-brittle materials: a unified interpretation of microstructural size, crack size and size-scale effectsIn this study, a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power-law equations used to characterize the fatigue behaviour of quasi-brittle materials. According to this theoretical approach, the microstructural-size (related to the volumetric content of fibres in fibre-reinforced concrete), the crack-size, and the size-scale effects on the Paris’ law and the Wöhler equation are presented within a unified mathematical framework. Relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. All these information are expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is herein elucidated.Marco Paggimarco.paggi@imtlucca.itGiuseppe Ferro2013-12-12T13:07:39Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2055This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20552013-12-12T13:07:39ZContact mechanics of functionally graded rough surfacesIn this paper the Greenwood and Williamson contact theory for microscopically
rough surfaces is generalized by considering a grading on the elastic modulus of the asperities.
This situation can be representative of surfaces receiving superficial treatments or characterized by
a chemical degradation. The effect of an exponential grading on the applied normal load, on the
relationship between the real contact area and the load, on the plasticity index, as well as on the
contact conductance is illustrated with detailed numerical examples.Marco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-12-12T12:59:27Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2054This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20542013-12-12T12:59:27ZA theoretical and numerical approach to the interaction between buckling and resonance instabilities in discrete and continuous mechanical systemsThe paper deals with the interaction between buckling and resonance instabilities of
mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of
motion through the geometric stiffness matrix, the problem is reduced to a generalized eigenproblem
where both the loading multiplier and the natural frequency of the system are unknown. According
to this approach, all the forms of instabilities intermediate between those of pure buckling and pure
forced resonance can be investigated. Numerous examples including discrete mechanical systems
and continuous mechanical systems, such as oscillating deflected beams subjected to a compressive
axial load and oscillating beams subjected to lateral-torsional buckling, are analyzed. The proposed
results provide a new insight in the interpretation of coupled phenomena such as flutter instability of
long-span or high-rise structures.Marco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-12T11:46:29Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2053This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20532013-12-12T11:46:29ZA unified mathematical formulation for the asymptotic analysis of singular elastic and electromagnetic fieldsIn the present contribution, the mathematical analogy existing between the singular stress field in elasticity due to antiplane loading and the singular electromagnetic fields in electromagnetism is derived with reference to the problem of isotropic multi-material wedges. These
configurations, where dissimilar sectors converge to the same vertex, are very commonly observed in composite materials and may lead to stress-singularities. The proposed analogy permits to extend several elastic solutions already available in the literature to the analogous electromagnetic problems, without the need of performing new calculations.Marco Paggimarco.paggi@imtlucca.itAlberto CarpinteriRenato Orta2013-12-05T14:44:50Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2052This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20522013-12-05T14:44:50ZImprovement in the plastic rotation evaluation by means of fracture mechanics conceptsThe well-known Cohesive Crack Model describes strain localization with a softening stress variation in concrete members subjected to tension. Based on the assumption that strain localization also occurs in compression, the Ovelapping Crack Model, analogous to the cohesive one, is proposed to simulate material compenetration due to crushing. By applying this model, it is possible to describe the size effects in compression in a rational way. The two aforementioned elementary models are then merged into a more complex algorithm based on the finite element method, able to describe both cracking and crushing growths during loading processes in RC members. With this algorithm in hand, it is possible to investigate on the influence of the reinforcement percentage and/or the structural size of RC beams, with special attention to their rotational capacity. The obtained results evidence that the prescriptions concerning the plastic rotations provided by codes of practice, not taking into account the scale effects, are not conservative in the case of large structural sizes. Mauro CorradoAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.itGiuseppe Mancini2013-12-05T13:20:29Z2014-10-09T09:20:23Zhttp://eprints.imtlucca.it/id/eprint/2050This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20502013-12-05T13:20:29ZModelling strain localization by cohesive (overlapping) zones in tension (compression): brittleness size effects and scaling in material propertiesThe present paper is a state-of-the-art review of the research carried out at the Politecnico di Torino during the last two decades on the modelling of strain localization. Introducing the elementary cohesive/overlapping models in tension/compression, it will be shown that it is possible to get a deep insight into the ductile-to-brittle transition and into the scaling of the material properties usually detected when testing quasi-brittle material specimens or structures at different size-scales.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-05T12:47:35Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2049This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20492013-12-05T12:47:35ZNew correlations for the cyclic properties of engineering materialsA phenomelogical description of the fatigue life of engineering components can be given either by plotting the applied stress range as a function of the total number of the cycles to failure, i.e., according to the Wöhler’s curve, or, after the advent of fracture mechanics, by plotting the crack growth rate in terms of the stress-intensity factor range, i.e., using the Paris’ curve. In this work, an analytical approach is proposed for the study of the relationships existing between the Wöhler’s and the Paris’ representations of fatigue. According to dimensional analysis and the concepts of complete and incomplete self-similarity, generalized Wöhler and Paris equations are determined, which provide a rational interpretation to a majority of empirical power-law criteria used in fatigue.
Then, by integration of the generalized Paris’ law, the relationship between the aforementioned generalized representations of fatigue is established, providing the link between the cumulative fatigue damage and the fatigue crack propagation approaches. Moreover, paying attention to the limit points defining the range of validity of the classical Wöhler and Paris power-law relationships, whose co-ordinates are referred to as cyclic of fatigue properties, alternative expressions for the classical laws of fatigue are proposed. Finally, the correlations between such fatigue properties are determined according to theoretical arguments, giving an interpretation of the empirical trends observed in the material property charts.
Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-05T11:15:08Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/2048This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20482013-12-05T11:15:08ZSulla seconda edizione della Mécanique Analytique di Lagrange: lettura critica e prospettive attualiAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-04T15:43:07Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2046This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20462013-12-04T15:43:07ZStructural integrity of hierarchical compositesInterface mechanical problems are of paramount importance in engineering and materials science.
Traditionally, due to the complexity of modelling their mechanical behaviour, interfaces are often treated as
defects and their features are not explored. In this study, a different approach is illustrated, where the interfaces
play an active role in the design of innovative hierarchical composites and are fundamental for their structural
integrity. Numerical examples regarding cutting tools made of hierarchical cellular polycrystalline materials are
proposed, showing that tailoring of interface properties at the different scales is the way to achieve superior
mechanical responses that cannot be obtained using standard materialsMarco Paggimarco.paggi@imtlucca.it2013-12-04T15:18:01Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2044This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20442013-12-04T15:18:01ZNumerical modelling of microcracking in PV modules induced by thermo-mechanical loads Abstract Micro-cracking in polycrystalline Silicon is a serious concern for the durability of photovoltaic (PV) modules due to the resulting electrical power-loss. In this contribution, a thermo-mechanical cohesive zone model is proposed to predict the evolution of micro-cracks under the action of mechanical and thermal loads. The classical nonlinear cohesive zone approach, used in fracture mechanics to depict the phenomenon of cracking as a result of progressive breakage of atomic bonds, is extended to thermo-elastic fields. The additional thermal resistance of micro-cracks due to imperfect bonding is estimated according to an analogy with a contact mechanics formulation, where the dependency on the crack opening is suitably accounted for. A numerical example shows the applicability of the proposed approach to practical problems. Marco Paggimarco.paggi@imtlucca.itAlberto Sapora2013-12-04T15:11:37Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2043This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20432013-12-04T15:11:37ZA numerical investigation of the interplay between cohesive cracking and plasticity in polycrystalline materials Abstract The interplay between cohesive cracking and plasticity in polycrystals is herein investigated. A unified finite element formulation with elasto-plastic elements for the grains and interface elements for the grain boundaries is proposed. This approach is suitable for the analysis of polycrystalline materials with a response ranging from that of brittle ceramics to that of ductile metals. Crystal plasticity theory is used for 3D computations, whereas isotropic von Mises plasticity is adopted for the 2D tests on plane strain cross-sections. Regarding the grain boundaries, a cohesive zone model (CZM) accounting for Mode Mixity is used for the constitutive relation of 2D and 3D interface elements. First, the analysis of the difference between 3D and 2D simulations is proposed. Then, considering all the nonlinearities in the model, their interplay is numerically investigated. It is found that the {CZM} nonlinearity prevails over plasticity for low deformation levels. Afterwards, plasticity prevails over CZM. Finally, for very large deformation, failure is ruled by the {CZM} formulation which induces softening. The meso-scale numerical results show that the simultaneous use of cohesive interface elements for the grain boundaries and plasticity theory for the grains is a suitable strategy for capturing the experimental response of uniaxial tensile tests. Marco Paggimarco.paggi@imtlucca.itEva LehmannChristoph WeberAlberto CarpinteriPeter WriggersM. Schaper2013-12-04T15:00:03Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2042This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20422013-12-04T15:00:03ZA multiscale approach for the seismic analysis of concrete gravity dams Abstract In this article, the problem of cracking in concrete gravity dams subjected to seismic loadings is examined under a multiscale perspective. Preliminarily, the size-scale effects on the mechanical parameters entering the nonlinear constitutive models of the interface crack are discussed. From a wide review of existing experimental results, it is shown that the material tensile strength, the fracture energy, the friction coefficient and the concrete compressive strength are strongly size-scale dependent. This evidence pinpoints the necessity of performing experimental testing on large scale specimens to assess the value of the parameters to be used in nonlinear fracture mechanics simulations. Moreover, the size-scale dependency of the interface constitutive properties implies the necessity of updating their values during crack propagation simulations. To do so, interface properties are not given in input a priori, but they are selected at each step of the simulation according to the specified scaling laws. The numerical simulations, based on the finite element method and a generalized interface constitutive law for contact and decohesion implemented in the node-to-segment contact strategy, show the high sensitivity of the phenomenon of crack propagation by the parameters of the damage law used to degrade the cohesive zone properties in case of repeated cycles. Marco Paggimarco.paggi@imtlucca.itGiuseppe FerroFranco Braga2013-12-04T14:56:41Z2017-03-27T14:48:32Zhttp://eprints.imtlucca.it/id/eprint/2041This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20412013-12-04T14:56:41ZA multi-physics and multi-scale numerical approach to microcracking and power-loss in photovoltaic modulesA multi-physics and multi-scale computational approach is proposed in the present work to study the evolution of microcracking in polycrystalline Silicon (Si) solar cells composing photovoltaic (PV) modules. Coupling between the elastic and the electric fields is provided according to an equivalent circuit model for the PV module where the electrically inactive area is determined from the analysis of the microcrack pattern. The structural scale of the {PV} laminate (the macro-model) is coupled to the scale of the polycrystals (the micro-model) using a multiscale nonlinear finite element approach where the macro-scale displacements of the Si cell borders are used as boundary conditions for the micro-model. Intergranular cracking in the Si cell is simulated using a nonlinear fracture mechanics cohesive zone model (CZM). A case-study shows the potentiality of the method, in particular as regards the analysis of the microcrack orientation and distribution, as well as of the effect of cracking on the electric characteristics of the PV module.Marco Paggimarco.paggi@imtlucca.itMauro CorradoMaria Alejandra Rodriguez2013-12-03T14:45:35Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2015This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20152013-12-03T14:45:35ZModelling strain localization by cohesive/overlapping zones in tension/compression: Brittleness size effects and scaling in material propertiesThe present paper is a state-of-the-art review of the research carried out at the Politecnico di Torino during the last two decades on the modelling of strain localization. Introducing the elementary cohesive/overlapping models in tension/compression, it will be shown that it is possible to get a deep insight into the ductile-to-brittle transition and into the scaling of the material properties usually detected when testing quasi-brittle material specimens or structures at different size-scalesAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-03T14:13:43Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2012This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20122013-12-03T14:13:43ZCrack propagation in honeycomb cellular materials: a computational approachComputational models based on the finite element method and linear or nonlinear fracture mechanics are herein proposed to study the mechanical response of functionally designed cellular components. It is demonstrated that, via a suitable tailoring of the properties of interfaces present in the meso- and micro-structures, the tensile strength can be substantially increased as compared to that of a standard polycrystalline material. Moreover, numerical examples regarding the structural response of these components when subjected to loading conditions typical of cutting operations are provided. As a general trend, the occurrence of tortuous crack paths is highly favorable: stable crack propagation can be achieved in case of critical crack growth, whereas an increased fatigue life can be obtained for a sub-critical crack propagation.Marco Paggimarco.paggi@imtlucca.it2013-12-03T14:06:17Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2010This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20102013-12-03T14:06:17ZStiffness and strength of hierarchical polycrystalline materials with imperfect interfaces In this study we investigate the effect of imperfect (not perfectly bonded) interfaces on the stiffness and strength of hierarchical polycrystalline materials. As a case study we consider a honeycomb cellular polycrystal used for drilling and cutting tools. The conclusions of the analysis are, however, general and applicable to any material with structural hierarchy. Regarding the stiffness, generalized expressions for the Voigt and Reuss estimates of the bounds to the effective elastic modulus of heterogeneous materials are derived. The generalizations regard two aspects that are not included in the standard Reuss and Voigt estimates. The first novelty consists in considering finite thickness interfaces between the constituents undergoing damage up to final debonding. The second generalization consists of interfaces not perpendicular or parallel to the loading direction, i.e., when isostress or isostrain conditions are not satisfied. In this case, approximate expressions for the effective elastic modulus are obtained by performing a computational homogenization approach. In the second part of the paper, the homogenized response of a representative volume element (RVE) of the honeycomb cellular polycrystalline material with one or two levels of hierarchy is numerically investigated. This is put forward by using the cohesive zone model (CZM) for finite thickness interfaces recently proposed by the authors and implemented in the finite element program FEAP. From tensile tests we find that the interface nonlinearity significantly contributes to the deformability of the material. Increasing the number of hierarchical levels, the deformability increases. The RVE is tested in two different directions and, due to different orientations of the interfaces and Mixed Mode deformation, anisotropy in stiffness and strength is observed. Stiffness anisotropy is amplified by increasing the number of hierarchical levels. Finally, the interaction between interfaces at different hierarchical levels is numerically characterized. A condition for scale separation, which corresponds to the independence of the material tensile strength from the properties of the interfaces in the second level, is established. When this condition is fulfilled, the material microstructure at the second level can be efficiently replaced by an effective homogeneous continuum with a homogenized stress–strain response. From the engineering point of view, the proposed criterion of scale separation suggests how to design the optimal microstructure of a hierarchical level to maximize the material tensile strength. An interpretation of this phenomenon according to the concept of flaw tolerance is finally presented. Marco Paggimarco.paggi@imtlucca.itPeter Wriggers2013-12-03T14:02:14Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2008This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20082013-12-03T14:02:14ZA cohesive crack model coupled with damage for interface fatigue problemsAn semi-analytical formulation based on the cohesive crack model is proposed to describe the phenomenon of fatigue crack growth along an interface. Since the process of material separation under cyclic loading is physically governed by cumulative damage, the material deterioration due to fatigue is taken into account in terms of interfacial cohesive properties degradation. More specifically, the damage increment is determined by the current separation and a history variable. The damage variable is introduced into the constitutive cohesive crack law in order to capture the history-dependent property of fatigue. Parametric studies are presented to understand the influences of the two parameters entering the damage evolution law. An application to a pre-cracked double-cantilever beam is discussed. The model is validated by experimental data. Finally, the effect of using different shapes of the cohesive crack law is illustratedBaoming GongMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-03T13:54:01Z2017-03-27T14:54:46Zhttp://eprints.imtlucca.it/id/eprint/2007This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20072013-12-03T13:54:01ZA theoretical approach to the interaction between buckling and resonance instabilitiesThis article deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem is reduced to a generalized eigenproblem where both the loading multiplier and the natural frequency of the system are unknown. According to this approach, all of the forms of instabilities intermediate between those of pure buckling and pure forced resonance can be investigated. Numerous examples are analyzed, including discrete mechanical systems with one to n degrees of freedom, continuous mechanical systems, such as oscillating deflected beams subjected to a compressive axial load, as well as oscillating beams subjected to lateral–torsional buckling. A general finite element procedure is also outlined, with the possibility to apply the proposed approach to any general bi- or tri-dimensional framed structure. The proposed results provide a new insight in the interpretation of coupled phenomena such as flutter instability of long-span or high-rise structures.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-03T13:51:11Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2006This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20062013-12-03T13:51:11ZSize-scale effects on interaction diagrams for reinforced concrete columns The use of N–M interaction diagrams is well established in the design of reinforced concrete columns, when the second order effects can be neglected. According to the stress–strain constitutive laws usually adopted to compute the resistant domains, complex phenomena such as size effects and concrete confinement cannot be considered in practical applications. On the other hand, several experimental evidences, and some analytical models available in the literature, emphasize the influence of such effects. In the present paper, a numerical approach based on the integrated Cohesive/Overlapping Crack Model is applied to compute the interaction diagrams. Compared to classical approaches, different constitutive laws are assumed for concrete in compression and tension, based on Nonlinear Fracture Mechanics models, and a step-by-step analysis is performed instead of limit state analysis. The proposed model permits the size and the confinement effects to be predicted, according to the experimental results. Moreover, the obtained results completely agree with previous extensive applications of the model to plain concrete specimens subjected to uniaxial compression and reinforced concrete beams in bending. Alberto CarpinteriMauro CorradoGiusemaria GosoMarco Paggimarco.paggi@imtlucca.it2013-12-02T13:24:56Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2005This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20052013-12-02T13:24:56ZNumerical modelling of intergranular fracture in polycrystalline materials and grain size effectsABSTRACT. In this paper, the phenomenon of intergranular fracture in polycrystalline materials is investigated
using a nonlinear fracture mechanics approach. The nonlocal cohesive zone model (CZM) for finite thickness
interfaces recently proposed by the present authors is used to describe the phenomenon of grain boundary
separation. From the modelling point of view, considering the dependency of the grain boundary thickness on
the grain size observed in polycrystals, a distribution of interface thicknesses is obtained. Since the shape and
the parameters of the nonlocal CZM depend on the interface thickness, a distribution of interface fracture
energies is obtained as a consequence of the randomness of the material microstructure. Using these data,
fracture mechanics simulations are performed and the homogenized stress-strain curves of 2D representative
volume elements (RVEs) are computed. Failure is the result of a diffuse microcrack pattern leading to a main
macroscopic crack after coalescence, in good agreement with the experimental observation. Finally, testing
microstructures characterized by different average grain sizes, the computed peak stresses are found to be
dependent on the grain size, in agreement with the trend expected according to the Hall-Petch law.
SOMMARIO. In questo articolo, il fenomeno della frattura intergranulare nei material policristallini è studiato
mediante un approccio di meccanica della frattura non lineare. Il modello non locale di frattura coesiva per
interfacce con spessore finito recentemente proposto dai presenti autori è impiegato per descrivere il fenomeno
di separazione ai bordi di grano. Da un punto di vista modellistico, considerando la dipendenza dello spessore
dei bordi di grano dalla dimensione del grano stesso, si è ottenuta una distribuzione delle proprietà meccaniche
delle interfacce. Essendo la forma ed i parametri del modello non locale della frattura coesiva dipendenti dallo
spessore dell'interfaccia, si ottiene una distribuzione di energie di frattura come conseguenza della variabilità
statistica della microstruttura del materiale. Usando tali dati si conducono simulazioni di meccanica della frattura
su elementi di volumi rappresentativi (RVE) in 2D e si determinano le rispettive curve di tensionedeformazione.
La frattura è il risultato di un insieme di microfessure diffuse che danno luogo alla propagazione
di una fessura macroscopica principale, in ottimo accordo con quanto osservato sperimentalmente. Infine,
testando microstrutture dotate di diversi diametri medi dei grani, si osserva come le tensioniMarco Paggimarco.paggi@imtlucca.itPeter Wriggers2013-12-02T13:20:31Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2004This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20042013-12-02T13:20:31ZThermomechanical deformations in photovoltaic laminatesRecent experimental results based on the digital image correlation technique (U. Eitner, M. Köntges, R. Brendel, Solar Energy Mater. Solar Cells, 2010, 94, 1346–1351) show that the gap between solar cells embedded into a standard photovoltaic laminate varies with temperature. The variation of this gap is an important quantity to assess the integrity of the electric connection between solar cells when exposed to service conditions. In this paper, the thermo-elastic deformations in photovoltaic laminates are analytically investigated by developing different approximate models based on the multilayered beam theory. It is found that the temperature-dependent thermo-elastic properties of the encapsulating polymer layer are responsible for the deviation from linearity experimentally observed in the diagram relating the gap variation to the temperature. The contribution of the different material constituents to the homogenized elastic modulus and thermal expansion coefficient of the composite system is also properly quantified through the definition of weight factors of practical engineering use. Marco Paggimarco.paggi@imtlucca.itSarah Kajari-SchröderUlrich Eitner2013-12-02T13:11:20Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2003This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20032013-12-02T13:11:20ZSeismic analysis of concrete gravity dams: nonlinear fracture mechanics models and size-scale effectsThe phenomenon of interface crack propagation in concrete gravity dams underseismic loading is herein addressed. This problem is particularly important from the engineeringpoint of view. In fact, besides Mixed-Mode crack growth in concrete, dam failure is oftenthe result of crack propagation along the rock-concrete interface at the dam foundation. Toanalyze such a problem, the generalized interface constitutive law recently proposed by the¯rst author is used to proper modelling the phenomenon of crack closing and reopening at theinterface. A damage variable is also introduced in the cohesive zone formulation in order topredict crack propagation under repeated loadings. Special attention is given to the complexityresulting from the solution of the nonlinear dynamic problem and to the choice of the interfaceconstitutive parameters, taking into account the important size-scale e®ects observed in thesecyclopic structures. Numerical examples will show the capabilities of the proposed approachwhen applied to concrete gravity dams.Marco Paggimarco.paggi@imtlucca.itGiuseppe FerroFranco Braga2013-12-02T13:06:05Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/2000This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/20002013-12-02T13:06:05ZAn analytical model based on strain localisation for the study of size-scale and slenderness effects in uniaxial compression testsIn this paper, an analytical model based on the concept of strain localisation is proposed for the analysis and prediction of the response of quasi-brittle materials in uniaxial compression tests, such as mortar, plain concrete with different compression strengths, as well as fibre-reinforced concrete. The proposed approach, referred to as Overlapping Crack Model, relies only on a pair of material constitutive laws, in close analogy with the Cohesive Crack Model: a stress–strain relationship describing the pre-peak behaviour of the material and a stress–interpenetration relationship for the description of the post-peak response. In the paper it will be shown how the stress–interpenetration relationship can be deduced from experimental data and how it depends on the compression strength and on the crushing energy of the tested materials. A wide comparison between the stress–displacement curves predicted by the proposed model and those experimentally found in the literature will show the effectiveness of the present approach to capture both stable softening or sharp snap-back post-peak branches by varying the slenderness or the size-scale of the tested samples.Alberto CarpinteriMauro CorradoMarco Paggimarco.paggi@imtlucca.it2013-12-02T12:56:31Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1999This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19992013-12-02T12:56:31ZContact conductance of rough surfaces composed of modified RMD patches The dependence of the contact conductance of self-affine rough surfaces on the applied pressure is studied using the electric-mechanical analogy which relates the contact conductance to the normal stiffness. According to dimensional analysis arguments, an efficient dimensionless formulation is proposed which minimizes the number of dimensionless variables governing the phenomenon. Assuming incomplete similarity in the dimensionless pressure, a power-law dependence between contact conductance and mean pressure is proposed. This is confirmed by earlier semi-empirical correlations that are recovered as special cases of the proposed formulation. To compute the exponent β of the power-law, and relate it to the morphological properties of the surfaces, we numerically test self-affine rough surfaces composed of random midpoint displacement (RMD) patches. Such patches are generated using a modified {RMD} algorithm in order to decouple the effect of the long wavelength cut-off from that due to microscale roughness. Numerical results show that the long wavelength cut-off has an important effect on the contact conductance, whereas the sampling interval and the fractal dimension are less important. The effect of elastic interaction between asperities has also been quantified and it significantly influences the predicted power-law exponent β. Marco Paggimarco.paggi@imtlucca.itJ.R. Barber2013-12-02T12:40:31Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1998This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19982013-12-02T12:40:31ZDimensional analysis and fractal modeling of fatigue crack growthIn the present paper, generalized Paris and Wöhler equations are derived according to dimensional analysis and incomplete similarity concepts. They provide a rational interpretation to a majority of empirical power-law criteria used in fatigue. In particular, they are able to model the effects of the grain size, of the initial crack length, as well as of the size-scale of the tested specimen on the crack growth rate and on the fatigue life. Regarding the important issue of crack-size dependencies of the Paris’ coefficient C and of the fatigue threshold, an independent approach, based on the application of fractal geometry concepts, is proposed to model such an anomalous behavior. As a straightforward consequence of the fractality of the crack surfaces, the fractal approach provides scaling laws fully consistent with those determined from dimensional analysis arguments. The proposed scaling laws are applied to relevant experimental data related to the crack-size and to the structural-size dependencies of the fatigue parameters in metals and in quasi-brittle materials. Finally, paying attention to the limit points defining the range of validity of the classical Wöhler and Paris power-law relationships, correlations between the so-called cyclic or fatigue properties are proposed, giving a rational explanation to the experimental trends observed in the material property charts.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-02T12:35:40Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1997This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19972013-12-02T12:35:40ZContact mechanics of microscopically rough surfaces with graded elasticity The well-known Greenwood and Williamson contact theory for microscopically homogeneous rough surfaces is generalized by considering functionally graded elastic rough surfaces. In particular, two distinct cases giving rise to a non-constant Young’s modulus with depth are considered: (I) an initially plane layered (or graded) solid which is non-uniformly eroded, so that the final product is a rough surface with asperities having an elastic modulus depending on the height; (II) an initially homogeneous rough surface which receives a surface treatment or a chemical degradation which modify the elastic properties of the asperities as a function of the depth from the exposed surface. These Functionally Graded Surfaces (FGS) can be observed both in biological systems and in mechanical components. The effects of graded elasticity on the relationship between real contact area versus applied load, and on the plasticity index are quantified and illustrated with numerical examples. It will be shown that the contact response may differ up to one order of magnitude with respect to that of a homogeneous surface. Comparison between Case I and Case II also shows that, for special surface properties, the two types of grading can provide the same mechanical response. Marco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-12-02T12:12:14Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1996This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19962013-12-02T12:12:14ZA nonlocal cohesive zone model for finite thickness interfaces – Part II: FE implementation and application to polycrystalline materials Numerical aspects of the nonlocal cohesive zone model (CZM) presented in Part I are discussed in this companion paper. They include the FE implementation of the proposed nonlocal CZM in the framework of zero-thickness interface elements and the numerical treatment of the related nonlocality. In particular, a Newton–Raphson method, combined with a series expansion to obtain tentative values for the cohesive tractions, is used to efficiently compute the tangent stiffness matrix and the residual vector of the interface elements. Then, numerical applications to polycrystalline materials are proposed, focusing on the constitutive modelling of the finite thickness interfaces between the grains. It will be shown that the parameters of the nonlocal CZM (shape, peak stress, fracture energy) depend on the thickness of the interface. The CZM is able to produce statistical distributions of Mode I fracture energies consistent with those assumed a priori in stochastic fracture mechanics studies. The statistical variability of fracture parameters, originating from the natural variability of the interface thicknesses, has an important influence on the crack patterns observed from simulated tensile tests. Finally, we show that the relation between interface thickness and grain size can be used to explain the grain-size effects on the material tensile strength. In particular, considering a sublinear relation between the interface thickness and the grain diameter at the microscale, the nonlocal CZM is able to recover the Hall–Petch law. Therefore, the proposed model suggests that an inverse relation between the interface thickness and the grain size would lead to an inversion of the Hall–Petch law as well. This new interpretation seems to be confirmed by experimental data at the nanoscale, where the inversion of the Hall–Petch law coincides with the anomalous increase of the interface thickness by reducing the grain size. Marco Paggimarco.paggi@imtlucca.itPeter Wriggers2013-12-02T12:05:06Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1995This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19952013-12-02T12:05:06ZA nonlocal cohesive zone model for finite thickness interfaces – Part I: Mathematical formulation and validation with molecular dynamics A nonlocal cohesive zone model is derived taking into account the properties of finite thickness interfaces. The functional expression of the stress–separation relationship, which bridges the gap between continuum damage mechanics and nonlinear fracture mechanics, depends on the complex failure phenomena affecting the material microstructure of the interface region. More specifically, the shape of the nonlocal cohesive zone model is found to be dependent on the damage evolution. On the other hand, damage is in its turn a function of dissipative mechanisms occurring at lower length scales, such as dislocation motion, breaking of interatomic bonds, formation of free surfaces and microvoids, that are usually analyzed according to molecular dynamics. Hence, the relationship intercurring between the parameters of the damage law and the outcome of molecular dynamics simulations available in the literature is also established. Therefore, the proposed nonlocal cohesive zone model provides also the proper mathematical framework for interpreting molecular dynamics-based stress–separation relationships that are typically nonlocal, since they always refer to a finite number of atom layers. Marco Paggimarco.paggi@imtlucca.itPeter Wriggers2013-12-02T12:02:08Z2016-04-06T09:38:43Zhttp://eprints.imtlucca.it/id/eprint/1994This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19942013-12-02T12:02:08ZA dimensional analysis interpretation to grain size and loading frequency dependencies of the Paris and Wöhler curves In this paper, a mathematical model based on dimensional analysis and incomplete self-similarity is proposed for the interpretation of the grain size and loading frequency effects on the Paris and Wöhler regimes in metals. In particular, it is demonstrated that these effects correspond to a violation of the physical similitude hypothesis underlying the simplest Paris’ and Wöhler power-law fatigue relationships. As a consequence, generalized representations of fatigue have to be invoked. From the physical point of view, the incomplete similarity behaviour can be regarded as the result of the multiscale character of the problem, where the crack length and the grain size are the two length scales interacting together. Moreover, it will be shown that the relationship between strength and grain size (Hall–Petch relationship) has also to be considered in order to consistently interpret the two opposite effects of the grain size on the Paris and Wöhler regimes within a unified framework. The incomplete similarity exponents are suitably quantified according to experimental results for Aluminum, Copper, Titanium and Nickel. The derived scaling laws are expected to be of paramount importance today, especially after the advent of ultra fine grained materials that offer unique mechanical properties owing to their fine microstructure. Oleg Plekhovpoa@icmm.ruMarco Paggimarco.paggi@imtlucca.itO. NaimarkAlberto Carpinteri2013-12-02T11:46:18Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1992This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19922013-12-02T11:46:18ZSingular harmonic problems at a wedge vertex: mathematical analogies between elasticity, diffusion, electromagnetism, and fluid dynamicsMultimaterial wedges are frequently observed in composite materials. They consist of two or more sectors of dissimilar materials joined together, whose interfaces converge at the same vertex. Due to the mismatch in material properties such as Young’s modulus, thermal conductivity, dielectric permittivity, or magnetic permeability, these geometrical configurations can lead to singular fields at the junction vertex. This paper discusses mathematical analogies, focused on singular harmonic problems, between antiplane shear problem in elasticity due to mode III loading or torsion, the steady-state heat transfer problem, and the diffraction of waves in electromagnetism. In the case of a single material wedge, a mathematical analogy between elasticity and fluid dynamics is also outlined. The proposed unified mathematical formulation is particularly convenient for the identification of common types of singularities (power-law or logarithmic type), the definition of a standardized method to solve nonlinear eigenvalue problems, and the determination of common geometrical and material configurations allowing the relief or removal of different singularities. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-02T11:32:14Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1991This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19912013-12-02T11:32:14ZModelling fatigue in quasi-brittle materials with incomplete self-similarity conceptsIn this study, a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth is proposed in order to highlight and explain the deviations from the classical power–law equations used to characterize the fatigue behaviour of quasi-brittle materials. According to this theoretical approach, the microstructural-size (related to the volumetric content of fibers in fiber-reinforced concrete), the crack-size, and the size-scale effects on the Paris’ law and on the Wöhler equation are presented within a unified mathematical framework. Relevant experimental results taken from the literature are used to confirm the theoretical trends and to determine the values of the incomplete self-similarity exponents. All this information is expected to be useful for the design of experiments, since the role of the different dimensionless numbers governing the phenomenon of fatigue is herein elucidated. Finally, a numerical model based on damage mechanics and nonlinear fracture mechanics is proposed for the prediction of uniaxial S–N curves, showing how to efficiently use the information gained from dimensional analysis and how the shape of the S–N curves is influenced by the parameters of the damage model.Marco Paggimarco.paggi@imtlucca.it2013-12-02T11:29:32Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1990This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19902013-12-02T11:29:32ZLimits to plastic analysis due to size-scale effects on the rotational capacity of reinforced concrete cross sectionsReinforced concrete (RC) structures are usually designed to provide a ductile response under bending loadings. To this aim, most codes of practice impose lower and upper limits to the steel ratio in order to prevent unstable crack propagation and to avoid brittle failure due to concrete crushing without steel yielding. Within these limitations, elastic analysis with moment redistribution or even plastic analysis can be adopted for RC structures. In this context, size-scale effects are usually disregarded, leading to unsafe design conditions in the case of large structures.
In the present study, the limitations of the prescriptions provided by the European and American building codes concerning the admissible plastic rotation and moment redistribution are highlighted. In particular, using a numerical algorithm based on the finite element method and on nonlinear fracture mechanics concepts recently developed by the present authors, the mechanical behaviour of the plastic hinge region of RC beams in bending is simulated. The results show that the effect of the structural dimension should be explicitly introduced in the code prescriptions for a safe structural design, by considering different design curves depending on the size-scale of the beams. Mauro CorradoMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-02T11:20:20Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1989This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19892013-12-02T11:20:20ZSingular, hypersingular and singular free electromagnetic fields at wedge tips in metamaterials The engineering response of metamaterials has a dramatic impact on the physics, optics and engineering communities, because they offer electromagnetic properties that are difficult or impossible to achieve with conventional materials. In this paper, an asymptotic analysis of the electromagnetic fields at multi-material wedges composed of metamaterials is proposed. This is made possible by removing the assumption of positive electric permittivities and magnetic permeabilities, an hypothesis which usually applies to conventional materials. Exploring the whole range of variability of these electromagnetic properties, it is shown that, in addition to the classical real eigenvalues 0 ⩽ λ < 1 leading to power-law singularities of the type O(rλ−1) as r → 0, it is also possible to find imaginary eigenvalues leading to hypersingular solutions, as well as nonsingular configurations for a suitable choice of the negative electric permittivities and magnetic permeabilities of the media. Moreover, to fully characterize the asymptotic fields, the analysis is not only restricted to the determination of the lowest real and complex eigenvalues, but is also extended to the evaluation of the higher-order nonsingular ones. The obtained analytical results collected in synthetic diagrams are expected to have impact on the design of micro- and nano-electro-mechanical systems. Marco Paggimarco.paggi@imtlucca.it2013-12-02T11:08:47Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1988This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19882013-12-02T11:08:47ZThe coefficient of proportionality κ between real contact area and load, with new asperity models Most recent numerical works on fractal surfaces have simply compared the low load limit of the coefficient of proportionality κ of the relationship between real contact area and load. In particular, that provided by Persson's theory, and that obtained from the Bush, Gibson and Thomas (BGT-A) asperity contact theory, which is a generalized form of the Greenwood and Williamson (GW) one. The two theories differ only by a numerical constant κ = √8/π ≈ 1.6 vs κ = √2 π ≈ 2.5 , but neither of the two provide an accurate prediction, Persson's value being generally too low, and BGT-A's limit being only valid for extremely large separations. A detailed numerical comparison using a range of generated fractal surfaces permits to compare the existing models, finding for example that bandwidth is more important than Gaussianity of the surfaces. Then, we propose two new theoretical equations generalizing {GW} and {BGT} to take into account interaction effects in an approximate way (GW-I and BGT-I, respectively), which significantly improve the accuracy of original asperity models. Further, as a practical alternative to the tribologist, we suggest a new very simple discrete form of the {GW} model (called GW-RI) whose accuracy is similar to BGT-I, but with much lower computational cost, comparable to analytical solutions since the latter require the evaluation of the variance of the profile slopes, σ m 2 , with a surface defined at a given set of points. The GW-RI model additionally avoids an ambiguity over how to define numerically the variance of the profile slopes, σ m 2 . Marco Paggimarco.paggi@imtlucca.itMichele Ciavarella2013-12-02T11:06:15Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1987This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19872013-12-02T11:06:15ZA mathematical analogy and a unified asymptotic formulation for singular elastic and electromagnetic fields at multimaterial wedgesIn the present contribution, the mathematical analogy existing between the singular stress field in elasticity due to antiplane loading and the singular electromagnetic fields in electromagnetism is derived with reference to the problem of isotropic multimaterial wedges. These configurations, where dissimilar sectors converge to the same vertex, are commonly observed in composite materials and may lead to singularities. The proposed analogy permits to extend several elastic solutions for the power of the stress-singularity already available in the elasticity literature to the analogous electromagnetic problems and viceversa. Finally, electromagnetic structures that cannot be treated according to the proposed analogy, such as those related to bi-isotropic multimaterial wedges, are discussed.Marco Paggimarco.paggi@imtlucca.itAlberto CarpinteriRenato Orta2013-12-02T11:02:49Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1986This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19862013-12-02T11:02:49ZAn integrated cohesive/overlapping crack model for the analysis of flexural cracking and crushing in RC beamsIn the present paper, a new fracture-mechanics based model is proposed for the analysis of reinforced concrete beams in bending describing both cracking and crushing growths taking place during the loading process by means of the concept of strain localization. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which considers a material interpenetration when the elastic limit is overcome, in close analogy with the Cohesive Crack Model, routinely adopted for modelling the tensile behaviour of concrete. On the basis of different nonlinear contributions due to concrete and steel, a numerical finite element algorithm is proposed. According to this approach, the flexural behaviour of reinforced concrete structural elements is analyzed by varying the main geometrical and mechanical parameters. Particular regard is given to the role of the size-scale effects on the ductility of plastic hinges, which is available at the ultimate load conditions.Alberto CarpinteriMauro CorradoMarco Paggimarco.paggi@imtlucca.it2013-12-02T10:59:47Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1985This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19852013-12-02T10:59:47ZA generalisation of the Hillerborg's model for the analytical evaluation of ductility of RC beams in bendingIn this study, a generalised analytical model for the evaluation of the plastic rotations of reinforced concrete beams in bending is proposed. To this aim, the pioneering Hillerborg's model is here extended by taking into account also the contribution of reinforcement in compression. Moreover, a detailed comparison with the experimental results by Bosco and Debernardi on three-point bending reinforced concrete beams by varying the reinforcement percentage and the size-scale of the structural elements is carried out. This permits study of the influence of the parameter β, related to the length of strain localisation of concrete in compression, on the ductility response and how to tune this parameter according to experiments. The proposed generalisation of the Hillerborg model is then suitably applied to over-reinforced concrete beams in bending, where concrete crushing is the prevailing non-linearity; it is shown that the model is able to capture the phenomenon of size-scale effectsErica CadamuroMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-12-02T10:55:31Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1984This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19842013-12-02T10:55:31ZAnalysis of snap-back instability due to end-plate debonding in strengthened beamsThe problem of end-plate debonding of the external reinforcement in strengthened concrete beams is analyzed in this paper. As experimentally observed, this mode of failure is highly brittle and poses severe limitations to the efficacy of the strengthening technique. A numerical analysis of the full-range behavior of strengthened beams in bending is herein proposed to study the stages of nucleation and propagation of interfacial cracks between the external reinforcement and the concrete substrate. This is achieved by modeling the nonlinear interface behavior according to a cohesive law accounting for Mode Mixity. The numerically obtained load versus midspan deflection curves for three- or four-point bending beams show that the process of end-plate debonding is the result of a snap-back instability, which is fully interpreted in the framework of the Catastrophe Theory. To capture the softening branch with positive slope, the interface crack-length control scheme is proposed in the numerical simulations. The results of a wide parametric study exploring the effect of the relative reinforcement length, the mechanical percentage of fiber-reinforced polymer sheets, the beam slenderness, and the ratio between Mode II and Mode I fracture energies are collected in useful diagrams. Finally, an experimental assessment of the proposed model completes the paper.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-02T10:38:28Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1983This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19832013-12-02T10:38:28ZTechnical Papers: Linear elastic fracture mechanics approach to plate end debonding in rectilinear and curved plated beamsThis paper proposes a linear elastic fracture mechanics approach for the prediction of plate end debonding in rectilinear and curved plated beams. The analytical model results in simple equations, suitable for immediate design use. The load-deflection curve of a plated beam, from the onset of debonding up to the complete separation of the plate, is obtained by controlling the length of the interfacial debonding crack. Its shape clearly shows that snap-back or snap-through instabilities may arise when the beam is loaded under displacement or force control. Analytical predictions are also compared with finite element results based on an interfacial cohesive crack model. It is shown that the predictions of the proposed analytical model match closely the numerical solution, provided that an effective crack length accounting for the size of the fracture process zone is used in the calculations.Giorgio ZavariseAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.itLaura De Lorenzis2013-12-02T10:29:18Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1982This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19822013-12-02T10:29:18ZA unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing modelsIn this paper, a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue is proposed. The enhanced ability to detect and measure very short cracks has in fact pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris’ constant C are only two notable examples of these anomalous scaling laws. In this context, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. A new generalized theory based on fractal geometry is herein proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical framework. The proposed model is used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals. As a main result, the model gives an explanation to the experimentally observed variability in the slope of the asymptote of the scaling law for the fatigue threshold in the short crack regime.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-12-02T10:25:30Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1981This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19812013-12-02T10:25:30ZA dimensional analysis approach to fatigue in quasi-brittle materialsRIASSUNTO. Nel presente lavoro si propone uno studio di analisi dimensionale del fenomeno della fatica nei
materiali quasi-fragili. Esso costituisce una generalizzazione della metodologia pionieristica proposta da
Barenblatt e Botvina e si prefigge di interpretare le deviazioni dalle leggi di potenza classiche usate per
caratterizzare il comportamento a fatica dei materiali. In base a questo approccio teorico, gli effetti dovuti alla
dimensione microstrutturale (correlabile al contenuto volumetrico di fibre nei calcestruzzi fibrorinforzati), alla
dimensione delle fessure e alla scala strutturale sulla legge di Paris e sulle curve di Wöhler sono discussi in un
contesto matematico unificato. Il modello teorico è confermato dal confronto con rilevanti risultati sperimentali
disponibili in letteratura, usati per determinare i valori degli esponenti di autosimilarità incompleta. Le
informazioni fornite da questa teoria possono essere particolarmente utili per guidare la progettazione di nuovi
esperimenti, dal momento che viene chiarito il ruolo delle diverse variabili adimensionalizzate che governano il
fenomeno della fatica.
ABSTRACT. In this study, a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack
growth is proposed in order to highlight and explain the deviations from the classical power-law equations used
to characterize the fatigue behaviour of quasi-brittle materials. According to this theoretical approach, the
microstructural-size (related to the volumetric content of fibres in fibre-reinforced concrete), the crack-size, and
the size-scale effects on the Paris’ law and the Wöhler equation are presented within a unified mathematical
framework. Relevant experimental results taken from the literature are used to confirm the theoretical trends
and to determine the values of the incomplete self-similarity exponents. All these information are expected to
be useful for the design of experiments, since the role of the different dimensionless numbers governing the
phenomenon of fatigue is herein elucidated.Marco Paggimarco.paggi@imtlucca.it2013-12-02T10:18:03Z2014-10-09T09:20:24Zhttp://eprints.imtlucca.it/id/eprint/1980This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19802013-12-02T10:18:03ZIl modello della fessura coesiva in trazione e compressione per la valutazione della duttilità degli elementi strutturali in calcestruzzo armatoRIASSUNTO. Il problema della valutazione della duttilità degli elementi in calcestruzzo armato soggetti a flessione o presso-flessione è stato largamente studiato negli ultimi decenni, sia da un punto di vista sperimentale che analitico. Data l’influenza di numerosi parametri di progetto sulla duttilità, tuttavia, è difficile sviluppare un modello in grado di descrivere completamente la risposta meccanica di elementi strutturali, tenendo conto di tutti gli effetti dovuti alla non-linearità dei materiali. Nel passato, in particolare, si è studiato in maniera approfondita l’effetto della classe di duttilità dell’acciaio, mentre il ruolo degli effetti di scala, evidenziato da più campagne sperimentali, non è stato ancora del tutto chiarito. Una delle ragioni principali è l’inadeguatezza dei modelli tradizionali, basati su leggi costitutive tra tensioni e deformazioni. Nel presente lavoro, si propone un nuovo modello basato sul concetto della localizzazione delle deformazioni, capace di descrivere la propagazione della fessura e l’avanzamento del crushing durante il processo di carico. In tale contesto, il comportamento non-lineare del calcestruzzo in compressione è modellato attraverso l’Overlapping Crack Model, modello analogo a quello coesivo valido per la trazione, che descrive la localizzazione delle deformazioni dovuta al danneggiamento del calcestruzzo mediante una compenetrazione del materiale. Con questo nuovo algoritmo è possibile cogliere l’effettiva risposta flessionale di elementi strutturali in calcestruzzo armato al variare della percentuale di armatura e della scala dimensionale. Applicazioni numeriche riguardano l’analisi della risposta post-picco di provini in calcestruzzo soggetti a compressione e la valutazione delle rotazioni plastiche di travi in calcestruzzo armato soggette a flessione su tre punti. Si propone infine un ampio confronto con i risultati di prove sperimentali, con lo scopo di dimostrare la validità del nuovo approccio.
ABSTRACT. The problem of assessing the ductility of reinforced concrete (RC) structural elements in bending or under the action of eccentric forces has been largely investigated from both the experimental and the analytical point of view during the last decades. Since the development of ductility is influenced by several design parameters, it is difficult to develop a predictive model able to fully describe the mechanical behaviour of the structural element. In particular, the role of the size-scale effect, which has been evidenced by some experimental tests, is not yet completely understood. One of the main reasons is the inadequacy of the traditional models based on ad hoc stress-strain constitutive laws. In the present contribution, a new model based on the concept of strain localization is proposed, which is able to describe both cracking and crushing growths during the loading process. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which describes the strain localization due to crushing by means of a material compenetration. With this numerical algorithm in hand, it is possible to effectively capture the flexural behaviour of RC structural elements by varying the reinforcement percentage and/or the structural size. Numerical applications regard the analysis of the post-peak nonlinear response of concrete specimens subjected to eccentric compression tests and the evaluation of the plastic rotation of RC beams under three-point bending. An extensive comparison with experimental results is also proposed, fully demonstrating the effectiveness of the proposed approach.Alberto CarpinteriAndrea CorradiniGiuseppe ManciniMarco Paggimarco.paggi@imtlucca.it2013-11-29T13:51:34Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1979This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19792013-11-29T13:51:34ZCusp-catastrophe interpretation of the stick-slip behaviour of rough surfacesThe stick-slip instability is a typical manifestation of the nonlinearity of the frictional response of rough surfaces. As recently demonstrated by several researchers, the problem of contact loss is also inherently connected to the stick-slip instability and it has been detected both in elastically soft materials, such as rubber or gelatine, and in elastic stiff materials, such as for earthquake faults. Treating the problem of tangential contact in the framework of micromechanical contact models, the effect of the phenomenon of contact loss on the micro-slip behavior of rough surfaces is herein investigated. To this aim, the stick and slip components of the total applied tangential force and of the total real contact area are properly determined as functions of the total applied tangential force. A comparison with the behavior of smooth surfaces, such as spheres, cylinders and flat surfaces, is presented. Then, simulating the problem of tangential loading followed by a reduction of the applied normal force, it will be shown that the phenomenon of contact loss gives rise to energy release due to snap-back instability in the diagram relating the tangential force to the sliding displacement. This result provides for the very first time an explanation to the phenomenon of stick-slip according to the Catastrophe Theory, in close analogy with the cusp-catastrophe instability of Mode I crack propagation in cohesive solids.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-11-29T13:47:57Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1978This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19782013-11-29T13:47:57ZTowards a unified approach for the analysis of failure modes in FRP-retrofitted concrete beamsThe application of the external reinforcement makes rather complex the scenario of the possible failure modes in reinforced concrete beams retrofitted with FRP. The far more commonly observed failure modes are: (i) edge debonding of the FRP sheet, (ii) intermediate crack induced debonding and (iii) beam failure due to diagonal (shear) crack propagation. In the present study we revisited the competition between all the possible failure modes that can occur in this structural element. To this aim, different analytical models based on linear and non-linear fracture mechanics are developed and harmonized. As a result, useful failure maps are analytically determined, giving, for each failure mode, the critical load of activation as a function of the main parameters governing the problem, i.e. the mechanical properties of the constituent materials, the amount of reinforcement and its bonding length, as well as the size and slenderness of the structural element. The studies presented in this paper are mainly intended to establish guidelines for the future development of these concepts towards a unified mathematical approach. Indeed, once the validity of this unified approach is confirmed, also by comparison with further experimental data, it will be possible to remove some of the simplifying assumptions we used in this analysis to reach a more comprehensive analytical formulation.Marco Paggimarco.paggi@imtlucca.itGiuseppe LacidognaPietro CornettiAlberto Carpinteri2013-11-29T13:35:55Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1977This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19772013-11-29T13:35:55ZA numerical approach to modelling size effects on the flexural ductility of RC beamsThe problem of evaluating the rotation capacity of reinforced concrete (RC) beams in bending has been largely investigated from both the experimental and the analytical point of view during the last decades. Since the development of ductility is influenced by several design parameters, it is difficult to develop a predictive model that can fully describe the mechanical behaviour of RC beams. In particular, the role of the size-scale effect, which has been evidenced by some experimental tests, is not yet completely understood. One of the main reasons is the inadequacy of the traditional models based on ad hoc stress–strain constitutive laws. In the present paper, a new model based on the concept of strain localization is proposed, which is able to describe both cracking and crushing growths in RC beams during the loading process. In particular, the nonlinear behaviour of concrete in compression is modelled by the Overlapping Crack Model, which describes the strain localization due to crushing by means of a material interpenetration. With this algorithm in hand, it is possible to effectively capture the flexural behaviour of RC beams by varying the reinforcement percentage and/or the beam depth. An extensive comparison with experimental results demonstrates the effectiveness of the proposed approach.Alberto CarpinteriMauro CorradoGiuseppe ManciniMarco Paggimarco.paggi@imtlucca.it2013-11-29T13:33:31Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1976This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19762013-11-29T13:33:31ZSize-scale effects on plastic rotational capacity of reinforced concrete beamsA complete numerical algorithm that assumes a strain localization in concrete, both in tension and compression, is proposed for modeling cracking and crushing growths during the loading process of reinforced concrete beams in bending. With this algorithm based on nonlinear fracture mechanics models, it is possible to investigate the effects of the main mechanical and geometrical parameters on the rotational capacity with particular regard to the reinforcement percentage and the element size. A comparison with experimental results demonstrates the effectiveness of the proposed approach for a wide range of reinforcement percentages and beam depths. The obtained results show that the prescriptions concerning the admissible plastic rotations provided by the existing design formulas are not conservative in the case of large structural sizes. To overcome such a drawback, a new design diagram is proposed for practical purposes.Alberto CarpinteriMauro CorradoGiuseppe ManciniMarco Paggimarco.paggi@imtlucca.it2013-11-29T12:57:06Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1975This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19752013-11-29T12:57:06ZA top-down approach for the prediction of hardness and toughness of hierarchical materials Many natural and man-made materials exhibit structure over more than one length scale. In this paper, we deal with hierarchical grained composite materials that have recently been designed to achieve superior hardness and toughness as compared to their traditional counterparts. Their nested structure, where meso-grains are recursively composed of smaller and smaller micro-grains at the different scales with a fractal-like topology, is herein studied from a hierarchical perspective. Considering a top-down approach, i.e. from the largest to the smallest scale, we propose a recursive micromechanical model coupled with a generalized fractal mixture rule for the prediction of hardness and toughness of a grained material with n hierarchical levels. A relationship between hardness and toughness is also derived and the analytical predictions are compared with experimental data. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-29T12:22:03Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1974This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19742013-11-29T12:22:03ZA unified interpretation of the power laws in fatigue and the analytical correlations between cyclic properties of engineering materials A phenomenological description of the fatigue life of engineering components can be given either by plotting the applied stress range as a function of the total number of cycles to failure, i.e., according to the Wöhler’s curve, or, after the advent of fracture mechanics, by plotting the crack growth rate in terms of the stress-intensity factor range, i.e., using the Paris’ curve. In this work, an analytical approach is proposed for the study of the relationships existing between the Wöhler’s and the Paris’ representations of fatigue. According to dimensional analysis and the concepts of complete and incomplete self-similarity, generalized Wöhler and Paris equations are determined, which provide a rational interpretation to a majority of empirical power-law criteria used in fatigue. Then, by integration of the generalized Paris’ law, the relationship between the aforementioned generalized representations of fatigue is established, providing the link between the cumulative fatigue damage and the fatigue crack propagation approaches. Moreover, paying attention to the limit points defining the range of validity of the classical Wöhler and Paris power-law relationships, whose co-ordinates are referred to as cyclic or fatigue properties, alternative expressions for the classical laws of fatigue are proposed. Finally, the correlations between such fatigue properties are determined according to theoretical arguments, giving an interpretation of the empirical trends observed in the material property charts. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-29T12:09:25Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1973This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19732013-11-29T12:09:25ZAsymptotic analysis in Linear Elasticity: from the pioneering studies by Wieghardt and Irwin until today The asymptotic analysis of the stress distribution around an elastic wedge-shaped domain is one of the most fundamental problems in Linear Elasticity. In occasion of the century anniversary of the pioneering paper by Wieghardt on splitting and cracking of elastic bodies, and of the half-a-century anniversary of the Irwin’s paper on the analysis of stresses and strains near the end of a crack, we propose a review of the most important contributions leading to fundamental advances in this research field. Special focus will be given to the epistemological steps towards a full appreciation of the mathematical and engineering relevance of the stress-singularities. We also provide the reader with a review of the geometrical configurations and mechanical conditions that can relieve or remove the singularities, including: re-entrant corners; power-law hardening constitutive laws; fractal cracks; multi-material junctions and wedges; nonhomogeneous materials. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-29T11:58:45Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1972This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19722013-11-29T11:58:45ZThe overlapping crack model for uniaxial and eccentric concrete compression testsAn analytical/numerical model, referred to as the overlapping crack model, is proposed in the present paper for the analysis of the mechanical behaviour of concrete in compression. Starting from the experimental evidence of strain localisation in uniaxial compression tests, the present model is based on a couple of constitutive laws for the description of the compression behaviour of concrete: a stress–strain law until the achievement of the compression strength and a stress–displacement relationship describing the post-peak softening behaviour. The displacement would correspond to a fictitious interpenetration and therefore the concept of overlapping crack in compression is analogous to the cohesive crack in tension. According to this approach, the slenderness and size-scale effects of concrete specimens tested under uniaxial compression are interpreted from an analytical point of view. Then, implementing the overlapping crack model into the finite element method, eccentric compression tests are numerically simulated and compared with experimental results. The influence of the size-scale, the specimen slenderness, as well as the degree of load eccentricity, is discussed in detail, quantifying the effect of each parameter on the ductility of concrete specimens.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itMauro CorradoGiuseppe Mancini2013-11-29T11:55:29Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1971This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19712013-11-29T11:55:29ZFractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue The enhanced ability to detect and measure very short cracks, along with a great interest in applying fracture mechanics formulae to smaller and smaller crack sizes, has pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris’ constant C are only two notable examples of these anomalous scaling laws. In this framework, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. In this paper, we propose a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue. The limitations of each model are put into evidence and removed. At the end, a new generalized theory based on fractal geometry is proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical formulation. Finally, this approach is herein used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals. Marco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-11-29T11:52:17Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1970This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19702013-11-29T11:52:17ZA fractal interpretation of size-scale effects on strength, friction and fracture energy of faults Experimental results indicate that large faults involved in earthquakes possess low strength, low friction coefficient and high fracture energy, in comparison with data obtained according to small scale laboratory tests on the same material. The reasons for such an unexpected anomalous behaviour have been the subject of several researches in the past and are still under debate in the Scientific Community. In this note, we propose a unifying interpretation of these size-scale effects according to fractal geometry, which represents the proper mathematical framework for the analysis of the multi-scale properties of rough surfaces in contact. This contribution sheds a new light on the non-linear properties of friction and on the understanding the fundamental physics governing the scaling of the mechanical properties in geophysics from the laboratory to a planetary scale. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-29T11:48:33Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1969This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19692013-11-29T11:48:33ZOne, no one, and one hundred thousand crack propagation laws: a generalized Barenblatt and Botvina dimensional analysis approach to fatigue crack growth Barenblatt and Botvina with elegant dimensional analysis arguments have elucidated that Paris’ power-law is a weak form of scaling, so that the Paris’ parameters C and m should not be taken as material constants. On the contrary, they are expected to depend on all the dimensionless parameters of the problem, and are really “constants” only within some specific ranges of all these. In the present paper, the dimensional analysis approach by Barenblatt and Botvina is generalized to explore the functional dependencies of m and C on more dimensionless parameters than the original Barenblatt and Botvina, and experimental results are interpreted for a wider range of materials including both metals and concrete. In particular, we find that the size-scale dependencies of m and C and the resulting correlation between C and m are quite different for metals and for quasi-brittle materials, as it is already suggested from the fact the fatigue crack propagation processes lead to m = 2 – 5 in metals and m = 10 – 50 in quasi-brittle materials. Therefore, according to the concepts of complete and incomplete self-similarities, the experimentally observed breakdowns of the classical Paris’ law are discussed and interpreted within a unified theoretical framework. Finally, we show that most attempts to address the deviations from the Paris’ law or the empirical correlations between the constants can be explained with this approach. We also suggest that “incomplete similarity” corresponds to the difficulties encountered so far by the “damage tolerant” approach which, after nearly 50 years since the introduction of Paris’ law, is still not a reliable calculation of damage, as Paris himself admits in a recent review. Michele CiavarellaMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-11-29T11:40:25Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1968This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19682013-11-29T11:40:25ZSize-Scale effects on strength, friction and fracture energy of faults: a unified interpretation according to fractal geometryExperimental results clearly indicate that large faults involved in earthquakes possess low strength, low friction coefficient and high fracture energy, in comparison with data obtained from small scale laboratory tests on rock samples. The reasons for such an unexpected anomalous behaviour have been the subject of several studies in the past and are still under debate in the Scientific Community. In this paper we propose a unifying interpretation of these size-scale effects on the basis of fractal geometry, which represents the proper mathematical framework for the analysis of multi-scale properties of rough surfaces in contact. A rather good agreement between the proposed scaling laws and the experimental data ranging from the laboratory scale up to the planetary scale typical of natural faults is achieved.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-29T11:34:44Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1967This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19672013-11-29T11:34:44ZThermo-elastic mismatch in nonhomogeneous beamsThe problem of thermo-elastic stress analysis in multi-layered nonhomogeneous beams is considered. The proposed analytical approach based on the multi-layered beam theory permits to take into account an arbitrary distribution of the Young’s modulus, of the thermal-expansion coefficient, and of the temperature variation along the beam depth. The effect of shear deformability of the interfaces is also carefully analyzed. Useful closed-form solutions for the normal stresses in the layers and for the interface tangential stresses are provided in the case of nonhomogeneous bi- and tri-layered beams. The obtained results show the effectiveness of using functionally graded materials to relieve stress-concentrations due to the thermo-elastic mismatch typical of laminated beams with homogeneous layers.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-29T11:31:55Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1966This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19662013-11-29T11:31:55ZInclusion of “interaction” in the Greenwood and Williamson contact theory Recent direct implementation of asperity theories is reinterpreted here to formulate an improved version of the Greenwood and Williamson (GW) theory with the inclusion of interaction between asperities. This is achieved by treating the contact pressures as uniformly distributed over the apparent contact area and the resulting deformation as uniform. The correction is equivalent to an increase of the effective separation of the mean planes by a quantity proportional to the nominal pressure, resulting in a reduction of the “real” area of contact and of total load for a given separation. However, the area–load relationship is unchanged. The correction effectively depends on the ratio between the nominal pressure and the elastic modulus multiplied by the ratio between the size of the nominal contact area and standard deviation of the asperity heights. For contacts much larger than the size of roughness, uniform interaction effects would be dominant at relatively modest pressures (particularly for soft materials). This also means that the effect of interaction is unlimited. However, the only significant change is in the prediction of gas-tightness, it is harder to seal a large area than a small one. The modification of the theory has a significant effect on stiffness and conductance. Indeed, a parallel is drawn between this correction and the “clustering” terms of resistance in the Holm–Greenwood formulae for a cluster of circular spots. Finally, numerical contact simulations using Weierstrass–Mandelbrot (WM) surfaces show a general agreement with the improved theory but also significant scatter for low load levels. Taking into account the effect of asperity interaction, the improved {GW} theory is now able to predict the numerically obtained contact response for intermediate load levels. Michele CiavarellaJ.A. GreenwoodMarco Paggimarco.paggi@imtlucca.it2013-11-28T14:52:23Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1965This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19652013-11-28T14:52:23ZThe effect of contact on the decohesion of laminated beams with multiple microcracks The problem of interface decohesion in laminated beams is addressed with reference to the debonding double cantilever beam test geometry (DCB). The paper deals with the analysis of the influence of nonuniform bonding properties or interfacial defects on the crack propagation process and its stability. To this aim, the classical analytical approach based on the Euler–Bernoulli beam on an elastic foundation is extended to the presence of a general distribution of microcracks ahead of the macrocrack tip. The main features and limitations of this approach are carefully analyzed. In particular, it is shown that this simplified approach does not consider the unilateral contact condition along the interface, thus admitting a penetration between the two arms of the beam. A comparison with a finite element formulation is proposed to assess if this violation of the constraints inequalities, usually adopted in the case of uniform bonding, is still acceptable when interfacial defects are present. In order to fully describe the whole nonlinear behavior of the interface, a generalized interface constitutive law is used. The models comparison shows that, in the presence of interfacial defects, the effect of contact plays a crucial role in the description of the mechanical response of the joint. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-11-28T14:49:26Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1964This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19642013-11-28T14:49:26ZOn the stress singularities at multimaterial interfaces and related analogies with fluid dynamics and diffusionJoining of different materials is a situation frequently observed in mechanical engineering and in materials science. Due to the difference in the elastic properties of the constituent materials, the junction points can be the origin of stress singularities and a possible source of damage. Hence, a full appreciation of these critical situations is of fundamental importance both from the mathematical and the engineering standpoints. In this paper, an overview of interface mechanical problems leading to stress singularities is proposed to show their relevance in engineering. The mathematical methods for the asymptotic analysis of stress singularities in multimaterial junctions and wedges composed of isotropic linear-elastic materials are reviewed and compared, with special attention to in-plane and out-of-plane loadings. This analysis mathematically demonstrates in a historical retrospective the equivalence of the eigenfunction expansion method, of the complex function representation, and of the Mellin transform technique for the determination of the order of the stress singularity in such problems. The analogies between linear elasticity and the Stokes flow of dissimilar immiscible fluids, the steady-state heat transfer across different materials, and the St. Venant torsion of composite bars are also discussed. Finally, advanced issues for the stress singularities due to joining of angularly nonhomogeneous elastic wedges are presented. This review article contains 147 references.Marco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-11-28T14:42:11Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1963This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19632013-11-28T14:42:11ZSpecimen shape and the problem of contact in the assessment of concrete compressive strengthThis paper proposes a critical analysis of the studies which, since the 1950s, have attempted to quantify the influence of specimen shape on the determination of concrete compressive strength, with special regard to the problem of conversion from cylinder to cube strength and vice versa. From such a retrospective analysis, it emerges that the problem of contact between the platens of the testing machine and the concrete specimen plays a crucial role for the explanation of the variability of the concrete compressive strength as a function of specimen shape. To obtain quantitative predictions and to investigate on the influence of the friction coefficient, uniaxial compressive tests are numerically simulated by using a nonlinear finite element model. Both the constitutive nonlinearity of concrete and the nonlinearity due to contact are taken into account in the formulation. The results of the proposed parametric analysis permit to evaluate the evolution of the conversion ratio between cylinder and cube strength as a function of the friction coefficient. This sheds a new light on the complex nature of this nonlinear relationship, whose value approaches 1 for a friction coefficient close to 0.01, simulating the presence of Teflon, and then approaches asymptotically 0.78 for f = 0.60, as is typical of steel-concrete interfaces.Ferdinando IndelicatoMarco Paggimarco.paggi@imtlucca.it2013-11-28T14:15:28Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1961This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19612013-11-28T14:15:28ZNumerical analysis of fracture mechanisms and failure modes in bi-layered structural componentsThe problem of crack propagation in bi-layered structural components is addressed. Due to the presence of the bi-material interface and depending on the loading direction, a competition between different crack trajectories (failure modes) can take place. The quantification of the dominant failure mode and of the prevailing fracture mechanism is very often a challenging task, although it is crucial for design purposes. In this contribution, starting from the experimental observation of failure modes in a variety of engineering applications involving bi-layered structural components, an interpretation is proposed in the framework of the finite elements discretization and linear elastic fracture mechanics. The effect of thermo-elastic and residual stresses on the stability of crack propagation is carefully examined. Numerical results confirm the qualitative experimental observations of failure modes in bi-layered structural elements used for rock drilling applications. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-28T14:04:38Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1959This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19592013-11-28T14:04:38ZAcoustic emission monitoring and numerical modeling of FRP delamination in RC beams with non-rectangular cross-sectionA case study concerning both numerical modeling and in-situ monitoring of a retrofitted RC beam with non-rectangular cross-section is presented. Before retrofitting, non-destructive techniques, such as pull-out and impact tests, were used to estimate the mechanical parameters of concrete. At the same time, a long-term monitoring with the Acoustic Emission (AE) technique was carried out in order to investigate on creep effects and microcracking phenomena. Then, after a complete removal of the overload and retrofitting with FRP sheets, an in-situ loading test was performed. At that stage, the AE technique was again profitably used for the analysis of the cracking progression leading to FRP debonding. A numerical model of the structure is then proposed in the framework of the FE discretization with mechanical parameters estimated according to an inverse analysis on the monitored mechanical behavior of the structure before retrofitting. According to this model it is shown that, when the flexural inertia of the retrofitted beam is considerably higher than that of the unrepaired beam, snap-back instabilities can take place. Finally, considering the self-similarity between the acoustic emission phenomenon and seismicity, an analogy between the snap-back instability of the FRP delamination and that occurring during fault growth is proposed.Alberto CarpinteriGiuseppe LacidognaMarco Paggimarco.paggi@imtlucca.it2013-11-28T12:56:37Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1958This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19582013-11-28T12:56:37ZOn the resolution dependence of micromechanical contact models In this study we deal with the problem of normal contact between rough surfaces. A power spectral density of the asperity heights which obeys a power-law within a given range of wavelengths has been considered. Hence, the resolution dependence of the statistical parameters computed according to the random process theory, of the plasticity index and of the contact predictions provided by stochastic and fractal contact models is discussed and emphasized. It is demonstrated that the plasticity index diverges to infinity when the lower cut-off length of the system vanishes, whereas the slope of the real contact area versus normal load curve tends to zero. In this limit case stochastic and fractal approaches predict either a vanishing real contact area or an infinite normal pressure, regardless of the asperity deformation assumptions. On the other hand, when a non-zero lower cut-off length exists, finite contact predictions can be obtained by applying the contact models at that scale length. This possibility is numerically investigated and, comparing contact results of several models, it is shown that the plasticity index plays an important role for the characterization of the interface mechanical response. Giorgio ZavariseMauro Borri BrunettoMarco Paggimarco.paggi@imtlucca.it2013-11-28T12:53:08Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1957This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19572013-11-28T12:53:08ZAnalytical study of the singularities arising at multi-material interfaces in 2D linear elastic problems The problem of stress singularities due to multi-material junctions in the material microstructure is addressed in the framework of the eigenfunction expansion method, provided that the eigenvalues are explicitly assumed complex. A novel efficient numerical procedure for computing the order of the stress singularity is presented. The numerical method can also be used to solve analogous singularity problems in anisotropic elasticity. According to this procedure, new problems of bi- and tri-material junctions occurring in the material microstructure are examined, paying special attention to the role played by Mode-I and Mode-II deformation. The effects of both the properties of the matrix and of the presence of transgranular cracks on the order of stress singularities are carefully investigated. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T15:07:49Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1955This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19552013-11-25T15:07:49ZSelf-similarity and crack growth instability in the correlation between the Paris’ constants In this note the question about the existence of a correlation between the parameters C and m of the Paris’ law is re-examined. According to dimensional analysis and incomplete self-similarity concepts applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating the parameter C to m and to the governing variables of fatigue is derived. Then, from the observation that the Griffith–Irwin instability must coincide with the Paris’ instability at the onset of rapid crack growth, the exponents entering this correlation are determined. A fair good agreement is found between the proposed theory and extensive experimental data. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T14:54:27Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1954This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19542013-11-25T14:54:27Zctal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigueMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-11-25T14:45:53Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1953This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19532013-11-25T14:45:53ZCohesive versus overlapping crack model for a size effect analysis of RC elements in bendingThe well-known Cohesive Crack Model describes strain localization with a softening stress
variation in concrete members subjected to tension. An analogous behaviour is also observed in compression,
when strain localization takes place in a damaged zone and the stress reaches the compressive strength with
surface energy dissipation. In the present paper, we propose the new concept of Overlapping Crack Model,
which is analogous to the cohesive one and permits to simulate material compenetration. The two aforementioned elementary models are merged into a more complex algorithm able to describe both cracking and crushing growths during loading processes in RC members. A numerical procedure based on elastic coefficients is developed, taking into account the proposed constitutive laws in tension and compression. With this algorithm, it is possible to effectively capture the flexural behaviour of RC beams by varying the reinforcement percentage and/or the beam depthAlberto CarpinteriMauro CorradoMarco Paggimarco.paggi@imtlucca.itGiuseppe Mancini2013-11-25T14:33:22Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1952This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19522013-11-25T14:33:22ZOn the competition between delamination and shear failure in retrofitted concrete beams and related scale effectsMarco Paggimarco.paggi@imtlucca.itAlberto CarpinteriGiuseppe Lacidogna2013-11-25T14:14:28Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1951This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19512013-11-25T14:14:28ZSnap-back and snap-through instabilities due to contact loss in the stick-slip motion of rough surfacesMarco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-11-25T13:46:28Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1950This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19502013-11-25T13:46:28ZA Coupled Contact and Decohesion Analysis of Laminated BeamsThe problem of interface decohesion in laminated beams is addressed with reference to the double cantilever beam (DCB) geometry. The paper deals with the analysis of the influence of non-uniform bonding properties or interfacial defects on the crack propagation process and its stability. In spite of the relative simplicity of the considered case study, which is under pure Mode I deformation, a contact problem takes place due to the decohesion. The occurrence of contact makes the problem highly non-linear, since the extension of the contact area is a priori unknown. The finite element method with a generalized interface constitutive law is used to enforce the contact constraint along the interface and to model the progress of the delamination process.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-11-25T13:17:08Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1949This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19492013-11-25T13:17:08ZAre the Paris’ law parameters dependent on each other?The question about the existence of a correlation between the parameters C and m of the
Paris’ law is re-examined in this paper. According to dimensional analysis and incomplete self-similarity
concepts applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating
the parameter C to m and to the governing variables of the fatigue phenomenon is derived. Then, from the
observation that the Griffith-Irwin instability must coincide with the Paris’ instability at the onset of rapid
crack growth, the exponents entering this correlation are determined. A fair good agreement is found between
the proposed correlation and the experimental data concerning Aluminium, Titanium and steel alloys.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T12:21:56Z2014-10-09T09:20:25Zhttp://eprints.imtlucca.it/id/eprint/1948This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19482013-11-25T12:21:56ZAre the Paris' law parameters dependent on each other?The question about the existence of a correlation between the parameters C and m of the Paris’ law is
re-examined in this paper. According to dimensional analysis and incomplete self-similarity concepts
applied to the linear range of fatigue crack growth, a power-law asymptotic representation relating the
parameter C to m and to the governing variables of the fatigue phenomenon is derived. Then, from the
observation that the Griffith-Irwin instability must coincide with the Paris’ instability at the onset of rapid
crack growth, the exponents entering this correlation are determined. A fair good agreement is found
between the proposed correlation and the experimental data concerning Aluminium, Titanium and steel
alloysAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T12:04:38Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1947This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19472013-11-25T12:04:38ZNumerical evaluation of generalized stress-intensity factors in multi-layered composites The problem of the evaluation of the generalized stress-intensity factors for re-entrant corners in multi-layered structural components is addressed. An approximate analytical model based on the theory of multi-layered beams is presented. This approach provides a simple closed-form solution for the direct computation of the Mode I stress-intensity factor for the general problem of a re-entrant corner symmetrically meeting a bi-material interface. For the self-consistency of the theory, re-entrant corners in homogeneous materials and cracks perpendicular to bi-material interfaces can also be gained as limit cases of this formulation. According to this approach, the effects of the elastic mismatch parameters, the value of the notch angle and the thicknesses of the layers on the stress-intensity factor are carefully quantified and the results are compared with {FE} solutions. {FE} results are obtained by applying a combination of analytical and numerical techniques based on the knowledge a priori of the asymptotic stress field for re-entrant corners perpendicular to a bi-material interface and on the use of generalized isoparametric singular finite elements at the notch tip. A good agreement between approximate and analytical/numerical predictions is achieved, showing the effectiveness of this approach. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itNicola Pugno2013-11-25T12:01:39Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1946This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19462013-11-25T12:01:39ZInfluence of the intermediate material on the singular stress field in trimaterial junctionsBy the method of eigenfunctions, we analyze the stresses formed at the vertex of a multicomponent wedge formed by homogeneous elastic wedges under the conditions of plane stress state or plane deformation. The exponent of the singularity of stresses in the case of opening and shift of the wedges is numerically determined. The singular stresses formed near the vertex are investigated both for softer and stiffer wedges.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T11:58:56Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1945This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19452013-11-25T11:58:56ZAn analytical approach for fracture and fatigue in functionally graded materialsThe problem of brittle crack propagation and fatigue crack growth in functionally graded materials (FGMs) is addressed. The proposed analytical approach can be used to estimate the variation of the stress-intensity factor as a function of the crack length in FGMs. Furthermore, according to the Paris’ law, the fatigue life and the crack-tip velocity of crack propagation can be predicted in the case of fatigue crack growth. A comparison with numerical results obtained according to the Finite Element method will show the effectiveness of the proposed approach. Detailed examples are provided in the case of three-point bending beam problems with either a FGM interlayer, or a FGM external coating. A comparison is presented between two types of grading in the elastic modulus: a continuous linear variation in the FGM layer and a discrete approximation with a multi-layered beam and a constant Young’s modulus in each layer.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itNicola Pugno2013-11-25T11:54:22Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1944This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19442013-11-25T11:54:22ZMultiscale models for contact mechanics of rough surfacesMarco Paggimarco.paggi@imtlucca.itBernardino ChiaiaMauro Borri Brunetto2013-11-25T11:39:06Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1943This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19432013-11-25T11:39:06ZA unified interface constitutive law for the study of fracture and contact problems in heterogeneous materialsA unified interface constitutive law for the description of contact and decohesion at bi-material interfaces is proposed. To this aim, a synthesis of the nonlinear models pertaining to Fracture and Contact Mechanics is presented. The issues pertinent to the implementation within the FE discretization framework are also discussed in detail. Finally, a numerical example of fatigue modeling at the mesoscopical level in a fiber-reinforced composite is provided.Marco Paggimarco.paggi@imtlucca.itAlberto CarpinteriGiorgio Zavarise2013-11-25T11:07:25Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1942This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19422013-11-25T11:07:25ZCorrelation Between Paris’ Law Parameters Based on Self-Similarity and Criticality ConditionFatigue crack growth data are usually presented in terms of the crack growth rate, da / dN, and the stress-intensity factor range, ΔK. The typical fatigue crack propagation curve is shown in Fig.1, where Region I is referred to as the near-threshold region, Region II as the power-law region and Region III as the rapid crack propagation region where K max → K IC and crack growth instability occurs. In Region II the Paris’ equation (Paris and Erdogan [1]) provides a good approximation to the majority of experimental data: (1) dadN=C(ΔK)m
where C and m are empirical constants usually referred to as Paris’ law parameters.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T10:31:11Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1940This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19402013-11-25T10:31:11ZA numerical model for the analysis of decohesion at bi-material interfaces with random propertiesMarco Paggimarco.paggi@imtlucca.itAlberto CarpinteriGiorgio Zavarise2013-11-25T10:19:29Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1939This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19392013-11-25T10:19:29ZOn the asymptotic stress field in angularly nonhomogeneous materialsThe problem of multi-material junctions composed of angularly nonhomogeneous elastic wedges in plane elasticity is addressed. For this new type of grading the governing equation for the Airy stress function is derived and, by applying the eigenfunction expansion method, a fourth-order ODE with nonconstant coefficients for the eigenequation is obtained. The solution to this ODE permits the formulation of an eigenvalue problem similar to that valid for material junctions between homogenous different materials. It is mathematically demonstrated that the angular grading influences the order of the stress-singularity. The potentials of the use of this new class of materials in joining technology are carefully investigated and some illustrative examples are deeply discussed. Comparisons with the corresponding results obtained from homogeneous materials are made.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T10:15:57Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1937This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19372013-11-25T10:15:57ZSnap-back instability in micro-structured composites and its connection with superplasticityInstability phenomena occurring in the microstructure of micro-structured composites are numerically investigated. To this aim, an interface constitutive law is proposed to describe both decohesion and contact at bi-material interfaces. These formulations are implemented in the FE code FEAP. Then, by applying dimensional analysis, the nondimensional parameters governing the macroscopic response of the composite are identified. According to this model, transverse debonding with respect to the fiber direction is simulated and the transition from snap-back instability in case of coarse fiber diameters, to a stable mechanical response for finer reinforcements is quantified. These results provide a possible quantitative explanation to the role played by the size of the reinforcement on the instability phenomena experimentally observed during superplastic deformation.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-11-25T10:04:08Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1936This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19362013-11-25T10:04:08ZSize-scale effects on the friction coefficient An overview of the classical friction laws holding at the macro-scale and the new developments at the nano-level are proposed. Furthermore, two opposite phenomena are addressed: the former concerning the apparent weakness of the San Andreas fault, the latter regarding the strong frictional behavior which appears at the nano-scale. An interpretation of these size effects on the friction coefficient is attempted making use of the renormalization group procedure which allows to explain the frictional phenomena over all the scales. Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-25T09:57:50Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1935This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19352013-11-25T09:57:50ZInterface mechanical problems in heterogeneous materialsThe simplified assumption of material homogeneity underlying many problems of structural
mechanics is very often far from the complex reality we have to cope with. Junctions and
interfaces between di®erent materials must typically sustain mechanical and thermo-elastic
stresses without failure. Consequently, they exert an important and sometimes controlling
influence on the overall performance of the material. Therefore, current attempts in materials
engineering to increase the strength and ductility of materials require a full appreciation of
material interfaces, their properties and characterization.
Since interface problems are one of the main concern in civil, mechanical and electronic
engineering, as well as in biomechanics and in materials science, this research field is characterized
by multidisciplinary aspects. New concepts in engineering the material microstructure
mark the beginning of a paradigm shift in the way we think about materials and structures.
Due to recent advances in material processing, material and structural design considerations
are moving toward a full integration.
With this respect, it is evident that a proper modeling of the mechanical behavior of
interfaces at di®erent length scales is an outstanding point. The possibility of controlling the
mechanical behavior of the material over all the scales by tailoring interfaces clearly emerges
as one of the new challenges of the scientific community.
This thesis aims at giving a reasonably complete overview of the most relevant mathematical
and numerical techniques that can be applied to solve interface mechanical problems
in heterogeneous materials. With this objective in mind, the connections between the wide
literature of Linear Elastic and nonlinear Fracture Mechanics and Contact Mechanics are
deeply investigated and emphasized.
Novel features of this work include: (1) theoretical and numerical characterization of
stress-singularities arising at multi-material interfaces in 2D linear elastic problems; (2) numerical
and experimental study of brittle and fatigue crack growth in multi-layered materials;
(3) definition of a unified interface constitutive law for the study of decohesion and contact
problems at bi-material interfaces; and (4) interpretation of size-scale e®ects in new advanced
composite materials, such as the prediction of the critical grain sizes for the activation of
the superplastic behavior in fine grained composites and for the inversion of the Hall-Petch
relationship at the nano-scale.Marco Paggimarco.paggi@imtlucca.it2013-11-25T09:43:14Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1934This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19342013-11-25T09:43:14ZMicro-slip of rough surfaces under cyclic tangential loadingA numerical model based on the solution of the normal contact between elastic half-spaces and subsequent post-processing according to the Mindlin and Deresiewicz solution for cyclic tangential loading is presented. Thanks to a recent extension of the Cattaneo-Mindlin analogy to the solution of tangential contact between non-convex domains, the proposed approach enables the study of cyclic micro-slip and energy dissipation between elastic bodies with general shapes in contact. In order to make the procedure straightforward and as general as possible, a non-dimensional formulation, based only on the normal contact load displacement curve, is proposed. The cyclic behaviour of the tangential contact of self-affine fractal surfaces, like those generated by fracture of concrete or rock, is described with several examples.Mauro Borri BrunettoAlberto CarpinteriStefano InvernizziMarco Paggimarco.paggi@imtlucca.it2013-11-22T12:07:24Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1933This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19332013-11-22T12:07:24ZCyclic Micro-slip and Energy Dissipation on Elastic Rough InterfacesA generalized approach is proposed, following the Mindlin and Deresiewicz procedure, to study
the cyclic behavior of surfaces in contact under a small oscillating tangential force. In order to
make the procedure straightforward and as general as possible, a non-dimensional formulation,
based only on the normal contact load-displacement curve, has been provided. It turns out that the
non-dimensional behavior under normal or tangential loading, as well as the energy dissipation
involved in cyclic loading, strongly depends on the exponent
α . This exponent can be calculated
explicitly in the case of profiles described by mathematical expressions (e.g. cylinders and
spheres), or can be determined from best fitting of experimental or numerical data (e.g. from
ICARUS simulations).
The larger is the exponent
α , the larger is the energy dissipated in small amplitude (partialslip)
tangential cycles.
Moreover, a comparison has been provided, without any claims of completeness, among some
of the theoretical models for the tangential interaction of rough surfaces available in the literature.
The calculation of the exponent α allows us to show the influence of different statistical
distribution assumptions of surface heights on the hysteretic energy dissipation.
Finally, the stick-slip behavior of rough surfaces subjected to oscillating loads has been
interpreted in terms of an analogy with the shake-down phenomenon described by the theory of
plasticity.Mauro Borri BrunettoStefano InvernizziMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-11-22T11:53:51Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1932This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19322013-11-22T11:53:51ZDelamination in FRP-strengthened structures: acoustic emission monitoring and numerical modelingA case study concerning both numerical modeling and in-situ monitoring of a retrofitted RC beam
with non-rectangular cross-section is presented. Before retrofitting, non-destructive techniques,
such as pull-out and impact tests, were used to estimate the mechanical parameters of concrete. At
the same time, a long-term monitoring with the Acoustic Emission (AE) technique was carried out
in order to investigate on creep effects and microcracking phenomena. Then, after a complete
removal of the overload and retrofitting with FRP sheets, an in-situ loading test was performed. At
that stage, the AE technique was again profitably used for the analysis of the cracking progression
leading to FRP debonding. A numerical model of the structure is then proposed in the framework
of the FE discretization with mechanical parameters estimated according to an inverse analysis on
the monitored mechanical behavior of the structure before retrofitting. According to this model, it
is clearly demonstrated that, when the flexural inertia of the retrofitted beam is considerably
higher than that of the unrepaired beam, snap-back instabilities can take place. Finally,
considering the self-similarity between the acoustic emission phenomenon and seismicity, an
analogy between the snap-back instability of the FRP delamination and that occurring during fault
growth is proposed.Giuseppe LacidognaMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-11-22T11:19:24Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1931This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19312013-11-22T11:19:24ZMulti-material junctions with functionally graded materialsComposites frequently involve situations where nonhomogeneous materials are either present
naturally, or used intentionally to attain a required mechanical performance. Starting from Bogy
(1968), bi- and multi-material junctions between different homogeneous materials have been
characterized from the stress-singularity point of view. In these studies, the material parameters
were assumed to be constant inside each material region and an abrupt discontinuity of the elastic
properties at the interfaces was allowed.
More recently, another class of materials, conventionally referred to as functionally graded
materials (FGMs), has been proposed, which involves materials whose elastic properties vary
continuously. When two materials are joined together, an abrupt discontinuity of the elastic
parameters, which is usually assumed for analytical purposes, does not exist in reality. On the
contrary, materials in the proximity of the interface possess continuous, rapidly varying elastic
moduli (Eischen (1987), Paulino (2002)).
In this paper the problem of stress-singularity due to multi-material junctions composed of
angularly nonhomogeneous elastic wedges in plane elasticity is addressed. For this new type of
grading the governing equation for the Airy stress function is derived and, by applying the
eigenfunction expansion method, a fourth order ODE with nonconstant coefficients for the
eigenequation is obtained. The solution to this ODE permits to formulate an eigenvalue problem
similar to that valid for material junctions between homogenous different materials. Moreover, it
is mathematically demonstrated that the angular grading influences the order of the stresssingularity.
The potentials of the use of this new class of materials in joining technology are
carefully investigated and some illustrative examples involving three-material junctions are deeply
discussed. ComparisonsMarco Paggimarco.paggi@imtlucca.itAlberto Carpinteri2013-11-22T11:04:09Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1930This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19302013-11-22T11:04:09ZSoftening and snap-back instability in superplastic deformationThe mechanical behavior of micro-structured composites has been experimentally and theoretically proven to be strongly dependent on the size of the reinforcement. In other words,
keeping constant the reinforcement volumetric fraction and the mechanical properties of the constituent materials, size effects on the mechanical response are observed by varying the diameter of the inclusion. From the technological point of view, an important example where this
size effect is noticed is represented by superplasticity (Langdon, 1995). Instability phenomena occurring in the microstructure of micro-structured composites are
numerically investigated in this paper. To this aim, an interface constitutive law is proposed to
describe both decohesion and contact at bi-material interfaces. These formulations are
implemented in the FE code FEAP. Then, by applying dimensional analysis (Carpinteri, 1989),
the nondimensional parameters governing the macroscopic response of the composite are
identified. According to this model, transverse debonding with respect to the fiber/particle
direction is simulated and the transition from snap-back instability in case of coarse inclusion
diameters to a stable mechanical response for finer reinforcement is quantified. These results
provide a possible quantitative explanation to the role played by the size of the reinforcement on
the instability phenomena experimentally observed during superplastic deformation.Marco Paggimarco.paggi@imtlucca.itGiorgio ZavariseAlberto Carpinteri2013-11-22T10:24:43Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1929This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19292013-11-22T10:24:43ZAcoustic emission monitoring and numerical modelling of a FRP-strengthened concrete structureAlberto CarpinteriGiuseppe LacidognaMarco Paggimarco.paggi@imtlucca.itNicola Pugno2013-11-22T10:10:05Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1928This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19282013-11-22T10:10:05ZInfluence of the intermediate material on the singular stress field in tri-material junctionsAccording to the mathematical formalism of the eigenfunction expansion method, the problem of stress-singularities arising from multi-material junctions is addressed. The wedges are composed of isotropic homogeneous materials and are in a condition of plane stress or strain. The order of the stress-singularity is provided for tri-material junctions, paying special attention to the role played by Mode-I and Mode-II deformation. The effect of cracks inside either the softer or the stiffer material is also investigated. Numerical results can be profitably used for establishing optimum material configurations.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-22T09:59:13Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1927This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19272013-11-22T09:59:13ZTheoretical and numerical investigation on internal instability phenomena in composite materialsInstability phenomena occurring in the microstructure of composite materials are investigated. To this aim, a complete description of the mechanical behavior of bi-material interfaces in composite materials requires the definition of both a cohesive law involving damage for the debonding stage, and a contact model during the closure of the interface. Both formulations are herein presented and implemented in the FE code FEAP. Numerical examples showing the transition from a snap-back instability to a stable mechanical response are presented.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.itGiorgio Zavarise2013-11-22T09:45:24Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1926This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19262013-11-22T09:45:24ZOn the reliability of microscopical contact models In this paper a comparison among several micromechanical contact models is presented. The aim of the research is to provide a degree of confidence about the differences between the predictions of the contact behavior provided by the models. For this purpose some ideal microscopically rough surfaces with self-affine topography have been generated by means of a numerical algorithm. From such surfaces all the parameters needed to characterize them from the statistical viewpoint have been extracted. The predictions provided by the models with increasing normal load for the evolution of the real contact area, the number of contact points and other useful parameters have been outlined with diagrams, clearly showing the existing differences. Giorgio ZavariseMauro Borri BrunettoMarco Paggimarco.paggi@imtlucca.it2013-11-22T09:38:18Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1925This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19252013-11-22T09:38:18ZInterface crack propagation in concrete composites: symptotic analysis of stress-singularitiesAlberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-21T15:17:43Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1924This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19242013-11-21T15:17:43ZInfluence of interface bonding strength on brittle crack propagation in bi-material structural componentsThe influence of the interface bonding strength on brittle crack propagation in bi-material structures is investigated. In this study a crack is set at the vertex of the interface between two joined dissimilar materials. Competition between several possible crack trajectories is endeavoured, paying special attention to the effect of thermo-elastic and residual stresses on crack propagation.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-21T15:03:00Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1923This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19232013-11-21T15:03:00ZInfluence of the intermediate material on the singular stress field in tri-material junctionsAccording to the mathematical formalism of the eigenfunction expansion method, the problem of stress-singularities arising from multi-material junctions is addressed. The wedges are composed of isotropic homogeneous materials and are in a condition of plane stress or strain. The order of the stress-singularity is provided for tri-material junctions, paying special attention to the role played by Mode-I and Mode-II deformation. The effect of cracks inside either the softer or the stiffer material is also investigated. Numerical results can be profitably used for establishing optimum material configurations.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-21T14:56:44Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1922This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19222013-11-21T14:56:44ZTheoretical and numerical investigation on internal instability phenomena in composite materialsInstability phenomena occurring in the microstructure of composite materials are investigated. To this aim, a
complete description of the mechanical behavior of bi-material interfaces in composite materials requires the
definition of both a cohesive law involving damage for the debonding stage, and a contact model during the
closure of the interface. Both formulations are herein presented and implemented in the FE code FEAP.
Numerical examples showing the transition from a snap-back instability to a stable mechanical response are
presented.Alberto CarpinteriMarco Paggimarco.paggi@imtlucca.it2013-11-21T14:33:25Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1921This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19212013-11-21T14:33:25ZPrediction of real contact area for interfacial debonding damage in fibrous composite materialsGiorgio ZavariseMauro Borri BrunettoMarco Paggimarco.paggi@imtlucca.it2013-11-21T13:54:59Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1920This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19202013-11-21T13:54:59ZA comparison of the mechanical behavior of microscopical contact modelsGiorgio ZavariseMauro Borri BrunettoMarco Paggimarco.paggi@imtlucca.it2013-11-19T15:42:35Z2014-10-09T09:20:26Zhttp://eprints.imtlucca.it/id/eprint/1914This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/19142013-11-19T15:42:35ZReliability of Micromechanical Contact Models: a Still Open IssueThe assumption of perfectly flat surfaces within the context of the contact problems constitutes very often an oversimplification of the reality. In fact, when real surfaces are examined more in details, roughness can be found at different scale lengths. This fundamental feature poses enormous difficulties on the mathematical modeling of the physics of the contact problems. Nevertheless, the study of the effect of the multiscale roughness on the contact predictions is crucial from the engineering point of view. To deal with this problem several micromechanical contact models have been developed since the middle of the 19th Century. Such models are based on very different mathematical frameworks, with a consequent lack of standardization. The recent perspective to apply such models to smaller and smaller scale lengths, down to the nanoscale, makes the reliability of these models a still open issue. The basic aim of this chapter is to provide a detailed review of the most popular contact models available in the literature. Moreover we focus one the crucial intent of providing a degree of confidence about the differences between the contact predictions provided by the models. For this purpose a critical comparison of the outcomes of such models by applying them to numerically generated rough surfaces is then proposed.Giorgio ZavariseMarco Paggimarco.paggi@imtlucca.it2013-02-20T10:52:50Z2013-02-20T10:52:50Zhttp://eprints.imtlucca.it/id/eprint/1487This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14872013-02-20T10:52:50ZApproximate Explicit MPC on Simplicial Partitions with Guaranteed Stability for Constrained Linear SystemsThis paper proposes an approximate explicit model predictive control design approach for regulating linear time-invariant systems subject to both state and control constraints. The proposed control law is implemented as a piecewise-affine function defined on a regular simplicial partition, and has two main positive features. First, the regularity of the simplicial partition allows a very efficient implementation of the control law on digital circuits, with computation performed in tens of nanoseconds. Second, the asymptotic stability of the closed-loop system is enforced a priori by design.Matteo RubagottiDavide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.it2013-02-20T10:41:16Z2013-02-20T10:41:16Zhttp://eprints.imtlucca.it/id/eprint/1486This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14862013-02-20T10:41:16ZSimple and Certifiable Quadratic Programming Algorithms for Embedded Linear Model Predictive ControlIn this paper we review a dual fast gradient-projection approach to solving quadratic programming (QP) problems recently proposed in [Patrinos and Bemporad, 2012] that is particularly useful for embedded model predictive control (MPC) of linear systems subject to linear constraints on inputs and states. We show that the method has a computational effort aligned with several other existing QP solvers typically used in MPC, and in addition it is extremely easy to code, requires only basic and easily parallelizable arithmetic operations, and a number of iterations to reach a given accuracy in terms of optimality and feasibility of the primal solution that can be estimated quite tightly by solving an off-line mixed-integer linear programming problem. This research was largely motivated by ongoing research activities on embedded MPC for aerospace systems carried out in collaboration with the European Space Agency.Alberto Bemporadalberto.bemporad@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.it2013-02-20T10:24:10Z2014-07-01T12:51:19Zhttp://eprints.imtlucca.it/id/eprint/1485This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14852013-02-20T10:24:10ZA numerical algorithm for nonlinear L2-gain optimal control with application to vehicle yaw stability controlThis paper is concerned with L2-gain optimal control approach for coordinating the active front steering and differential braking to improve vehicle yaw stability and cornering control. The vehicle dynamics with respect to the tire slip angles is formulated and disturbances are added on the front and rear cornering forces characteristics modelling, for instance, variability on road friction. The mathematical model results in input-affine nonlinear system. A numerical algorithm based on conjugate gradient method to solve L2-gain optimal control problem is presented. The proposed algorithm, which has backward-in-time structure, directly finds the feedback control and the "worst case" disturbance variables. Simulations of the controller in closed-loop with the nonlinear vehicle model are shown and discussed.Vladimir MilicStefano Di CairanoJosip KasacAlberto Bemporadalberto.bemporad@imtlucca.itZeljko Situm2013-02-14T10:04:07Z2013-03-12T14:57:38Zhttp://eprints.imtlucca.it/id/eprint/1480This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14802013-02-14T10:04:07ZModel Predictive Control for Linear Impulsive SystemsLinear Impulsive Control Systems have been extensively studied with respect to their equilibrium points which, in most cases, are no other than the origin. However, the trajectory of the system cannot be stabilized to arbitrary desired points which imposes a significant restriction towards their utilization in various applications such as drug administration. In this paper, we study the equilibrium of Linear Impulsive Systems in light of target-sets instead of the standard equilibrium point approach. We properly extend the notion of invariant sets which is crucial in designing asymptotically stable Model Predictive Controllers (MPC).Pantelis Sopasakispantelis.sopasakis@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos SarimveisAlberto Bemporadalberto.bemporad@imtlucca.it2013-02-13T07:50:17Z2013-02-13T07:50:17Zhttp://eprints.imtlucca.it/id/eprint/1473This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14732013-02-13T07:50:17ZThe rendezvous dynamics under linear quadratic optimal controlThis paper investigates the dynamics of networks of systems achieving rendezvous under linear quadratic optimal control. While the dynamics of rendezvous were studied extensively for the symmetric case, where all systems have exactly the same dynamics (such as simple integrators), this paper investigates the rendezvous dynamics for the general case when the dynamics of the systems may be different. We show that the rendezvous is stable and that the post-rendezvous dynamics of the network of systems is entirely defined by the common eigenvalues with common eigenvectors output image. The approach is also extended to the case of constraints on systems states, inputs, and outputs.Stefano Di CairanoCarlo A. PascucciAlberto Bemporadalberto.bemporad@imtlucca.it2013-02-13T07:46:55Z2013-02-13T07:46:55Zhttp://eprints.imtlucca.it/id/eprint/1472This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14722013-02-13T07:46:55ZStability analysis of discrete-time piecewise-affine systems over non-invariant domainsThis paper analyzes stability of discrete-time piecewise-affine systems defined on non-invariant domains. An algorithm based on linear programming is proposed, in order to prove the exponential stability of the origin and to find a positively invariant estimate of the region of attraction. The theoretical results are based on the definition of a piecewise-affine, possibly discontinuous, Lyapunov function. The proposed method presents a relatively low computational burden, and is proven to lead to feasible solutions in a broader range of cases with respect to a previously proposed approach.Matteo RubagottiLuca ZaccarianAlberto Bemporadalberto.bemporad@imtlucca.it2013-02-12T12:11:05Z2013-02-12T12:11:05Zhttp://eprints.imtlucca.it/id/eprint/1471This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14712013-02-12T12:11:05ZPiecewise affine direct virtual sensors with Reduced ComplexityIn this paper, a piecewise-affine direct virtual sensor is proposed for the estimation of unmeasured outputs of nonlinear systems whose dynamical model is unknown. In order to overcome the lack of a model, the virtual sensor is designed directly from measured inputs and outputs. The proposed approach generalizes a previous contribution, allowing one to design lower-complexity estimators. Indeed, the reduced-complexity approach strongly reduces the effect of the so-called "curse of dimensionality", and can be applied to relatively high-order systems, while enjoying all the convergence and optimality properties of the original approach.Matteo RubagottiTomaso PoggiAlberto Bemporadalberto.bemporad@imtlucca.itMarco Storace2013-02-12T12:03:40Z2013-02-12T12:03:40Zhttp://eprints.imtlucca.it/id/eprint/1470This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14702013-02-12T12:03:40ZAn accelerated dual gradient-projection algorithm for linear model predictive controlThis paper proposes a dual fast gradient-projection method for solving quadratic programming problems that arise in linear model predictive control with general polyhedral constraints on inputs and states. The proposed algorithm is quite suitable for embedded control applications in that: (1) it is extremely simple and easy to code; (2) the number of iterations to reach a given accuracy in terms of optimality and feasibility of the primal solution can be estimated quite tightly; (3) the computational cost per iteration increases only linearly with the prediction horizon; and (4) the algorithm is also applicable to linear time-varying (LTV) model predictive control problems, with an extra on-line computational effort that is still linear with the prediction horizon.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2012-11-30T08:27:56Z2012-11-30T08:27:56Zhttp://eprints.imtlucca.it/id/eprint/1439This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14392012-11-30T08:27:56ZSimulation-Optimization in Modeling Ionic Polymer-Metal Composites ActuatorsThe increasing pressure on the development time of new materials and devices has changed the modelling and design process over the years. In the past, they mainly consisted of experimentation and physical prototyping. Clearly, it is hard to incorporate changes in finished prototypes, while producing a variety of different prototypes at once may be very expensive. To this aim, computer simulation models such as circuit design models and continuous system simulation models are widely used in engineering modelling, design and analysis. The studies towards a better understanding of complex systems require quantitative model development, making optimisation and experimental data fitting tools indispensable. In this framework, the modelling of ionic polymer-metal composites (IPMCs) is studied. In particular, this paper deals with simulation-optimisation issues arising in the model calibration of a particular IPMC-based actuator in air. We consider a non-linear dynamical model of the device, with lumped parameters, able to estimate the IPMC actuator absorbed current, together with the mechanical quantities of interest, which, in the case under study, are the free deflection and/or the blocked force. Two optimisation problems have been formulated, focusing on different stages of the model parameters identification. The strategies adopted to solve the problems allow to achieve some promising - although preliminary - results.Gabriella Dellinogabriella.dellino@imtlucca.itPaolo LinoCarlo MeloniAlessandro RizzoClaudia BonomoLuigi FortunaPietro GiannoneSalvatore Graziani2012-10-15T08:09:17Z2012-10-15T08:09:17Zhttp://eprints.imtlucca.it/id/eprint/1401This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/14012012-10-15T08:09:17ZMOBY-DIC: A MATLAB Toolbox for Circuit-Oriented Design of Explicit MPCThis paper describes a MATLAB Toolbox for the integrated design of Model Predictive Control (MPC) state-feedback control laws and the digital circuits implementing
them. Explicit MPC laws can be designed using optimal and sub-optimal formulations, directly taking into account the specifications of the digital circuit implementing the control law (such as latency and size), together with the usual control specifications (stability, performance,
constraint satisfaction). Tools for a-posteriori stability analysis of the closed-loop system, and for the simulation of the circuit in Simulink, are also included in the toolbox.Alberto OliveriDavide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.itBart GenuitW.P.M.H. HeemelsTomaso PoggiMatteo RubagottiMarco Storace2012-10-04T08:28:37Z2012-10-04T08:28:37Zhttp://eprints.imtlucca.it/id/eprint/1387This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/13872012-10-04T08:28:37ZModel predictive control applications for planetary roversModel Predictive Control (MPC) is a well-known method for control of processes with low or moderate dynamics as found in power or chemical plants. Within space applications the typical domain of MPC is spacecraft attitude and orbit control. MPC for control of planetary rovers is a quite new technology and was recently investigated in the frame of the RobMPC project, under ESA contract. In this context the Robust-MPC approach was applied to three layers of the rover
control hierarchy dealing with medium to high dynamics control tasks: 1) guidance, 2) trajectory control and 3) wheel traction and steering control. The selected reference rover is ESA’s four-wheel EGP rover with rear axle steering and a mass of approximately 800 kg. The MPC control design flow is based on the MPCSofT Toolbox for MATLAB, a novel toolbox developed within the RobMPC project. The MPCSofT toolbox provides an environment for design and simulation of
MPC controllers, based on a quite general class of linear
time-varying models, constraints, and quadratic costs, possibly equipped with integral action to increase robustness. As MPC prediction models are easily specified by the user in Embedded MATLAB code, Ccode can be automatically generated within the MATLAB/Simulink environment for immediate rapid prototyping. The highest control level is shared between the nominal path planner (computed offline) and the MPC guidance function. When the rover slips outside the safety corridor around the nominal path, the guidance function continuously builds obstacle-free optimal contingency paths to bring back the vehicle to the nominal path, without the need of stopping the rover to compute a new nominal path. The LTV model included in the MPC optimization engine is used to reconstruct the guidance path from the computed optimal sequence of actions. The MPC trajectory control acts on the velocity vector of the vehicle in order to keep the vehicle within the nominal (guidance) path. This level takes into account the non-holonomic characteristics of the rover and
implements a kinematic LTV model of the vehicle. The lowest MPC level is dedicated to traction and steering The highest control level is shared between the nominal path planner (computed offline) and the MPC guidance function. When the rover slips outside the safety corridor around the nominal path, the guidance function continuously builds obstacle-free optimal contingency paths to bring back the vehicle to the nominal path, without the need of stopping the rover to compute a new nominal path. The LTV model included in the MPC optimization engine is used to reconstruct the guidance path from the computed optimal sequence of actions. The MPC trajectory control acts on the velocity vector of the vehicle in order to keep the vehicle within the nominal (guidance) path. This level takes into account the non-holonomic characteristics of the rover and
implements a kinematic LTV model of the vehicle. The lowest MPC level is dedicated to traction and steering control. This layer is controlling the steering angle and wheel velocity coordination and replaces typically the Ackermann control. Here, the MPC solution is based on a multi-body system model of the rover including the wheel-soil interaction dynamics. It is implemented as a stepwise LTI class problem with corresponding online linearization of the model. The paper will introduce the architecture of the entire control hierarchy together with selected details of the MPC specific implementation. The performance and
robustness analyses are presented based on results of
comprehensive Monte Carlo simulations. A profiling of
the code will give an outlook regarding readiness state
in terms of controller implementation on space qualified
computer hardware.Giovanni BinetRainer KrennAlberto Bemporadalberto.bemporad@imtlucca.it2012-04-26T10:50:14Z2012-07-06T12:20:13Zhttp://eprints.imtlucca.it/id/eprint/1264This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12642012-04-26T10:50:14ZAssessment of non-centralised model predictive control techniques for electrical power networks Model predictive control (MPC) is one of the few advanced control methodologies that have proven to be very successful in real-life applications. An attractive feature of MPC is its capability of explicitly taking state and input constraints into account. Recently, there has been an increasing interest in the usage of MPC schemes to control electrical power networks. The major obstacle for implementation lies in the large scale of these systems, which is prohibitive for a centralised approach. In this article, we therefore assess and compare the suitability of several non-centralised predictive control schemes for power balancing, to provide valuable insights that can contribute to the successful implementation of non-centralised MPC in the real-life electrical power system. Ralph M. HermansAndrej JokicMircea LazarAlessandro AlessioPaul Van den boschIan HiskensAlberto Bemporadalberto.bemporad@imtlucca.it2012-04-04T09:31:53Z2012-04-04T09:31:53Zhttp://eprints.imtlucca.it/id/eprint/1257This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12572012-04-04T09:31:53ZSynthesis of low-complexity stabilizing piecewise affine controllers: a control-Lyapunov function approachExplicit model predictive controllers computed exactly by multi-parametric optimization techniques often lead to piecewise affine (PWA) state feedback controllers with highly complex and irregular partitionings of the feasible set. In many cases complexity prohibits the implementation of the resulting MPC control law for fast or large-scale system. This paper presents a new approach to synthesize low-complexity PWA controllers on regular partitionings that enhance fast on-line implementation with low memory requirements. Based on a PWA control-Lyapunov function, which can be obtained as the optimal cost for a constrained linear system corresponding to a stabilizing MPC setup, the synthesis procedure for the low-complexity control law boils down to local linear programming (LP) feasibility problems, which guarantee stability, constraint satisfaction, and certain performance requirements. Initially, the PWA controllers are computed on a fixed regular partitioning. However, we also present an automatic refinement procedure to refine the partitioning where necessary in order to satisfy the design specifications. A numerical example show the effectiveness of the novel approach.Liang LuW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.it2012-03-28T12:48:36Z2012-04-03T07:52:20Zhttp://eprints.imtlucca.it/id/eprint/1250This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12502012-03-28T12:48:36ZMonitoring of human movements for fall detection and activities recognition in elderly care using wWireless sensor network: a surveyStefano Abbatestefano.abbate@alumni.imtlucca.itMarco AvvenutiPaolo CorsiniJanet LightAlessio Vecchio2012-03-28T10:49:35Z2012-04-03T07:50:44Zhttp://eprints.imtlucca.it/id/eprint/1246This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12462012-03-28T10:49:35ZMIMS: A Minimally Invasive Monitoring Sensor PlatformThis paper describes a minimally invasive sensor platform for active and passive monitoring of human movements and physiological signals. Such a system is needed in cases where 24 #x00D7; 7 monitoring is required, as in older adults with cognitive impairment, dementia and Alzheimer's disease. The passive monitoring systems used today are useful only in detecting events after they happen; the accuracy and speed of detection is questionable. The noninvasive nature of such systems does not bring trade off benefits to early detection and prevention of emergency incidents. We compare some existing sensor platforms and present our monitoring approach using minimally invasive wearable sensor device(s). With a Minimally Invasive Monitoring Sensor (MIMS), using advanced intelligent systems, we analyze the physiological signal data preceding potential emergency events in order to predict them quickly. The Virtual Hub is the core component of MIMS, which acts as a gateway between a monitored person and her/his caregivers, as well as a shared access point between active and passive sensing devices. Some preliminary results are presented here from our sleep-related fall study using two heterogeneous sensor systems.Stefano Abbatestefano.abbate@alumni.imtlucca.itMarco AvvenutiJanet Light2012-03-07T10:51:31Z2013-09-30T12:32:32Zhttp://eprints.imtlucca.it/id/eprint/1229This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12292012-03-07T10:51:31ZA sub-optimal second order sliding mode controller for systems with saturating actuatorsIn this technical note, the problem of the possible saturation of the continuous control variable in the sub-optimal second order sliding mode controller, applied to systems with saturating actuators, is addressed. It is proved that during the sliding phase, if basic assumptions are made, the continuous control variable never saturates. On the contrary, during the reaching phase, the presence of saturating actuators can make the steering of the sliding variable to zero in a finite time not always guaranteed. In the present technical note, the original algorithm is modified in order to solve this problem: a new strategy is proposed, which proves to be able to steer the sliding variable to zero in a finite time in spite of the presence of saturating actuators.Antonella FerraraMatteo Rubagotti2012-03-06T15:10:50Z2013-09-30T12:24:26Zhttp://eprints.imtlucca.it/id/eprint/1227This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12272012-03-06T15:10:50ZSliding mode control of a mobile robot for dynamic obstacle
avoidance based on a time-varying harmonic potential fieldIn this paper, a harmonic potential field method for dynamic environments is proposed to generate an on-line reference trajectory for a wheeled mobile robot. A sliding mode controller is used to make the robot move along the prescribed trajectory determined by the gradient lines. The potential field is modified on-line, in order to make the robot avoid the collision with obstacles which move along non a-priori known trajectories with time-varying speed. The mechanism through which the field is modified is based on the so-called ‘collision cone’ concept.Antonella FerraraMatteo Rubagotti2012-03-06T15:01:57Z2013-09-30T12:24:52Zhttp://eprints.imtlucca.it/id/eprint/1226This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12262012-03-06T15:01:57ZGradient tracking based second order sliding mode control
of a wheeled vehicleAntonella FerraraMatteo Rubagotti2012-03-06T14:41:51Z2013-09-30T12:25:11Zhttp://eprints.imtlucca.it/id/eprint/1224This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12242012-03-06T14:41:51ZRobust nonlinear MPC with integral sliding mode for systems with matched disturbancesMatteo RubagottiDavide Martino RaimondoAntonella FerraraLalo Magni2012-03-06T14:31:56Z2013-09-30T12:26:54Zhttp://eprints.imtlucca.it/id/eprint/1223This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12232012-03-06T14:31:56ZA sub-optimal second order sliding mode controller for current-fed induction motorsA second order sliding mode controller for current-fed induction motors is proposed in this paper. The design of the controller is based on a reduced order model of the machine, and the control variables are non-discontinuous currents, obtained integrating a discontinuous auxiliary control signal. The phase voltages are then generated using a current regulated pulse width modulation inverter, while the rotor flux value is obtained by means of a simple observer. The convergence properties of the proposed control strategy are studied in the paper, and verified in simulation.Antonella FerraraMatteo Rubagotti2012-03-06T13:42:41Z2013-09-30T12:26:11Zhttp://eprints.imtlucca.it/id/eprint/1222This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12222012-03-06T13:42:41ZDiagnosis and prognosis of automotive systems: motivations, history and some resultsThis paper presents an overview of diagnostic needs and methodologies in the automotive field. The field of automotive engineering has seen an explosion in the presence of electronic components and systems on-board vehicles since the 1970s. This growth was initially motivated by the introduction of emissions regulations that led to the widespread application of electronic engine controls. A secondary but important consequence of these developments was the adoption of on-board diagnostics regulations aimed at insiring that emission control systems remained functional for a prescribed period of time (or vehicle mileage). In addition, the presence of micro-controllers on-board the vehicle led to a proliferation of functions implemented through electronic systems and related software, related to safety and customer convenience, creating the need for more sophisticated on-board diagnostics. Today, a significant percentage of the software code in an automobile is devoted to diagnostic functions. This paper presents an overview of diagnostic needs and requirements in the automotive industry, illustrates some of the challenges that are associated with satisfying these requirements and proposes some future directions, in particular with respect to prognostics.Giorgio RizzoniSimona OnoriMatteo Rubagotti2012-03-06T13:33:24Z2013-09-30T12:27:16Zhttp://eprints.imtlucca.it/id/eprint/1221This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12212012-03-06T13:33:24ZA dynamic obstacle avoidance strategy for a mobile robot based on sliding mode controlIn this paper, a dynamic obstacle avoidance strategy for mobile robots is proposed. The strategy consists of two key elements: an on-line reference generator and a control scheme to make the robot track the reference signals so as to reach a pre-specified goal point. To generate the online reference signals, a harmonic potential field for dynamic environments is exploited. The potential field is modified on-line, in order to make the robot avoid the collision with obstacles which move along non a-priori known trajectories with timevarying speed. The proposed multi-level sliding mode controller is capable of making the robot move tracking the prescribed reference signals determined by the trajectory generator. The simulation results confirm the good performances of this approach.Antonella FerraraMatteo Rubagotti2012-03-06T13:28:10Z2013-09-30T12:25:32Zhttp://eprints.imtlucca.it/id/eprint/1220This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12202012-03-06T13:28:10ZRobust model predictive control of continuous-time sampled-data nonlinear systems with integral sliding modeA hierarchical Nonlinear Model Predictive Control (NMPC) scheme with guaranteed Input-to-State-practical- Stability (ISpS) is proposed. The controller is formed by an Integral Sliding Mode (ISM) controller and a NMPC one. The ISM, relying on the knowledge of the nominal continuous-time model of the system and of the piecewise constant control signal generated by the NMPC produces a control action aimed at reducing the difference between the dynamics of the nominal closed-loop system and the actual evolution of the state. The NMPC in this way can be designed based on a system with reduced uncertainty. In order to prove the stability of the overall control scheme, some general Regional ISpS results for continuous-time systems are proven.Matteo RubagottiDavide Martino RaimondoAntonella FerraraLalo Magni2012-03-06T13:19:59Z2013-09-30T12:26:33Zhttp://eprints.imtlucca.it/id/eprint/1219This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12192012-03-06T13:19:59ZAutomotive battery prognostics using dual Extended Kalman FilterThis paper proposes a strategy for estimating the remaining useful life of automotive batteries based on dual Extended Kalman Filter. A nonlinear model of the battery is exploited for the on-line estimation of the State of Charge, and this information is used to evaluate the actual capacity and predict its future evolution, from which an estimate of the remaining useful life is obtained with suitable margins of uncertainty. Simulation results using experimental data from lead-acid batteries show the effectiveness of the approachMatteo RubagottiSimona OnoriGiorgio Rizzoni2012-03-06T13:08:24Z2013-09-30T12:28:55Zhttp://eprints.imtlucca.it/id/eprint/1218This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12182012-03-06T13:08:24ZOptimal disturbance rejection via integral sliding mode control for uncertain systems in regular formThis paper considers the problem of using an integral sliding mode strategy to reduce the disturbance terms acting on nonlinear systems in regular form. It is proved that the definition of a suitable sliding manifold and the generation of sliding modes upon it can guarantee the minimization of the disturbance terms. Simulation examples shows the effectiveness of the proposal.Matteo RubagottiAntonio EstradaFernando CastanosAntonella FerraraLeonid Fridman2012-03-06T12:14:28Z2013-09-30T12:28:34Zhttp://eprints.imtlucca.it/id/eprint/1217This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12172012-03-06T12:14:28ZSecond order sliding mode control of a perturbed double integrator with state constraintsThis paper introduces a second order sliding mode controller for double integrators subject to external disturbances and model uncertainties, with both control and state constraints. The proposed control strategy proves to be able to robustly steer the system state to zero in a finite time, fulfilling the state constraints in spite of the uncertainties, provided that the initial state is inside a given region. The effectiveness of the proposal is then tested on a simulation example.Matteo RubagottiAntonella Ferrara2012-03-05T13:49:24Z2013-09-30T12:30:10Zhttp://eprints.imtlucca.it/id/eprint/1213This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12132012-03-05T13:49:24ZSliding mode observers for sensorless control of current-fed induction motorsThis paper presents the use of a higher order sliding mode scheme for sensorless control of induction motors. The second order sub-optimal control law is based on a reduced-order model of the motor, and produces the references for a current regulated PWM inverter. A nonlinear observer structure, based on Lyapunov theory and on different sliding mode techniques (first order, sub-optimal and super-twisting) generates the velocity and rotor flux estimates necessary for the controller, based only on the measurements of phase voltages and currents. The proposed control scheme and observers are tested on an experimental setup, showing a satisfactory performance.Daniele BulloAntonella FerraraMatteo Rubagotti2012-03-05T11:06:43Z2012-04-04T09:21:01Zhttp://eprints.imtlucca.it/id/eprint/1212This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12122012-03-05T11:06:43ZA multi-stage stochastic optimization approach to optimal bidding on energy marketsOne of the most challenging tasks for an energy producer is represented by the optimal bidding on energy markets. Each eligible plant has to submit bids for the spot market one day before the delivery time and bids for the ancillary services provision. Allocating the optimal amount of energy, jointly minimizing the risk and maximizing profits is not a trivial task, since one has to face several sources of stochasticity, such as the high volatility of energy prices and the uncertainty of the production, due to the deregulation and to the growing importance of renewable sources. In this paper the optimal bidding problem is formulated as a multi-stage optimization problem to be solved in a receding horizon fashion, where at each time step a risk measure is minimized in order to obtain optimal quantities to bid on the day ahead market, while reserving the remaining production to the ancillary market. Simulation results show the optimal bid profile for a trading day, based on stochastic models identified from historical data series from the Italian energy market.Laura PugliaDaniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2012-03-05T10:58:40Z2013-02-12T12:12:49Zhttp://eprints.imtlucca.it/id/eprint/1211This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12112012-03-05T10:58:40ZStability and invariance analysis of uncertain PWA systems based on linear programmingThis paper analyzes stability of discrete-time uncertain piecewise-affine systems whose dynamics are defined on a bounded set χ; that is not necessarily invariant. The objective is to prove the uniform asymptotic stability of the origin and to find an invariant domain of attraction. This goal is attained by defining a suitable extended dynamics (which is partially fictitious), and by using a numerical procedure based on linear programming. The theoretical results are based on the definition of a piecewise-affine, possibly discontinuous, Lyapunov function.Sergio TrimboliMatteo RubagottiAlberto Bemporadalberto.bemporad@imtlucca.it2012-03-02T15:42:26Z2013-09-30T12:25:51Zhttp://eprints.imtlucca.it/id/eprint/1209This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12092012-03-02T15:42:26ZA sub-optimal second order sliding mode controller for systems with saturating actuatorsIn this paper, the problem of the possible saturation of the continuous control variable in the sub-optimal second order sliding mode controller applied to relative degree one systems with saturating actuators is addressed. It is proved that during the sliding phase, if basic assumptions are made, the continuous control variable never saturates, while, during the reaching phase, the presence of saturating actuators can make the steering of the sliding variable to zero in finite time not always guaranteed. In the present paper, the original algorithm is modified in order to solve this problem: a new strategy is proposed, which proves to be able to steer the sliding variable to zero in a finite time in spite of the presence of saturating actuators.Antonella FerraraMatteo Rubagotti2012-03-02T15:30:33Z2013-09-30T12:33:14Zhttp://eprints.imtlucca.it/id/eprint/1208This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12082012-03-02T15:30:33ZRobust model predictive control with integral sliding mode in continuous-time sampled-data nonlinear systemsThis paper proposes a control strategy for nonlinear constrained continuous-time uncertain systems which combines robust model predictive control (MPC) with sliding mode control (SMC). In particular, the so-called Integral SMC approach is used to produce a control action aimed to reduce the difference between the nominal predicted dynamics of the closed-loop system and the actual one. In this way, the MPC strategy can be designed on a system with a reduced uncertainty. In order to prove the stability of the overall control scheme, some general regional input-to-state practical stability results for continuous-time systems are proved.Matteo RubagottiDavide Martino RaimondoAntonella FerraraLalo Magni2012-03-02T15:10:30Z2013-09-30T12:37:32Zhttp://eprints.imtlucca.it/id/eprint/1207This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12072012-03-02T15:10:30ZTime-optimal sliding-mode control of a mobile robot in a dynamic environmentIn this study, an original strategy to control a mobile robot in a dynamic environment is presented. The strategy consists of two main elements. The first is the method for the online trajectory generation based on harmonic potential fields, capable of generating velocity and orientation references, which extends classical results on harmonic potential fields for the case of static environments to the case when the presence of a moving obstacle with unknown motion is considered. The second is the design of sliding-mode controllers capable of making the controlled variables of the robot track in a finite minimum time both the velocity and the orientation references.Matteo RubagottiMarco L. Della VedovaAntonella Ferrara2012-03-02T14:47:20Z2013-09-30T12:38:13Zhttp://eprints.imtlucca.it/id/eprint/1205This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12052012-03-02T14:47:20ZHigh-Speed piecewise affine virtual sensorsThis paper proposes piecewise affine (PWA) virtual sensors for the estimation of unmeasured variables of nonlinear systems with unknown dynamics. The estimation functions are designed directly from measured inputs and outputs and have two important features. First, they enjoy convergence and optimality properties, based on classical results on parametric identification. Second, the PWA structure is based on a simplicial partition of the measurement space and allows one to implement very effectively the virtual sensor on a digital circuit. Due to the low cost of the required hardware for the implementation of such a particular structure and to the very high sampling frequencies that can be achieved, the approach is applicable to a wide range of industrial problems.Tomaso PoggiMatteo RubagottiAlberto Bemporadalberto.bemporad@imtlucca.itMarco Storace2012-03-02T14:37:36Z2015-05-12T13:23:25Zhttp://eprints.imtlucca.it/id/eprint/1203This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12032012-03-02T14:37:36ZModeling and control of an airbrake electro-hydraulic smart actuatorIn this paper, an accurate model of an airbrake electro-hydraulic smart actuator is obtained by physical considerations, and then different control strategies (variable-gain proportional control, PT1 control with switching integrator, and second order sub-optimal sliding mode control) are proposed and analyzed. This application is innovative in the avionic field, and is one of the first attempts to realize a fly-by-wire system for airbrakes, oriented to its immediate employment and installation on current aircraft. The project was carried on with the participation of the Italian Ministry of Defense, and was commissioned to MAG, a leading provider of integrated systems and aviation services for aerospace.Matteo RubagottiMarco CarminatiGiampiero ClementeRiccardo GrassettiAntonella Ferrara2012-02-29T16:10:39Z2012-02-29T16:10:39Zhttp://eprints.imtlucca.it/id/eprint/1200This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/12002012-02-29T16:10:39ZModel predictive control with delay compensation for air-to-fuel ratio controlTo meet increasingly stringent emission regulations modern internal combustion engines require highly accurate control of the air-to-fuel ratio. The performance of the conventional air-to-fuel ratio feedback loop is limited by the combustion delay between fuel injection and engine exhaust, and by the transport delay for the exhaust gas to propagate to the air-to-fuel ratio sensor location. The combined delay is variable, since it depends on engine speed and airflow. Drivability, fuel economy and emission requirements result in constraints on the deviations of the air-to-fuel ratio, stored oxygen in the three-way catalyst, and fuel injection. This paper proposes an approach for air-to-fuel ratio control based on Model Predictive Control (MPC). The approach systematically handles both variable time delays and pointwise-in-time constraints. A delay-free model is considered first, which takes into account the dynamic relations between the injected fuel and the air-to-fuel ratio and the dynamics of the oxygen stored in the catalyst. For the delay-free model, the explicit MPC law is computed. Delay compensation is obtained by estimating the delay online from engine operating conditions, and feeding the MPC law with the state predicted ahead over the time interval of the estimated delay. The predicted state is computed by combining measurement filtering with forward iterations of the nonlinear dynamic equations of the model. The achieved performance in tracking the air-to-fuel ratio and the oxygen storage setpoints while enforcing the constraints is demonstrated in simulation using real data profiles. Sergio TrimboliStefano Di CairanoAlberto Bemporadalberto.bemporad@imtlucca.itIlya Kolmanovsky2012-01-09T14:07:35Z2014-07-01T13:34:46Zhttp://eprints.imtlucca.it/id/eprint/1051This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10512012-01-09T14:07:35ZStabilizing model predictive control of stochastic constrained linear systemsThis paper investigates stochastic stabilization procedures based on quadratic and piecewise linear Lyapunov functions for discrete-time linear systems affected by multiplicative disturbances and subject to linear constraints on inputs and states. A stochastic model predictive control (SMPC) design approach is proposed to optimize closed-loop performance while enforcing constraints. Conditions for stochastic convergence and robust constraints fulfillment of the closed-loop system are enforced by solving linear matrix inequality problems off line. Performance is optimized on line using multi-stage stochastic optimization based on enumeration of scenarios, that amounts to solving a quadratic program subject to either quadratic or linear constraints. In the latter case, an explicit form is computable to ease the implementation of the proposed SMPC law. The approach can deal with a very general class of stochastic disturbance processes with discrete probability distribution. The effectiveness of the proposed SMPC formulation is shown on a numerical example and compared to traditional MPC schemes.Daniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2011-12-06T10:51:35Z2011-12-06T10:51:35Zhttp://eprints.imtlucca.it/id/eprint/1035This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10352011-12-06T10:51:35ZAn RBF based neuro-dynamic approach for the control of stochastic dynamic systemsThis paper presents a neuro-dynamic programming methodology for the control of markov decision processes. The proposed method can be considered as a variant of the optimistic policy iteration, where radial basis function (RBF) networks are employed as a compact representation of the cost-to-go function and the ॕ-LSPE is used for policy evaluation. We also emphasize the reformulation of the Bellman equation around the post-decision state in order to circumvent the calculation of the expectation. The proposed algorithm is applied to a retailer-inventory management problem.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2011-12-06T10:39:31Z2011-12-06T10:39:31Zhttp://eprints.imtlucca.it/id/eprint/1034This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10342011-12-06T10:39:31ZAn explicit optimal control approach for mean-risk dynamic portfolio allocationPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2011-12-06T10:31:11Z2011-12-06T10:31:11Zhttp://eprints.imtlucca.it/id/eprint/1033This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10332011-12-06T10:31:11ZRobust optimal control: calculation of the explicit
control law combining dynamic programming and multiparametric optimizationPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2011-12-06T10:15:20Z2013-03-12T14:57:39Zhttp://eprints.imtlucca.it/id/eprint/1032This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10322011-12-06T10:15:20ZExplicit control for nonlinear constrained systems combining fuzzy model predictive control and multiparametric
programmingPantelis Sopasakispantelis.sopasakis@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos Sarimveis2011-12-05T15:49:54Z2013-03-12T14:57:38Zhttp://eprints.imtlucca.it/id/eprint/1031This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10312011-12-05T15:49:54ZPhysiologically based pharmacokinetic modeling and predictive control: an integrated approach for optimal drug administrationThe barriers between systems engineering and medicine are slowly eroding as recently it has become evident that medicine has a lot to gain from systems technology. In particular, the drug administration problem can be cast as a control engineering problem, where the objective is to keep the drug concentration at certain organs in the body close to desired set-points. A number of constraints render the problem rather challenging. For example, hard constraints may be posed on drug concentration, because if it exceeds an upper limit, the effects of the drug are adverse and toxic.
In this paper we show that a popular method in control engineering can be used for determining the optimal drug administration. Specifically, the Model Predictive Control (MPC) technology can be adopted for taking optimal decisions regarding regulation of drug concentration in the human body, while posing constraints on both drug concentration and drug infusion rate.Pantelis Sopasakispantelis.sopasakis@imtlucca.itPanagiotis Patrinospanagiotis.patrinos@imtlucca.itStefania GiannikouHaralambos Sarimveis2011-12-05T14:19:43Z2013-03-12T14:57:38Zhttp://eprints.imtlucca.it/id/eprint/1030This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10302011-12-05T14:19:43ZStochastic model predictive control for constrained networked control systems with random time delayIn this paper the continuous time stochastic constrained optimal control problem is formulated for the class of networked control systems assuming that time delays follow a discrete-time, finite Markov chain . Polytopic overapproximations of the system's trajectories are employed to produce a polyhedral inner approximation of the non-convex constraint set resulting from imposing the constraints in continuous time. The problem is cast in a Markov jump linear systems (MJLS) framework and a stochastic MPC controller is calculated explicitly, oine, coupling dynamic programming with parametric piecewise quadratic (PWQ) optimization. The calculated control law leads to stochastic stability of the closed loop system, in the mean square sense and respects the state and input constraints in continuous time.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itPantelis Sopasakispantelis.sopasakis@imtlucca.itHaralambos Sarimveis2011-12-05T11:00:57Z2011-12-05T11:00:57Zhttp://eprints.imtlucca.it/id/eprint/1025This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10252011-12-05T11:00:57ZDynamic modeling and control of supply chain systems: a reviewSupply chains are complicated dynamical systems triggered by customer demands. Proper selection of equipment, machinery, buildings and transportation fleets is a key component for the success of such systems. However, efficiency of supply chains mostly depends on management decisions, which are often based on intuition and experience. Due to the increasing complexity of supply chain systems (which is the result of changes in customer preferences, the globalization of the economy and the stringy competition among companies), these decisions are often far from optimum. Another factor that causes difficulties in decision making is that different stages in supply chains are often supervised by different groups of people with different managing philosophies. From the early 1950s it became evident that a rigorous framework for analyzing the dynamics of supply chains and taking proper decisions could improve substantially the performance of the systems. Due to the resemblance of supply chains to engineering dynamical systems, control theory has provided a solid background for building such a framework. During the last half century many mathematical tools emerging from the control literature have been applied to the supply chain management problem. These tools vary from classical transfer function analysis to highly sophisticated control methodologies, such as model predictive control (MPC) and neuro-dynamic programming. The aim of this paper is to provide a review of this effort. The reader will find representative references of many alternative control philosophies and identify the advantages, weaknesses and complexities of each one. The bottom line of this review is that a joint co-operation between control experts and supply chain managers has the potential to introduce more realism to the dynamical models and develop improved supply chain management policies.Haralambos SarimveisPanagiotis Patrinospanagiotis.patrinos@imtlucca.itChris D. TarantilisChris T. Kiranoudis2011-12-05T09:47:20Z2013-03-12T14:57:38Zhttp://eprints.imtlucca.it/id/eprint/1022This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10222011-12-05T09:47:20ZA global piecewise smooth Newton method for fast large-scale model predictive controlIn this paper, the strictly convex quadratic program (QP) arising in model predictive control (MPC) for constrained linear systems is reformulated as a system of piecewise affine equations. A regularized piecewise smooth Newton method with exact line search on a convex, differentiable, piecewise-quadratic merit function is proposed for the solution of the reformulated problem. The algorithm has considerable merits when applied to MPC over standard active set or interior point algorithms. Its performance is tested and compared against state-of-the-art QP solvers on a series of benchmark problems. The proposed algorithm is orders of magnitudes faster, especially for large-scale problems and long horizons. For example, for the challenging crude distillation unit model of Pannocchia, Rawlings, and Wright (2007) with 252 states, 32 inputs, and 90 outputs, the average running time of the proposed approach is 1.57 ms.Panagiotis Patrinospanagiotis.patrinos@imtlucca.itHaralambos SarimveisPantelis Sopasakispantelis.sopasakis@imtlucca.it2011-11-18T14:02:09Z2014-07-01T14:45:43Zhttp://eprints.imtlucca.it/id/eprint/1009This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/10092011-11-18T14:02:09ZOptimization-based AFC automatic flatness control in cold tandem rolling : an integrated flatness optimization approach for the whole tandem millCold tandem mills have the purpose of reducing the thickness of flat steel by means of consecutive rolling stands.This type of process is widely deployed in order to supply a wide variety of industries, from food processing to automotive manufacturing.In the recent years, the production of steel (and other metals, like copper and alluminium as well) by cold rolling has been subject of research efforts to reach ultra-thin gauges and to advance the production performance together with the quality of the material.Alberto Bemporadalberto.bemporad@imtlucca.itDaniele Bernardinidaniele.bernardini@imtlucca.itAndrea SpinelliFrancesco Alessandro Cuzzola2011-08-03T13:33:34Z2012-03-05T10:25:09Zhttp://eprints.imtlucca.it/id/eprint/766This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7662011-08-03T13:33:34ZAppliance operation scheduling for electricity consumption optimizationThis paper concerns the problem of optimally scheduling a set of appliances at the end-user premises. The user's energy fee varies over time, and moreover, in the context of smart grids, the user may receive a reward from an energy aggregator if he/she reduces consumption during certain time intervals. In a household, the problem is to decide when to schedule the operation of the appliances, in order to meet a number of goals, namely overall costs, climatic comfort level and timeliness. We devise a model accounting for a typical household user, and present computational results showing that it can be efficiently solved in real-life instances.Alessandro AgnetisGabriella Dellinogabriella.dellino@imtlucca.itPaolo DettiGianluca De PascaleGiacomo InnocentiAntonio Vicino2011-08-03T10:42:23Z2011-08-04T07:30:21Zhttp://eprints.imtlucca.it/id/eprint/764This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7642011-08-03T10:42:23ZModeling and simulation study for the design of controlled IPMC actuatorsGabriella Dellinogabriella.dellino@imtlucca.itPaolo LinoCarlo MeloniAlessandro RizzoPaolo Di GiambernardinoAndrea Usai2011-08-02T10:15:15Z2011-08-08T08:41:01Zhttp://eprints.imtlucca.it/id/eprint/762This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7622011-08-02T10:15:15ZOptimization issues in modeling IPMC devicesClaudia BonomoGabriella Dellinogabriella.dellino@imtlucca.itLuigi FortunaPietro GiannoneSalvatore GrazianiPaolo LinoCarlo MeloniAlessandro Rizzo2011-07-29T10:53:35Z2012-07-09T09:26:08Zhttp://eprints.imtlucca.it/id/eprint/744This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7442011-07-29T10:53:35ZDecentralized hierarchical multi-rate control of constrained linear systemsThis paper proposes a decentralized hierarchical multi-rate control scheme for large-scale dynamically-coupled linear systems subject to linear constraints on input and state variables. At the lower level, a set of decentralized and independent linear controllers stabilizes the process, without taking care of the constraints. Each controller receives reference signals from its own upper-level controller, that runs at a lower sampling frequency. By optimally constraining the magnitude and rate of variation of the reference signals to each lower-level controller, quantitative criteria are provided for selecting the ratio between the sampling rates of the upper and lower layers of control at each location, in a way that closed-loop stability is preserved and the fulfillment of the prescribed constraints is guaranteed.Alberto Bemporadalberto.bemporad@imtlucca.itDavide BarcelliGiulio Ripaccioli2011-07-29T10:53:22Z2012-07-06T13:14:36Zhttp://eprints.imtlucca.it/id/eprint/742This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7422011-07-29T10:53:22ZExplicit hybrid model predictive control: discontinuous piecewise-affine approximation and FPGA implementationIn this paper we introduce a digital architecture implementing the explicit solution of a switched model predictive control problem. Given a mixed-logic dynamical system, we derive an explicit controller in the form of a possibly discontinuous piecewise-affine function. This function is then approximated by resorting to piecewise-affine simplicial functions, which can be implemented on a circuit by extending the representation capabilities of a previously proposed architecture to evaluate the control action. The architecture has been implemented on FPGA and validated on a benchmark example related to an air conditioning system.Tomaso PoggiSergio TrimboliAlberto Bemporadalberto.bemporad@imtlucca.itMarco Storace2011-07-29T10:53:06Z2012-07-09T09:32:53Zhttp://eprints.imtlucca.it/id/eprint/741This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7412011-07-29T10:53:06ZHybrid dynamic optimization for cruise speeed controlThe cruise control problem of transferring the speed of a vehicle between two values in a fixed interval of time using a predefined sequence of gears is solved in this paper. This is a hybrid dynamic optimization problem since the control variables include both a continuous variable (fuel flow) and a discrete variable (the gear to apply at each instant). The solution is given in the form of a hybrid optimal control algorithm that computes the optimal switching times between gears using Dynamic Programming and the optimal fuel profile between successive gear boundaries using a gradient algorithm to approximate the optimum conditions. In order to reduce the search of the optimal switching times to a search in a finite dimension graph, a procedure based on a changing grid is used. The algorithm is illustrated by a simulation using a diesel one-dimensional car model.Tiago JorgeJoao M. LemosMiguel BarãoAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-29T10:52:58Z2013-09-30T12:29:47Zhttp://eprints.imtlucca.it/id/eprint/740This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7402011-07-29T10:52:58ZStability and invariance analysis of approximate explicit MPC based on PWA Lyapunov functionsFor piecewise affine (PWA) systems whose dynamics are only defined in a bounded and possibly non-invariant set X, this paper proposes a numerical approach to analyze the stability of the origin and to find a region of attraction. The approach relies on introducing fake dynamics outside X and on synthesizing a piecewise affine and possibly discontinuous Lyapunov function on a larger bounded set containing X by solving a linear program. The existence of a solution proves that the origin is an asymptotically stable equilibrium of the original PWA system and determines a region of attraction contained in X. The procedure is particularly useful in practical applications for analyzing a posteriori the stability properties of approximate explicit model predictive control laws defined over a bounded set X of states, and to determine whether, for a given set of initial states, the closed-loop system evolves within the domain X where the control law is defined.Matteo RubagottiSergio TrimboliDaniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-29T10:52:50Z2011-08-04T07:29:05Zhttp://eprints.imtlucca.it/id/eprint/739This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7392011-07-29T10:52:50ZScenario-based stochastic model predictive control for dynamic option hedgingFor a rather broad class of financial options, this paper proposes a stochastic model predictive control (SMPC) approach for dynamically hedging a portfolio of underlying assets. By employing an option pricing engine to estimate future realizations of option prices on a finite set of one-step-ahead scenarios, the resulting stochastic optimization problem is easily solved as a least-squares problem at each trading date with as many variables as the number of traded assets and as many constraints as the number of predicted scenarios. After formulating the dynamic hedging problem as a stochastic control problem, we test its ability to replicate the payoff at expiration date for plain vanilla and exotic options. We show not only that relatively small hedging errors are obtained in spite of price realizations, but also that the approach is robust with respect to market modeling errors.Alberto Bemporadalberto.bemporad@imtlucca.itTommaso GabbrielliniLaura PugliaLeonardo Bellucci2011-07-29T10:52:30Z2011-08-05T12:20:39Zhttp://eprints.imtlucca.it/id/eprint/736This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7362011-07-29T10:52:30ZHierarchical multi-rate control design for constrained linear systemsThis paper proposes a hierarchical multi-rate control design approach to linear systems subject to linear constraints on input and output variables. At the lower level, a linear controller stabilizes the open-loop process without considering the constraints. A higher-level controller commands reference signals at a lower sampling frequency so as to enforce linear constraints on the variables of the process. By optimally constraining the magnitude and the rate of variation of the reference signals applied to the lower control layer, we provide quantitative criteria for selecting the ratio between the sampling rates of the upper and lower layers to preserve closed-loop stability without violating the prescribed constraints.Davide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.itGiulio Ripaccioli2011-07-29T10:49:00Z2011-08-04T07:29:05Zhttp://eprints.imtlucca.it/id/eprint/737This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7372011-07-29T10:49:00ZSynthesis of stabilizing model predictive controllers via canonical piecewise affine approximationsThis paper proposes the use of canonical piecewise affine (PWA) functions for the approximation of linear MPC controllers over a regular simplicial partition of a given set of states of interest. Analysis tools based on the construction of PWA Lyapunov functions are provided for certifying the asymptotic stability of the resulting closed-loop system. The main advantage of the proposed controller synthesis approach is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds.Alberto Bemporadalberto.bemporad@imtlucca.itAlberto OliveriTomaso PoggiMarco Storace2011-07-29T10:18:42Z2011-11-17T11:05:36Zhttp://eprints.imtlucca.it/id/eprint/735This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7352011-07-29T10:18:42ZSynthesis of networked switching linear decentralized controllersThis paper proposes an approach based on linear matrix inequalities for synthesizing a set of decentralized regulators for discrete-time linear systems subject to input and state constraints. Measurements and command signals are exchanged over a sensor/actuator network, in which some links are subject to packet dropout. The resulting closed-loop system is guaranteed to asymptotically reach the origin, even if every local actuator can exploit only a (possibly time-varying) subset of state measurements. A model of packet dropout based on a finite-state Markov chain is also considered to exploit available knowledge about the stochastic nature of the network. For such model, a set of decentralized switching linear controllers is synthesized that guarantees mean-square stability of the overall controlled process under packet dropout and soft input and state constraints.Davide BarcelliDaniele Bernardinidaniele.bernardini@imtlucca.itAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-29T10:18:25Z2011-11-16T11:50:12Zhttp://eprints.imtlucca.it/id/eprint/734This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7342011-07-29T10:18:25ZA model predictive control approach for stochastic networked control systemsIn this paper we present a stochastic model predictive control (SMPC) approach for networked control systems (NCSs) that are subject to time-varying sampling intervals and time-varying transmission delays. These network-induced uncertain parameters are assumed to be described by random processes, having a bounded support and an arbitrary continuous probability density function. Assuming that the controlled plant can be modeled as a linear system, we present a SMPC formulation based on scenario enumeration and quadratic programming that optimizes a stochastic performance index and provides closed-loop stability in the mean-square sense. Simulation results are shown to demonstrate the performance of the proposed approach.Daniele Bernardinidaniele.bernardini@imtlucca.itM.C.F. DonkersAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. Heemels2011-07-29T10:18:09Z2011-08-05T12:30:43Zhttp://eprints.imtlucca.it/id/eprint/733This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7332011-07-29T10:18:09ZDecentralized model predictive control of drinking water networks using an automatic subsystem decomposition approachThis paper proposes an automatic model decomposition approach for decentralized model predictive control (DMPC) of drinking water networks (DWNs). For a given DWN, the proposed algorithm partitions the network in a set of subnetworks by taking advantage of the topology of the network, of the information about the use of actuators, and of system management heuristics. The derived suboptimal DMPC strategy results in a hierarchical solution with a set of MPC controllers used for each partition. A comparative study between centralized MPC (CMPC) and DMPC approaches is described for the considered case study, which consists of an aggregate version of the Barcelona DWN. Results on several simulation scenarios show the effectiveness of the proposed DMPC approach in terms of the reduced computation burden and, at the same time, of the admissible lost of performance.Davide BarcelliCarlos Ocampo-MartinezVincenç Puig CayuelaAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-28T10:49:45Z2014-07-02T14:14:52Zhttp://eprints.imtlucca.it/id/eprint/731This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7312011-07-28T10:49:45ZDecentralized model predictive control Decentralized and distributed model predictive control (DMPC) addresses the problem of controlling a multivariable dynamical process, composed by several interacting subsystems and subject to constraints, in a computation and communication efficient way. Compared to a centralized MPC setup, where a global optimal control problem must be solved on-line with respect to all actuator commands given the entire set of states, in DMPC the control problem is divided into a set of local MPCs of smaller size, that cooperate by communicating each other a certain information set, such as local state measurements, local decisions, optimal local predictions. Each controller is based on a partial (local) model of the overall dynamics, possibly neglecting existing dynamical interactions. The global performance objective is suitably mapped into a local objective for each of the local MPC problems.
This chapter surveys some of the main contributions to DMPC, with an emphasis on a method developed by the authors, by illustrating the ideas on motivating examples. Some novel ideas to address the problem of hierarchical MPC design are also included in the chapter.
Alberto Bemporadalberto.bemporad@imtlucca.itDavide Barcelli2011-07-28T09:52:57Z2012-04-03T07:18:16Zhttp://eprints.imtlucca.it/id/eprint/729This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7292011-07-28T09:52:57ZModel predictive idle speed control: design, analysis, and experimental evaluationIdle speed control is a landmark application of feedback control in automotive vehicles that continues to be of significant interest to automotive industry practitioners, since improved idle performance and robustness translate into better fuel economy, emissions and drivability. In this paper, we develop a model predictive control (MPC) strategy for regulating the engine speed to the idle speed set-point by actuating the electronic throttle and the spark timing. The MPC controller coordinates the two actuators according to a specified cost function, while explicitly taking into account constraints on the control and requirements on the acceptable engine speed range, e.g., to avoid engine stalls. Following a process proposed here for the implementation of MPC in automotive applications, an MPC controller is obtained with excellent performance and robustness as demonstrated in actual vehicle tests. In particular, the MPC controller performs better than an existing baseline controller in the vehicle, is robust to changes in operating conditions, and to different types of disturbances. It is also shown that the MPC computational complexity is well within the capability of production electronic control unit and that the improved performance achieved by the MPC controller can translate into fuel economy improvements.Stefano Di CairanoDiana YanakievAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat2011-07-28T09:52:43Z2011-08-04T07:29:05Zhttp://eprints.imtlucca.it/id/eprint/728This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7282011-07-28T09:52:43ZModel-predictive control of discrete hybrid stochastic automataThis paper focuses on optimal and receding horizon control of a class of hybrid dynamical systems, called Discrete Hybrid Stochastic Automata (DHSA), whose discrete-state transitions depend on both deterministic and stochastic events. A finite-time optimal control approach “optimistically”; determines the trajectory that provides the best tradeoff between tracking performance and the probability of the trajectory to actually execute, under possible chance constraints. The approach is also robustified, less optimistically, to ensure that the system satisfies a set of constraints for all possible realizations of the stochastic events, or alternatively for those having enough probability to realize. Sufficient conditions for asymptotic convergence in probability are given for the receding-horizon implementation of the optimal control solution. The effectiveness of the suggested stochastic hybrid control techniques is shown on a case study in supply chain management.Alberto Bemporadalberto.bemporad@imtlucca.itStefano Di Cairano2011-07-28T09:52:00Z2012-07-06T12:30:20Zhttp://eprints.imtlucca.it/id/eprint/730This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7302011-07-28T09:52:00ZUltra-fast stabilizing model predictive control via canonical piecewise affine approximationsThis paper investigates the use of canonical piecewise affine (PWA) functions for approximation and fast implementation of linear MPC controllers. The control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest. The stability properties of the resulting closed-loop system are analyzed by constructing a suitable PWA Lyapunov function. The main advantage of the proposed approach to the implementation of MPC controllers is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds.Alberto Bemporadalberto.bemporad@imtlucca.itAlberto OliveriTomaso PoggiMarco Storace2011-07-27T12:51:25Z2011-08-05T11:12:37Zhttp://eprints.imtlucca.it/id/eprint/725This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/7252011-07-27T12:51:25ZDecentralized model predictive control of dynamically coupled linear systemsThis paper proposes a decentralized model predictive control (DMPC) scheme for large-scale dynamical processes subject to input constraints. The global model of the process is approximated as the decomposition of several (possibly overlapping) smaller models used for local predictions. The degree of decoupling among submodels represents a tuning knob of the approach: the less coupled are the submodels, the lighter the computational burden and the load for transmission of shared information; but the smaller is the degree of cooperativeness of the decentralized controllers and the overall performance of the control system. Sufficient criteria for analyzing asymptotic closed-loop stability are provided for input constrained open-loop asymptotically stable systems and for unconstrained open-loop unstable systems, under possible intermittent lack of communication of measurement data between controllers. The DMPC approach is also extended to asymptotic tracking of output set-points and rejection of constant measured disturbances. The effectiveness of the approach is shown on a relatively large-scale simulation example on decentralized temperature control based on wireless sensor feedback.Alessandro AlessioDavide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T10:59:59Z2011-08-08T08:08:51Zhttp://eprints.imtlucca.it/id/eprint/424This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4242011-07-27T10:59:59ZPredictive control for hybrid systems and its application to process controlK AsanoKoji TsudaAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T10:51:01Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/558This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5582011-07-27T10:51:01ZApproximate multiparametric convex programmingAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T09:22:05Z2014-07-16T12:54:37Zhttp://eprints.imtlucca.it/id/eprint/625This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6252011-07-27T09:22:05ZControllo predittivo in presenza di vincoli e gestione in linea del riferimentoAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:22:02Z2014-07-16T12:56:08Zhttp://eprints.imtlucca.it/id/eprint/620This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6202011-07-27T09:22:02ZConstraint fulfilment in feedback control via predictive reference managementThe problem of satisfying input and state-dependent inequality constraints in feedback control systems is addressed. The proposed solution is based on predicting the evolution of the constrained vector and, accordingly, selecting online the future reference based on both the current state and the desired set-point changes. The achievable performance is first investigated via simulations, and compared with the one obtained via a receding horizon controller which uses an online mathematical programming solver. Finally, an analysis is carried out so as to establish the stability and offset-free properties of the methodAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:22:00Z2014-01-28T09:18:20Zhttp://eprints.imtlucca.it/id/eprint/621This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6212011-07-27T09:22:00ZConstraint fulfilment in control systems via predictive reference managementThe problem of satisfying input and state-dependent inequality constraints in feedback control systems is addressed. The proposed solution is based on predicting the evolution of the constrained vector and, accordingly, selecting online the future reference based on both the current state and the desired set-point changes. An analysis is presented so as to establish stability and offset-free properties of the method when embodied in an LQ regulated system. Finally, simulations are used to evaluate the achievable performanceAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:20:44Z2014-07-16T12:57:47Zhttp://eprints.imtlucca.it/id/eprint/592This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5922011-07-27T09:20:44ZNonlinear predictive reference filtering for constrained trackingAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:20:39Z2014-07-16T13:07:37Zhttp://eprints.imtlucca.it/id/eprint/597This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5972011-07-27T09:20:39ZRobust nonlinear reference filtering for constrained linear systems with uncertain impulse/step responsesA method based on conceptual tools of predictive control is described for solving tracking problems wherein pointwise-in-time input and/or state inequality constraints and model uncertainties are present. It consists of adding to a primal compensated system a nonlinear device called predictive reference filter (PRF) which manipulates the desired trajectory in order to fulfill the prescribed constraints. Provided that an admissibility condition on the initial state is satisfied, the control scheme is proved to fulfill the constraints and be asymptotically stable for all the systems whose impulse-response and step-response descriptions lie within given uncertainty rangesAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:20:32Z2014-07-16T13:03:47Zhttp://eprints.imtlucca.it/id/eprint/595This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5952011-07-27T09:20:32ZA nonlinear command governor for constrained control systemsAlberto Bemporadalberto.bemporad@imtlucca.itAlessandro CasavolaEdoardo Mosca2011-07-27T09:20:29Z2014-07-16T13:01:51Zhttp://eprints.imtlucca.it/id/eprint/593This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5932011-07-27T09:20:29ZAnalog fuzzy implementation of a vehicle traction sliding-mode controlRoad adherence is an imprecise function of many parameters strongly affected by road conditions. In this paper, we propose a very robust control with a static nonlinear feedback law which can consider adherence and other model uncertainties, regulating the wheel slip at any desired value with good precision properties. A sliding-mode control has been designed to provide stability and reliability. Once designed, the control surface has been fuzzified and implemented with a programmable analog fuzzy circuit which uses a 0.7 mu m CMOS technology provided by SGS-Thomson Microelectronics. This implementation is carried out with a semi-automatic design flow and features high computational efficiency at it very low cost, especially when compared to a digital one. Moreover, the controller response time is less than 1 mu s. A flexible control of the slip coefficient has been performed. Results show that the desired slip coefficient is reached and kept with good approximation in compliance with theoretical results.A. BelliniAlberto Bemporadalberto.bemporad@imtlucca.itEleonora FranchiNicolò ManaresiRiccardo RovattiG. Torrini2011-07-27T09:20:28Z2014-07-16T14:09:27Zhttp://eprints.imtlucca.it/id/eprint/599This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5992011-07-27T09:20:28ZOn-line path parameterization for manipulators with input/state constraintsThis paper addresses the problem of satisfying input/state constraints for robotic systems tracking a given geometric path. According to a prediction of the evolution of the robot from the current state, a discrete-time device called {em Path Governor} (PG) generates on line a suitable time-parameterization of the path to be tracked, by solving at fixed intervals a constrained scalar optimization problem. Higher level switching commands are also taken into account by simply associating a different optimization criterion to each mode of operation.Alberto Bemporadalberto.bemporad@imtlucca.itTzyh-Jong Tarn2011-07-27T09:20:25Z2014-07-16T14:08:56Zhttp://eprints.imtlucca.it/id/eprint/603This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6032011-07-27T09:20:25ZConstrained predictive control with terminal ellipsoid constraint and artificial Lyapunov functionsWe deal with the problem of satisfying input and/or state hard constraints in set-point tracking problems. Stability is guaranteed by synthesizing a Lyapunov quadratic function for the system, and by imposing that the terminal state lies within a level set of the function. Algorithmic procedures to maximize the volume of such an ellipsoidal set are providedAlberto Bemporadalberto.bemporad@imtlucca.itEdoardo Mosca2011-07-27T09:19:38Z2014-07-16T13:56:27Zhttp://eprints.imtlucca.it/id/eprint/626This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6262011-07-27T09:19:38ZReference governors: on-line set-point optimization techniques for constraint fulfillmentThis dissertation presents a control technique to cope with set-point tracking problems in the presence of input and/or state constraints. The main idea consists of feeding to a conventional controller artificial set-points, which are calculated in real-time by manipulating the desired reference trajectory. For this reason, the resulting control tool is called {em reference governor} (RG). Set-point manipulation is performed on-line through an optimization procedure. This attempts at minimizing a performance index, which is evaluated by predicting the future evolution of the system. The RG is a high-level intelligent control module which supervises conventional controller operation, by ``smoothing out'' the reference trajectory when abrupt set-point changes would lead to constraint violation. The proposed control scheme is computationally light and easily implementable on low-cost hardware, and is general enough to cope systematically with different constrained tracking problems. We develop here theory and present simulation results of reference governors for linear, nonlinear, uncertain, robotic, and teleoperated control systems.Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:19:36Z2014-07-16T13:56:02Zhttp://eprints.imtlucca.it/id/eprint/600This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6002011-07-27T09:19:36ZControl of constrained nonlinear systems via reference managementFor a broad class of nonlinear continuous-time systems this paper addresses the problem of satisfying input and/or state hard constraints. The approach consists of adding a reference governor to a primal compensated nonlinear system. This is a predictive discrete-time device which, taking into account the current value of the state, filters the desired reference trajectory in such a way that a nonlinear primal compensated control system can operate in a stable way with satisfactory tracking performance and no constraint violation. The resulting hybrid system is proved to fulfil the constraints, as well as stability and tracking requirements, and the related computational burden turns out to be moderate and executable with current computing hardwareAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:19:34Z2014-07-16T13:52:23Zhttp://eprints.imtlucca.it/id/eprint/445This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4452011-07-27T09:19:34ZNonlinear control of constrained linear systems via predictive reference managementA method based on conceptual tools of predictive control is described for solving set-point tracking problems wherein pointwise-in-time input and/or state inequality constraints are present. It consists of adding to a primal compensated system a nonlinear device, called command governor (CG), whose action is based on the current state, set-point, and prescribed constraints. The CG selects at any time a virtual sequence among a family of linearly parameterized command sequences, by solving a convex constrained quadratic optimization problem, and feeds the primal system according to a receding horizon control philosophy. The overall system is proved to fulfill the constraints, be asymptotically stable, and exhibit an offset-free tracking behavior, provided that an admissibility condition on the initial state is satisfied. Though the CG can be tailored for the application at hand by appropriately choosing the available design knobs, the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problemAlberto Bemporadalberto.bemporad@imtlucca.itAlessandro CasavolaEdoardo Mosca2011-07-27T09:19:32Z2014-07-16T14:14:51Zhttp://eprints.imtlucca.it/id/eprint/605This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6052011-07-27T09:19:32ZReducing conservativeness in predictive control of constrained systems with disturbancesPredictive controllers which are able to guarantee constraint fulfilment in the presence of input disturbances, typically based on min-max formulations, often suffer excessive conservativeness. One of the main reasons for this is that the control action is based on the open-loop prediction of the evolution of the system, because the uncertainty due to the disturbance grows as time proceeds on the prediction horizon. On the other hand, such an effect can be moderated by adopting a closed-loop prediction. In this paper, closed-loop prediction is achieved by including a free feedback matrix gain in the set of optimization variables. This allows one to balance computational burden and reduction of conservativenessAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:19:30Z2014-07-16T14:13:47Zhttp://eprints.imtlucca.it/id/eprint/604This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6042011-07-27T09:19:30ZPredictive control of teleoperated constrained systems with unbounded communication delaysWe present a control technique which allows the teleoperation of systems subject to input/state constraints through transmission channels with unbounded time-delays, such as Internet TCP/IP connections. The main idea is based on the fact that predictive controllers provide, as a by-product, command sequences which can be executed as emergency maneuvers whenever the communication channel is broken by excessive time-delays. We show how this idea can be exploited by equipping the predictive controller with some additional control logic which enables the synchronization between plant, predictive controller, and human operatorAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:19:28Z2014-07-16T14:12:54Zhttp://eprints.imtlucca.it/id/eprint/466This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4662011-07-27T09:19:28ZReference governor for constrained nonlinear systemsThis paper addresses the problem of satisfying pointwise-in-time input and/or state hard constraints in nonlinear control systems. The approach is based on conceptual tools of predictive control and consists of adding to a primal compensated nonlinear system a reference governor. This is a discrete-time device which online handles the reference to be tracked, taking into account the current value of the state in order to satisfy the prescribed constraints. The resulting hybrid system is proved to fulfil the constraints as well as stability and tracking requirementsAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:19:26Z2014-07-16T14:11:36Zhttp://eprints.imtlucca.it/id/eprint/465This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4652011-07-27T09:19:26ZFulfilling hard constraints in uncertain linear systems by reference managingA method based on conceptual tools of predictive control is described for tackling tracking problems of uncertain linear systems wherein pointwise-in-time input and/or state inequality constraints are present. The method consists of adding to a primal compensated system a nonlinear device called predictive reference filter which manipulates the desired reference in order to fulfill the prescribed constraints. Provided that an admissibility condition on the initial state is satisfied, the control scheme is proved to fulfill the constraints, as well as stability and set-point tracking requirements, for all systems whose impulse/step responses lie within given uncertainty ranges.Alberto BemporadEdoardo Mosca2011-07-27T09:18:20Z2014-07-16T14:10:13Zhttp://eprints.imtlucca.it/id/eprint/467This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4672011-07-27T09:18:20ZA predictive controller with artificial Lyapunov function for linear systems with input/state constraintsThis paper copes with the problem of satisfying input and/or state hard constraints in set-point tracking problems. Stability is guaranteed by synthesizing a Lyapunov quadratic function for the system, and by imposing that the terminal state lies within a level set of the function. Procedures to maximize the volume of such an ellipsoidal set are provided, and interiorpoint methods to solve on-line optimization are considered.Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:18:17Z2014-07-16T14:27:00Zhttp://eprints.imtlucca.it/id/eprint/500This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5002011-07-27T09:18:17ZVerification of hybrid systems via mathematical programmingThis paper proposes a novel approach to the verification of hybrid systems based on linear and mixed-integer linear programming. Models are described using the Mixed Logical Dynamical (MLD) formalism introduced in [5]. The proposed technique is demonstrated on a verification case study for an automotive suspension system.Alberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:18:15Z2014-07-16T14:26:41Zhttp://eprints.imtlucca.it/id/eprint/518This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5182011-07-27T09:18:15ZRobust model predictive control: a surveyThis paper gives an overview of robustness in Model Predictive Control (MPC). After reviewing the basic concepts of MPC, we survey the uncertainty descriptions considered in the MPC literature, and the techniques proposed for robust constraint handling, stability, and performance. The key concept of “closedloop prediction” is discussed at length. The paper concludes with some comments on future research directions. Alberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:18:12Z2011-08-08T08:26:41Zhttp://eprints.imtlucca.it/id/eprint/608This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6082011-07-27T09:18:12ZA framework for control, fault detection, state estimation and verification of hybrid systemsThis paper presents a modeling formalism for hybrid systems which allows one to formulate and solve several practical problems, such as control, formal verification, state estimation, and fault detection. As an extension to previous works we report a technique that allows one to reduce the number of auxiliary binary variables in the modeling phase Domenico MignoneAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:18:11Z2014-07-16T14:26:17Zhttp://eprints.imtlucca.it/id/eprint/606This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6062011-07-27T09:18:11ZAn efficient branch and bound algorithm for state estimation and control of hybrid systemsThis paper presents a new Branch and Bound tree exploring strategy for solving Mixed Integer Quadratic Programs (MIQP) involving time evolutions of linear hybrid systems. In particular, we refer to the Mixed Logical Dynamical (MLD) models introduced by Bemporad and Morari, 1999, where the hybrid system is described by linear equations/inequalities involving continuous and integer variables. For the optimizations required by the controller synthesis and state estimation of MLD systems, the proposed algorithm reduces the average number of node explorations during the search of a global minimum. It also provides good local minima after a short number of steps of the Branch and Bound procedure.Alberto Bemporadalberto.bemporad@imtlucca.itDomenico MignoneManfred Morari2011-07-27T09:18:08Z2014-07-16T14:26:00Zhttp://eprints.imtlucca.it/id/eprint/609This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6092011-07-27T09:18:08ZMoving horizon estimation for hybrid systems and fault detectionAn approach for fault detection and state estimation of hybrid systems is presented. The method relies on the modeling framework for hybrid systems introduced by Bemporad and Morari (1999). This framework considers interacting propositional logic, automata, continuous dynamics and constraints. The proposed approach is illustrated by considering the fault detection problem of the three-tank benchmark systemAlberto Bemporadalberto.bemporad@imtlucca.itDomenico MignoneManfred Morari2011-07-27T09:18:05Z2014-07-16T14:22:27Zhttp://eprints.imtlucca.it/id/eprint/611This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6112011-07-27T09:18:05ZObservability and controllability of piecewise affine and hybrid systemsWe prove, in a constructive way, the equivalence between hybrid and piecewise affine systems. By focusing our investigation on the latter class, we show through counter-examples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems. Instead, we propose practical numerical tests based on mixed-integer linear programmingAlberto Bemporadalberto.bemporad@imtlucca.itGiancarlo Ferrari-TrecateManfred Morari2011-07-27T09:18:03Z2014-07-16T14:21:03Zhttp://eprints.imtlucca.it/id/eprint/610This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6102011-07-27T09:18:03ZModel predictive control - ideas for the next generationMixed Logical Dynamical (MLD) systems are introduced
as a new system type. The MLD form is capable to model
a broad class of systems arising in many applications: linear hybrid systems; sequential logical systems (finite state machines, automata); nonlinear dynamic systems, where
the nonlinearity can be expressed through combinational
logic; some classes of discrete event systems; constrained
linear systems. Controllability/verification and observability of MLD systems and other system theoretic properties are defined. Tests for these properties are formulated in the form of Mixed-Integer Linear Programs. Moving horizon control and estimation strategies with stability guarantees are proposed. These strategies require the iterative solution of Mixed-Integer Quadratic Programs.
Several examples communicate the power and versatility
of the proposed framework.Alberto Bemporadalberto.bemporad@imtlucca.itGiancarlo Ferrari-TrecateDomenico MignoneManfred MorariFabio Danilo Torrisi2011-07-27T09:16:40Z2014-07-17T12:22:02Zhttp://eprints.imtlucca.it/id/eprint/574This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5742011-07-27T09:16:40ZPerformance analysis of piecewise linear systems and model predictive control systemsBemporad and Morari (1999) provided a tool for obtaining the explicit solution of constrained model predictive control (MPG) problems by showing that the control law is a continuous piecewise affine (PWA) function of the state vector. Therefore, the feedback interconnection between the MPC controller and a linear system, or a PWA system (e.g., a PWA approximation of a nonlinear system), is a PWA system. For discrete-time PWA and hybrid systems, the present authors (2000) presented an algorithm for verification/reachability analysis. In this paper, we formulate the performance analysis problem of closed-loop PWA systems (including MPC feedback loops where the prediction model and the plant model could be different) as a reachability analysis problem, and use our algorithm to obtain a tool for characterizing (i) the set of states for which the evolution is feasible, (ii) the domain of stability, (iii) the performance of the closed-loopAlberto Bemporadalberto.bemporad@imtlucca.itFabio Danilo TorrisiManfred Morari2011-07-27T09:16:38Z2014-07-17T12:21:35Zhttp://eprints.imtlucca.it/id/eprint/499This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4992011-07-27T09:16:38ZOptimization-based verification and stability characterization of piecewise affine and hybrid systemsIn this paper, we formulate the problem of characterizing the stability of a piecewise affine (PWA) system as a verification problem. The basic idea is to take the whole IR n as the set of initial conditions, and check that all the trajectories go to the origin. More precisely, we test for semi-global stability by restricting the set of initial conditions to an (arbitrarily large) bounded set X(0), and label as “asymptotically stable in T steps” the trajectories that enter an invariant set around the origin within a finite time T, or as “unstable in T steps” the trajectories which enter a set X inst of (very large) states. Subsets of X(0) leading to none of the two previous cases are labeled as “non-classifiable in T steps”. The domain of asymptotical stability in T steps is a subset of the domain of attraction of an equilibrium point, and has the practical meaning of collecting the initial conditions from which the settling time to a specified set around the origin is smaller than T. In addition, it can be computed algorithmically in finite time. Such an algorithm requires the computation of reach sets, in a similar fashion as what has been proposed for verification of hybrid systems. In this paper we present a substantial extension of the verification algorithm presented in [6] for stability characterization of PWA systems, based on linear and mixed-integer linear programming. As a result, given a set of initial conditions we are able to determine its partition into subsets of trajectories which are asymptotically stable, or unstable, or non-classifiable in T steps. Alberto Bemporadalberto.bemporad@imtlucca.itFabio Danilo TorrisiManfred Morari2011-07-27T09:16:33Z2014-07-17T12:21:08Zhttp://eprints.imtlucca.it/id/eprint/569This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5692011-07-27T09:16:33ZThe explicit solution of model predictive control via multiparametric quadratic programming The control based on online optimization, popularly known as model predictive control (MPC), has long been recognized as the winning alternative for constrained systems. The main limitation of MPC is, however, its online computational complexity. For discrete-time linear time-invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly the state feedback control law associated with MPC, and show that it is piecewise linear and continuous. The controller inherits all the stability and performance properties of MPC, but the online computation is reduced to a simple linear function evaluation instead of the expensive quadratic program. The new technique is expected to enlarge the scope of applicability of MPC to small-size/fast-sampling applications which cannot be covered satisfactorily with anti-windup schemesAlberto Bemporadalberto.bemporad@imtlucca.itManfred MorariVivek DuaEfstratios N. Pistikopoulos2011-07-27T09:16:32Z2014-07-17T12:20:00Zhttp://eprints.imtlucca.it/id/eprint/517This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5172011-07-27T09:16:32ZPredictive control of constrained hybrid systemsThis paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD systems include linear hybrid systems, finite state machines, some classes of discrete event systems, constrained linear systems, and nonlinear systems which can be approximated by piecewise linear functions. A predictive control scheme is proposed which is able to stabilize MLD systems on desired reference trajectories while fulfilling operating constraints, and possibly take into account previous qualitative knowledge in the form of heuristic rules. Due to the presence of integer variables, the resulting on-line optimization procedures are solved through Mixed Integer Quadratic Programming (MIQP), for which efficient solvers have been recently developed. Some examples and a simulation case study on a complex gas supply system are reported. Alberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:16:29Z2014-07-17T12:22:25Zhttp://eprints.imtlucca.it/id/eprint/613This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6132011-07-27T09:16:29ZMulti-objective prioritisation and reconfiguration for the control of constrained hybrid systemsIn many applications, the control objectives and constraints can be assigned a hierarchy of levels of priority. Often a disturbance or a fault occurs, resulting in some constraints or objectives being violated. Inadequate handling of this situation might result in component or even system-wide failures. This paper presents several methods for handling a large class of multi-objective formulations and prioritisations for model predictive control of hybrid systems, using the new mixed logic dynamical (MLD) framework. A new method, which does not require logic variables for prioritising soft constraints, is also presentedEric C. KerriganAlberto Bemporadalberto.bemporad@imtlucca.itDomenico MignoneManfred MorariJan M. Maciejowski2011-07-27T09:16:24Z2014-07-17T12:19:02Zhttp://eprints.imtlucca.it/id/eprint/575This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5752011-07-27T09:16:24ZPerformance driven reachability analysis for optimal scheduling and control of hybrid systemsWe deal with the optimal control problem for piecewise linear and hybrid systems by using a computational approach based on performance-driven reachability analysis. The idea consists of coupling a reach-set exploration algorithm, essentially based on a repetitive use of linear programming, to a quadratic programming solver which selectively drives the exploration. In particular, an upper bound on the optimal cost is continually updated during the procedure, and used as a criterion to discern non-optimal evolutions and to prevent their exploration. The result is an efficient strategy of branch-and-bound nature, which is especially attractive for solving long-horizon hybrid optimal control and scheduling problemsAlberto Bemporadalberto.bemporad@imtlucca.itL. GiovanardiFabio Danilo Torrisi2011-07-27T09:16:21Z2014-07-17T12:18:33Zhttp://eprints.imtlucca.it/id/eprint/456This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4562011-07-27T09:16:21ZOutput-feedback predictive control of constrained linear systems with disturbances via set-membership state estimationThis paper combines model predictive control (MPC) and set-membership (SM) state estimation techniques for controlling systems subject to hard input and state constraints. Linear systems with unknown but bounded disturbances and partial state information are considered. The adopted approach guarantees that the constraints are satisfied for all the states which are compatible with the available information and for all the disturbances within given bounds. Properties of the proposed MPC-SM algorithm and simulation studies are reported.Alberto Bemporadalberto.bemporad@imtlucca.itAndrea Garulli2011-07-27T09:11:24Z2014-07-17T12:17:57Zhttp://eprints.imtlucca.it/id/eprint/612This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6122011-07-27T09:11:24ZModel predictive control: a multi-parametric programming approachIn this paper, linear model predictive control problems are formulated as multi-parametric quadratic programs, where the control variables are treated as optimization variables and the state variables as parameters. It is shown that the control variables are affine functions of the state variables and each of these affine functions is valid in a certain polyhedral region in the space of state variables. An approach for deriving the explicit expressions of all the affine functions and their corresponding polyhedral regions is presented. The key advantage of this approach is that the control actions are computed off-line: the on-line computation simply reduces to a function evaluation problem.Alberto Bemporadalberto.bemporad@imtlucca.itNikolaos A. BozinisVivek DuaManfred MorariEfstratios N. Pistikopoulos2011-07-27T09:11:21Z2014-07-17T12:17:38Zhttp://eprints.imtlucca.it/id/eprint/568This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5682011-07-27T09:11:21ZPiecewise linear optimal controllers for hybrid systemsWe propose a procedure for synthesizing piecewise linear optimal controllers for discrete-time hybrid systems. A stabilizing controller is obtained by designing a model predictive controller, which is based on the minimization of a weighted l1/∞-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a multiparametric mixed-integer linear program, which avoids solving mixed-integer programs online. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluationAlberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:11:18Z2014-07-17T12:17:22Zhttp://eprints.imtlucca.it/id/eprint/572This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5722011-07-27T09:11:18ZOptimal controllers for hybrid systems: stability and piecewise linear explicit formWe propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closed-loop stability. Hybrid systems are modeled in discrete-time within the mixed logical dynamical framework, or, equivalently, as piecewise affine systems. A stabilizing controller is obtained by designing a model predictive controller, which is based on the minimization of a weighted 1/∞-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a mixed-integer linear program (MILP) which depends on the current state. Although efficient branch and bound algorithms exist to solve MILPs, these are known to be NP-hard problems, which may prevent their online solution if the sampling-time is too small for the available computation power. Rather than solving the MILP online, we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of a heat exchange system shows the potential of the methodAlberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:11:16Z2014-07-17T12:16:28Zhttp://eprints.imtlucca.it/id/eprint/573This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5732011-07-27T09:11:16ZExplicit solution of LP-based model predictive controlFor discrete-time linear time-invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to optimal control problems that can be formulated using a linear program. In particular, we focus our attention on a receding horizon control scheme where the performance criterion is based on a mixed 1/∞-norm. We show that the optimal control profile is a piecewise linear and continuous function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the online computation of the resultant model predictive controller is reduced to a simple linear function evaluation, instead of the typical expensive linear program required up to now. The technique proposed has both theoretical and practical advantages. The proposed technique is attractive for a wide range of applications where the simplicity of the online computational complexity is a crucial requirementAlberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:11:14Z2014-07-17T12:15:37Zhttp://eprints.imtlucca.it/id/eprint/448This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4482011-07-27T09:11:14ZSonar-based wall-following control of mobile robotsIn this paper, the wall-following problem for low-velocity mobile robots, equipped with incremental encoders and one sonar sensor, is considered. A robust observer-based controller, which takes into account explicit constraints on the orientation of the sonar sensor with respect to the wall and the velocity of the wheels, is designed. The feedback controller provides convergence and fulfillment of the constraints, once an estimate of the position of the mobile robot, is available. Such an estimate is given by an Extended Kalman Filter (EKF), which is designed via a sensor fusion approach merging the velocity signals from the encoders and the distance measurements from the sonar. Some experimental tests are reported to discuss the robustness of the control scheme. Alberto Bemporadalberto.bemporad@imtlucca.itMauro Di MarcoAlberto Tesi2011-07-27T09:11:12Z2014-07-17T12:15:01Zhttp://eprints.imtlucca.it/id/eprint/446This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4462011-07-27T09:11:12ZObservability and controllability of piecewise affine and hybrid systemsWe prove, in a constructive way, the equivalence between piecewise affine systems and a broad class of hybrid systems described by interacting linear dynamics, automata, and propositional logic. By focusing our investigation on the former class, we show through counterexamples that observability and controllability properties cannot be easily deduced from those of the component linear subsystems. Instead, we propose practical numerical tests based on mixed-integer linear programming.Alberto Bemporadalberto.bemporad@imtlucca.itGiancarlo Ferrari-TrecateManfred Morari2011-07-27T09:11:10Z2014-07-17T12:48:08Zhttp://eprints.imtlucca.it/id/eprint/519This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5192011-07-27T09:11:10ZA hybrid approach to traction controlIn this paper we describe a hybrid model and an optimization-based control strategy for solving a traction control prob- lem currently under investigation at Ford Research Laboratories. We show through simulations on a model and a realistic set of parameters that good and robust performance is achieved. Furthermore, the result- ing optimal controller is a piecewise linear function of the measurements that can be implemented on low cost control hardware. Francesco BorrelliAlberto Bemporadalberto.bemporad@imtlucca.itMichael FodorDavor Hrovat2011-07-27T09:11:08Z2014-07-17T12:49:10Zhttp://eprints.imtlucca.it/id/eprint/582This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5822011-07-27T09:11:08ZDiscrete-time hybrid modeling and verificationFor hybrid systems described by interconnections of linear dynamical systems and logic devices, we recently (A. Bemporad et al., 2000, 2001) proposed mixed logical-dynamical (MLD) systems and the language HYSDEL (HYbrid System DEscription Language) as a modeling tool. For MLD models, we developed a reachability analysis algorithm which combines forward reach-set computation and feasibility analysis of trajectories by linear and mixed-integer linear programming. In this paper, the versatility of the overall analysis tool is illustrated in the verification of an automotive cruise control system for a car with a robotized manual gear shiftFabio Danilo TorrisiAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:11:06Z2014-07-17T12:48:51Zhttp://eprints.imtlucca.it/id/eprint/581This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5812011-07-27T09:11:06ZAn algorithm for multi-parametric quadratic programming and explicit MPC solutionsExplicit solutions to constrained linear model-predictive control (MPC) problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state space induced by the multi-parametric piecewise linear solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement in efficiencyPetter TondelTor Arne JohansenAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:09:10Z2014-07-17T12:47:36Zhttp://eprints.imtlucca.it/id/eprint/585This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5852011-07-27T09:09:10ZIdentification of hybrid systems via mixed-integer programmingAddresses the problem of identification of hybrid dynamical systems, by focusing the attention on hinging hyperplanes and Wiener piecewise affine autoregressive exogenous models. In particular, we provide algorithms based on mixed-integer linear or quadratic programming which are guaranteed to converge to a global optimumAlberto Bemporadalberto.bemporad@imtlucca.itJacob RollLennart Ljung2011-07-27T09:09:07Z2014-07-17T12:47:14Zhttp://eprints.imtlucca.it/id/eprint/577This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5772011-07-27T09:09:07ZOptimization-based hybrid control toolsThe paper discusses a framework for modeling, analyzing and controlling systems whose behavior is governed by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. They are described by linear dynamic equations subject to linear inequalities involving real and integer variables. MLD models are equivalent to various other system descriptions like Piecewise Affine (PWA) systems and Linear Complementarity (LC) systems. They have the advantage, however, that many problems of system analysis (like reachability/controllability, observability, and verification) and many problems of synthesis (like controller design and filter design) can be readily expressed as mixed integer linear or quadratic programs, for which many commercial software packages exist. In this paper we first recall MLD models and the modeling language HYSDEL (HYbrid Systems DEscription Language). Subsequently, we illustrate the use of Model Predictive Control (MPC) based on mixed-integer programming for hybrid MLD models, and the use of multiparametric programming for obtaining explicitly the equivalent piecewise linear control form of MPC. The eventual practical success of these methods will depend on progress in the development of the various optimization algorithms and tools so that problems of realistic size can be tackledAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:09:04Z2014-07-17T12:48:28Zhttp://eprints.imtlucca.it/id/eprint/583This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5832011-07-27T09:09:04ZOn the equivalence of classes of hybrid dynamical modelsWe establish equivalences among five classes of hybrid systems, that we have encountered in previous research: mixed logical dynamical systems, linear complementarity systems, extended linear complementarity systems, piecewise affine systems, and max-min-plus-scaling systems. These results are of paramount importance for transferring properties and tools from one class to anotherW.P.M.H. HeemelsBart De SchutterAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:09:02Z2014-07-17T12:46:56Zhttp://eprints.imtlucca.it/id/eprint/584This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5842011-07-27T09:09:02ZOn hybrid systems and closed-loop MPC systemsThe following five classes of hybrid systems were proved by W.P.M.H. Heemels et al. (2001) to be equivalent: linear complementarity (LC) systems, extended linear complementarity (ELC) systems, mixed logical-dynamical (MLD) systems, piecewise affine (PWA) systems and max-min-plus-scaling (MMPS) systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of system variables. In this paper, for closed-loop linear or hybrid plants with model-predictive control (MPC) based on a linear model and fulfilling linear constraints on the input and state variables, we provide a simple and direct proof that the closed-loop system (cl-MPC) is a subclass of any of the former five classes of hybrid systems. This result opens up the use of tools developed for hybrid systems (such as stability, robust stability and safety analysis tools) to study the closed-loop properties of MPCAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. HeemelsBart De Schutter2011-07-27T09:08:58Z2014-07-17T12:46:26Zhttp://eprints.imtlucca.it/id/eprint/586This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5862011-07-27T09:08:58ZSuboptimal explicit MPC via approximate multiparametric quadratic programmingAlgorithms for solving multiparametric quadratic programming (mp-QP) were proposed in Bemporad et al. (2001) and Tondel et al. (2001) for computing explicit model predictive control (MPC) laws. The reason for this interest is that the solution to mp-QP is a piecewise affine function of the state vector and thus it is easily implementable on-line. The main drawback of solving mp-QP exactly is that whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. We address the problem of finding approximate solutions to mp-QP, where the degree of approximation is arbitrary and allows a trade off between optimality and a smaller number of cells in the piecewise affine solutionAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T09:08:55Z2014-07-09T14:43:59Zhttp://eprints.imtlucca.it/id/eprint/580This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5802011-07-27T09:08:55ZEfficient on-line computation of constrained optimal control For discrete-time linear time-invariant systems with constraints on inputs and outputs, the constrained finite-time optimal controller can be obtained explicitly as a piecewise-affine function of the initial state via multi-parametric programming. By exploiting the properties of the value function, we present two algorithms that efficiently perform the online evaluation of the explicit optimal control law both in terms of storage demands and computational complexity. The algorithms are particularly effective when used for model-predictive control (MPC) where an open-loop constrained finite-time optimal control problem has to be solved at each sampling timeFrancesco BorrelliMato BaoticAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:08:53Z2014-07-17T12:46:08Zhttp://eprints.imtlucca.it/id/eprint/578This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5782011-07-27T09:08:53ZPiecewise linear robust model predictive controlFor discrete-time linear time-invariant systems with input disturbances and constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to robust optimal control problems based on min-max optimization. We show that the optimal control sequence is a piecewise linear function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the on-line computation of the resulting MPC controller is reduced to a simple linear function evaluation. In this paper the uncertainty is modeled as an additive norm-bounded input disturbance vector. The technique can be also extended to robust control of constrained systems affected by polyhedral parametric uncertainty.Alberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:08:51Z2014-07-17T12:40:36Zhttp://eprints.imtlucca.it/id/eprint/576This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5762011-07-27T09:08:51ZOptimal piecewise-linear control of dry clutch engagementBased on a discrete-time second order state-space dynamic model of the powertrain system, a piecewise feedback control for the dry clutch engagement process is proposed. The engine speed and the clutch disk speed are assumed to be measurable and the control input is the normal engaging force applied to the disks. The controller is designed by minimizing a quadratic performance index subject to constraints on the normal force, normal force derivative, and engine speed. The resulting Model Predictive Controller (MPC) is shown to consist of a piecewise linear feedback control: the state space can be divided into several regions, such that in each region an off-line computed linear controller must be implemented. The explicit piecewise linear form of the MPC law is obtained by using a multiparametric programming solver and can be tuned so that fast engagement, small friction losses and smooth lock-up are achieved. The paper reports numerical results, carried out by a Simulink/MPC Toolbox simulation scheme and a realistic set of parameters, showing the good performance of the closed-loop system.Alberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliLuigi GlielmoFrancesco Vasca2011-07-27T09:08:49Z2014-07-17T12:40:08Zhttp://eprints.imtlucca.it/id/eprint/579This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5792011-07-27T09:08:49ZHybrid control of dry clutch engagementThis paper proposes a novel piecewise linear feedback control strategy for the automotive dry clutch engagement process. Based on a dynamic model of the powertrain system, the controller is designed by minimizing a quadratic performance index subject to constraints on the inputs and on the states. The resulting model predictive controller is shown to consist of a piecewise linear feedback control and can be tuned so that fast engagement, small friction losses and smooth lock-up are achieved. Numerical results show the good performance of the closed-loop system.Alberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliLuigi GlielmoFrancesco Vasca2011-07-27T09:08:46Z2014-07-17T12:39:43Zhttp://eprints.imtlucca.it/id/eprint/458This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4582011-07-27T09:08:46ZDiscrete-time hybrid modeling and verification of the batch evaporator process benchmarkFor hybrid systems described by interconnections of linear discrete-time dynamical systems, automata, and propositional logic rules, we recently proposed the Mixed Logical Dynamical (MLD) systems formalism and the language HYSDEL (Hybrid System Descrip- tion Language) as a modeling tool. For MLD models, we developed a reachability analysis algorithm which combines forward reach set computation and feasibility analysis of trajectories by linear and mixed-integer linear programming. In this paper the versatility of the overall analysis tool is illustrated on the batch evaporator benchmark process. Alberto Bemporadalberto.bemporad@imtlucca.itFabio Danilo TorrisiManfred Morari2011-07-27T09:08:06Z2014-07-17T12:38:20Zhttp://eprints.imtlucca.it/id/eprint/457This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4572011-07-27T09:08:06ZEquivalence of hybrid dynamical modelsThis paper establishes equivalences among five classes of hybrid systems: mixed logical dynamical (MLD) systems, linear complementarity (LC) systems, extended linear complementarity (ELC) systems, piecewise affine (PWA) systems, and max-min-plus-scaling (MMPS) systems. Some of the equivalences are established under (rather mild) additional assumptions. These results are of paramount importance for transferring theoretical properties and tools from one class to another, with the consequence that for the study of a particular hybrid system that belongs to any of these classes, one can choose the most convenient hybrid modeling framework.W.P.M.H. HeemelsBart De SchutterAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:08:04Z2011-08-08T08:13:22Zhttp://eprints.imtlucca.it/id/eprint/547This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5472011-07-27T09:08:04ZComputation and approximation of piecewise affine control via binary search treeWe present an algorithm for generating a binary search tree that allows efficient computation of piecewise affine (PWA) functions defined on a polyhedral partition. This is useful for PWA control approaches, such as explicit model predictive control (MPC), as it allows the controller to be implemented on-line with small computational effort. The computation time is logarithmic in the number of regions in the PWA partition. A method for generating an approximate PWA function based on a binary search tree is also presented, giving further simplification of PWA control.Petter TondelTor Arne JohansenAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:08:00Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/590This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5902011-07-27T09:08:00ZAn iterative algorithm for the optimal control of continuous-time switched linear systemsFor continuous-time switched linear systems, this paper proposes an approach for solving infinite-horizon optimal control problems where the decision variables are the switching instants and the sequence of operating modes. The procedure iterates between a "master" procedure that finds an optimal switching sequence of modes, and a "slave" procedure that finds the optimal switching instants. The effectiveness of the approach is shown through simple simulation examples.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro GiuaCarla Seatzu2011-07-27T09:07:57Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/548This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5482011-07-27T09:07:57ZA hybrid system approach to modeling and optimal control of DISC enginesThis paper illustrates the application of hybrid modeling and optimal control to the problem of air-to-fuel ratio and torque control in advanced technology gasoline direct injection stratified charge (DISC) engines. DISC engines have two discrete modes of operation, stratified and homogeneous, and their dynamic behavior can be easily captured by a hybrid model. We show that the design flow (hybrid modeling and controller synthesis) is simple in terms of problem setup and tuning, provides good closed-loop performance, and leads to a control law that can be implemented on automotive hardware as a piecewise affine function of the measured and estimated quantities.Alberto Bemporadalberto.bemporad@imtlucca.itNicolò GiorgettiIlya KolmanovskyDavor Hrovat2011-07-27T09:07:53Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/546This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5462011-07-27T09:07:53ZHybrid modeling and control of a direct injection stratified charge engineThis paper illustrates the application of hybrid modeling and optimal control to the problem of air-to-fuel ratio and torque control in advanced technology gasoline direct injection stratified charge (DISC) engines. DISC engines have two discrete modes of operation, stratified and homogeneous, and their dynamic behavior can be easily captured by a hybrid model. We show that the design flow (hybrid modeling and controller synthesis) is simple in terms of problem setup and tuning, provides good closed-loop performance, and leads to a control law that can be implemented on automotive hardware as a piecewise affine function of the measured and estimated quantities. Alberto Bemporadalberto.bemporad@imtlucca.itNicolò GiorgettiIlya KolmanovskyDavor Hrovat2011-07-27T09:07:50Z2011-08-08T08:09:47Zhttp://eprints.imtlucca.it/id/eprint/587This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5872011-07-27T09:07:50ZMax-plus-algebraic problems and the extended linear complementarity problem - algorithmic aspectsMany fundamental problems in the max-plus-algebraic system theory for discrete event systems--among which the minimal state space realization problem--can be solved using an Extended Linear Complementarity Problem (ELCP). We present some new, more efficient methods to solve the ELCP. We show that an ELCP with a bounded feasible set can be recast as a standard Linear Complementarity Problem (LCP). Our proof results in three possible numerical solution methods for a given ELCP: regular ELCP algorithms, mixed integer linear programming algorithms, and regular LCP algorithms. We also apply these three methods to a basic max-plus-algebraic benchmark problem.Bart De SchutterW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:07:45Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/524This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5242011-07-27T09:07:45ZOn the optimal control law for linear discrete time hybrid systemsIn this paper we study the solution to optimal control problems for discrete time linear hybrid systems. First, we prove that the closed form of the state-feedback solution to finite time optimal control based on quadratic or linear norms performance criteria is a time-varying piecewise afine feedback control law. Then, we give an insight into the structure of the optimal state-feedback solution and of the value function. Finally, we briefly describe how the optimal control law can be computed by means of multiparametric programming. Alberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:07:43Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/551This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5512011-07-27T09:07:43ZAn efficient technique for translating mixed logical dynamical systems into piecewise affine systemsFor linear hybrid systems consisting of linear dynamic equations interacting with linear threshold events, automata, and logic propositions, provided in mixed-logical dynamical (MLD) form, this paper describes an efficient technique for transforming such systems into an equivalent piecewise affine (PWA) form, where equivalent means that for the same initial conditions and input sequences the trajectories of the system are identical.Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:05:54Z2011-08-04T07:29:09Zhttp://eprints.imtlucca.it/id/eprint/444This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4442011-07-27T09:05:54ZThe Explicit Linear Quadratic Regulator for Constrained SystemsFor discrete-time linear time invariant systems with constraints on inputs and states, we develop an algorithm to determine explicitly, the state feedback control law which minimizes a quadratic performance criterion. We show that the control law is piece-wise linear and continuous for both the finite horizon problem (model predictive control) and the usual infinite time measure (constrained linear quadratic regulation). Thus, the on-line control computation reduces to the simple evaluation of an explicitly defined piecewise linear function. By computing the inherent underlying controller structure, we also solve the equivalent of the Hamilton–Jacobi–Bellman equation for discrete-time linear constrained systems. Control based on on-line optimization has long been recognized as a superior alternative for constrained systems. The technique proposed in this paper is attractive for a wide range of practical problems where the computational complexity of on-line optimization is prohibitive. It also provides an insight into the structure underlying optimization-based controllers.Alberto BemporadManfred MorariVivek DuaEfstratios N. Pistikopoulos2011-07-27T09:05:47Z2014-07-17T12:52:10Zhttp://eprints.imtlucca.it/id/eprint/473This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4732011-07-27T09:05:47ZOn hybrid systems and closed-loop MPC systemsThe following five classes of hybrid systems were recently proven to be equivalent: linear complementarity, extended linear complementarity, mixed logical dynamical systems, piecewise affine systems and max-min-plus-scaling systems. Some of the equivalences were obtained under additional assumptions, such as boundedness of certain system variables. In this paper, for linear or hybrid plants in closed-loop with a model predictive control (MPC)controller based on a linear model fulfilling linear constraints on input and state variables and utilizing a quadratic cost criterion, we provide a simple and direct proof that the closed-loop system is a subclass of any of the former five classes of hybrid systems. This result is of extreme importance, as it opens up the use of tools developed for the mentioned hybrid model classes, such as (robust) stability and safety analysis tools, to study closed-loop properties of MPCAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. HeemelsBart De Schutter2011-07-27T09:05:43Z2014-07-17T12:51:18Zhttp://eprints.imtlucca.it/id/eprint/589This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5892011-07-27T09:05:43ZL2 anti-windup via receding horizon optimal controlThe nonlinear L2 anti-windup framework introduced by Teel and Kapoor (1997) reduces the anti-windup synthesis problem to a state feedback synthesis problem for linear systems with input saturation and input matched L2 disturbances. In this paper, such a state feedback is synthesized using receding horizon optimal control techniques, and its equivalent piecewise affine closed-form is computed using the techniques of Bemporad et al. (2002). The properties of the resulting anti-windup compensation scheme are analyzed in the paper, and its performance is investigated through a simulation example.Alberto Bemporadalberto.bemporad@imtlucca.itAndrew R. TeelLuca Zaccarian2011-07-27T09:05:40Z2014-07-17T12:50:59Zhttp://eprints.imtlucca.it/id/eprint/550This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5502011-07-27T09:05:40ZA master-slave algorithm for the optimal control of continuous-time switched affine systemsFor continuous-time switched affine systems, this paper proposes an approach for solving infinite-horizon optimal control problems where the decision variables are the switching instants and the sequence of operating modes. The procedure iterates between a "master" procedure that finds an optimal switching sequence of modes, and a "slave" procedure that finds the optimal switching instants.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro GiuaCarla Seatzu2011-07-27T09:05:38Z2014-07-17T12:50:41Zhttp://eprints.imtlucca.it/id/eprint/549This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5492011-07-27T09:05:38ZSynthesis of state-feedback optimal controllers for switched linear systemsThe paper deals with the optimal control of switched piecewise linear autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length: the unknown switching times and the switching sequence are the optimization parameters. We also assume that a cost may be associated to each switch. The optimal control for this class of systems takes the form of a state feedback, i.e., it is possible to identify a set of regions of the state space such that an optimal switch should occur if and only if the present state belongs to one of them. We show how the tables containing these regions can be computed off-line through a numerical procedure.Alberto Bemporadalberto.bemporad@imtlucca.itAlessandro GiuaCarla Seatzu2011-07-27T09:05:35Z2014-07-17T12:50:21Zhttp://eprints.imtlucca.it/id/eprint/474This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4742011-07-27T09:05:35ZModel Predictive Control Based on Linear Programming - The Explicit SolutionWe study model predictive control (MPC) schemes for discrete-time linear time-invariant systems with constraints on inputs and states, that can be formulated using a linear program (LP). In particular, we focus our attention on performance criteria based on a mixed 1 -norm, namely, 1-norm with respect to time and -norm with respect to space. First we provide a method to compute the terminal weight so that closed-loop stability is achieved. We then show that the optimal control profile is a piecewise affine and continuous function of the initial state and briefly describe the algorithm to compute it. The piecewise affine
form allows to eliminate online LP, as the computation associated with MPC becomes a simple function evaluation. Besides practical advantages, the availability of the explicit structure of the MPC controller provides an insight into the type of control action in different
regions of the state space, and highlights possible conditions of degeneracies of the LP, such as multiple optima.Alberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:05:32Z2011-08-05T14:09:02Zhttp://eprints.imtlucca.it/id/eprint/459This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4592011-07-27T09:05:32ZAn algorithm for multi-parametric quadratic programming and explicit MPC solutionsExplicit solutions to constrained linear model predictive control problems can be obtained by solving multi-parametric quadratic programs (mp-QP) where the parameters are the components of the state vector. We study the properties of the polyhedral partition of the state space induced by the multi-parametric piecewise affine solution and propose a new mp-QP solver. Compared to existing algorithms, our approach adopts a different exploration strategy for subdividing the parameter space, avoiding unnecessary partitioning and QP problem solving, with a significant improvement of efficiency.Petter TondelTor Arne JohansenAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:04:28Z2011-08-05T14:08:37Zhttp://eprints.imtlucca.it/id/eprint/460This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4602011-07-27T09:04:28ZEvaluation of piecewise affine control via binary search treeWe present an algorithm for generating a binary search tree that allows efficient computation of piecewise affine (PWA) functions defined on a polyhedral partition. This is useful for PWA control approaches, such as explicit model predictive control, as it allows the controller to be implemented online with small computational effort. The computation time is logarithmic in the number of regions in the PWA partition.Petter TondelTor Arne JohansenAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:04:23Z2011-08-05T14:08:12Zhttp://eprints.imtlucca.it/id/eprint/556This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5562011-07-27T09:04:23ZOptimal control of uncertain piecewise affine/mixed logical dynamical systemsThis paper proposes an approach to extend the mixed logical
dynamical modelling framework for synthesizing robust optimal control actions for constrained piecewise affine systems subject to bounded additive input disturbances. Rather than using closed-loop dynamic programming arguments, robustness is achieved here with an open-loop optimization strategy, such that the optimal control sequence optimizes nominal performance while robustly guaranteeing that safety/performance constraints are respected. The proposed approach is based on the robust mode control concept, which enforces the control input
to generate trajectories such that the mode of the system, at each time instant, is independent of the disturbances.Miguel Pedro SilvaAlberto Bemporadalberto.bemporad@imtlucca.itMiguel Ayala BottoJosé Sa da Costa2011-07-27T09:04:20Z2016-05-11T11:07:22Zhttp://eprints.imtlucca.it/id/eprint/487This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4872011-07-27T09:04:20ZHybrid modeling and optimal control of an asphalt base processBostjan PotocnikAlberto Bemporadalberto.bemporad@imtlucca.itFabio Danilo TorrisiGasper MusicBorut Zupancic2011-07-27T09:04:08Z2011-08-05T14:07:13Zhttp://eprints.imtlucca.it/id/eprint/552This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5522011-07-27T09:04:08ZReceding-horizon control of LTI systems with quantized inputsThis paper deals with the stabilization problem for a particular class of hybrid systems, namely discrete–time linear systems subject to a uniform (a priori fixed) quantization of the control set. Results of our previous work on the subject provided a description of minimal (in a specific sense) invariant sets that could be rendered maximally attractive under any quantized feedback strategy. In this paper, we consider the design of stabilizing laws that optimize a given cost index on the state and input evolution on a finite, receding horizon. Application of Model Predictive Control techniques for the solution of similar hybrid control problems through Mixed Logical Dynamical reformulations can provide a stabilizing control law, provided that the feasibility hypotheses are met. In this paper, we discuss precisely what are the shortest horizon length and the minimal invariant terminal set for which it can be guaranteed a stabilizing MPC scheme. The final paper will provide an example and simulations of the application of the control scheme to a practical quantized control problem.Bruno PicassoStefania PancantiAlberto Bemporadalberto.bemporad@imtlucca.itAntonio Bicchi2011-07-27T09:04:05Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/554This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5542011-07-27T09:04:05ZSet membership identification of piecewise affine modelsThis paper addresses the problem of identification of piecewise affine (PWA)models, which involves the joint estimations of both the parameters of the affine submodels and the partition of the PWA map from data. According to ideas from set-membership identification, the key approach is to characterize the model by its maximum allowed prediction error, which is used as a tuning knob for traning off between prediction accuracy and model complexity. At initialization, the proposed procedure for PWA identification exploits a technique per partitioning an infeasible system of linear inequalities into a (possibly minimum) number of feasible subsystems. This provides both an initial clustering of the datapoints and a guess of the number of required submodels, which therefore is not fixed a priori. A refinement procedure is then applied in order to improve both data classification and parameter estimation. The partition of the PWA maps is finally estimated by considering multicategory classification techniques.Alberto Bemporadalberto.bemporad@imtlucca.itAndrea GarulliSimone PaolettiAntonio Vicino2011-07-27T09:04:02Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/553This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5532011-07-27T09:04:02ZOptimal state-feedback quadratic regulation of linear hybrid automataFor linear hybrid automata, namely switched linear autonomous systems whose mode of operation is determined by a controlled automaton, in this paper we face the problem of optimal control, where the objective is to minimize a quadratic performance index over an infinite time horizon. The quantities to be optimized are the sequence of switching times and the sequence of modes (or ”locations”), under the following constraints: the sequence of modes has a finite length; the discrete dynamics of the automaton restricts the possible switches from a given location to
the next location, with a cost associated to each switch; the time interval between two consecutive switching times is greater than a fixed quantity. We show how a state-feedback solution can be computed off-line through a numerical procedure.Alberto Bemporadalberto.bemporad@imtlucca.itDaniele CoronaAlessandro GiuaCarla Seatzu2011-07-27T09:03:57Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/501This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5012011-07-27T09:03:57ZHybrid control of an automotive robotized gearbox for reduction of consumptions and emissionsThis paper describes the application of hybrid modeling and receding horizon optimal control techniques for supervising an automotive robotized gearbox, with the goal of reducing consumptions and emissions, a problem that is currently under investigation at Fiat Research Center (CRF). We show that the dynamic behavior of the vehicle can be easily approximated and captured by the hybrid model, and through simulations on standard speed patterns that a good closed loop performance can be achieved. The synthesized control law can be implemented on automotive hardware as a piecewise affine function of the measured and estimated quantities. Alberto Bemporadalberto.bemporad@imtlucca.itPandeli BorodaniMassimo Mannelli2011-07-27T09:03:54Z2014-01-24T14:29:49Zhttp://eprints.imtlucca.it/id/eprint/627This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6272011-07-27T09:03:54ZHybrid Toolbox for MATLAB - User's GuideThe Hybrid Toolbox is a MATLAB/Simulink toolbox for modeling, simulating, and verifying hybrid dynamical systems, for designing and simulating model predictive controllers for hybrid systems subject to constraints, and for generating linear and hybrid MPC control laws in piecewise affine form that can be directly embedded as C-code in real-time applications.Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:02:45Z2011-08-05T14:03:07Zhttp://eprints.imtlucca.it/id/eprint/555This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5552011-07-27T09:02:45ZAn efficient algorithm for computing the state feedback optimal control law for discrete time hybrid systemsFrancesco BorrelliMato BaoticAlberto Bemporadalberto.bemporad@imtlucca.itManfred Morari2011-07-27T09:02:43Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/472This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4722011-07-27T09:02:43ZMin-max control of constrained uncertain discrete-time linear systemsFor discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.Alberto Bemporadalberto.bemporad@imtlucca.itFrancesco BorrelliManfred Morari2011-07-27T09:02:41Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/483This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4832011-07-27T09:02:41ZCorrigendum to: "The explicit linear quadratic regulator for constrained systems" [Automatica 38(1) (2002) 3-20]We apologize that Example 7.1 as publishedin Bemporad,
Morari, Dua, andPistikopoulos (2002) is incorrect due to a
miscalculation of the weight matrix P on the terminal stateAlberto Bemporadalberto.bemporad@imtlucca.itManfred MorariVivek DuaEfstratios N. Pistikopoulos2011-07-27T09:02:38Z2011-08-05T14:01:58Zhttp://eprints.imtlucca.it/id/eprint/557This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5572011-07-27T09:02:38ZFurther results on multiparametric quadratic programmingIn this paper we extend results on strictly convex multiparametric quadratic programming (mpQP) to the convex case. An efficient method for computing the mpQP solution is provided. We give a fairly complete description of the mpQP solver, focusing on implementational issues such as degeneracy handling.Petter TondelTor Arne JohansenAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T09:02:37Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/559This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5592011-07-27T09:02:37ZLogic-based hybrid solvers for optimal control of hybrid systemsCombinatorial optimization over continuous and integer variables was proposed recently as an useful tool for solving complex optimal control problems for linear hybrid dynamical systems formulated in discrete-time. Current approaches are based on mixed-integer linear/quadratic programming (MIP), which provides the solution after solving a sequence of relaxed standard linear (or quadratic) programs (LP, QP). An MIP formulation has the drawback of requiring that the discrete/logic part of the hybrid problem needs to be converted to into mixed-integer inequalities. Although this operation can be done automatically, most of the original discrete structure of the problem is lost during the conversion. Moreover, the efficiency of the MIP solver only relies upon the tightness of the continuous LP/QP relaxations. In this paper we attempt at overcoming such difficulties by combining MIP and constraint programming (CP) techniques into a "hybrid" solver, taking advantage of CP for dealing efficiently with satisfiability of logic constraints. We detail how to model the hybrid dynamics so that the optimal control problem can be solved by the hybrid MIP+CP solver, and show on a case study that the achieved performance is superior to the one achieved by pure MIP solvers.Alberto Bemporadalberto.bemporad@imtlucca.itNicolò Giorgetti2011-07-27T09:02:33Z2011-08-04T07:29:08Zhttp://eprints.imtlucca.it/id/eprint/560This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5602011-07-27T09:02:33ZMultiparametric nonlinear integer programming and explicit quantized optimal controlThis paper deals with multiparametric nonlinear integer programming problems where the optimization variables belong to a finite set and where the cost function and the constraints depend in an arbitrary nonlinear fashion on the optimization variables and in a linear fashion on the parameters. We examine the main theoretical properties of the optimizer and of the optimum as a function of the parameters, and propose a solution algorithm. The methodology is employed to investigate properties of quantized optimal control laws and optimal performance, and to obtain their explicit representation as a function of the state vector.Alberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:54:00Z2011-08-05T13:56:12Zhttp://eprints.imtlucca.it/id/eprint/562This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5622011-07-27T08:54:00ZStabilizing receding horizon control of piecewise linear systems: An LMI approachReceding horizon control has recently been used for regulating discrete-time Piecewise Affine (PWA) systems. One of the obstructions for implementation consists in guaranteeing closed-loop stability a priori. This is an issue that has only been addressed marginally in the literature. In this paper we present an extension of the terminal cost method for guaranteeing stability in receding horizon control to the class of unconstrained Piecewise Linear (PWL) systems. A linear matrix inequalities set-up is developed to calculate the terminal weight matrix and the auxiliary feedback gains that ensure stability for quadratic cost based receding horizon control. It is shown that the PWL statefeedback control law employed in the stability proof globally asymptotically stabilizes the origin of the PWL system. The additional conditions needed to extend these results to constrained PWA systems are also pointed out. The implementation of the proposed method is illustrated by an example.Mircea LazarW.P.M.H. HeemelsSiep WeilandAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:53:22Z2011-08-05T13:57:21Zhttp://eprints.imtlucca.it/id/eprint/561This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5612011-07-27T08:53:22ZRobust optimal control of linear hybrid systems: An MLD approachA methodology for synthesizing robust optimal input trajectories for constrained linear hybrid systems subject to bounded additive disturbances is presented. The computed control sequence optimizes nominal performance while robustly guarantees that safety/performance constraints are respected. Specifically, for hybrid systems representable in the piecewise affine form, robustness is achieved with an open-loop optimization strategy based on the mixed logical
dynamical modelling framework.Miguel Pedro SilvaMiguel Ayala BottoLuis PinaAlberto Bemporadalberto.bemporad@imtlucca.itJosé Sa da Costa2011-07-27T08:47:42Z2011-08-05T13:54:34Zhttp://eprints.imtlucca.it/id/eprint/564This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5642011-07-27T08:47:42ZA dynamic programming approach for determining the explicit solution of MPC controllersRecently multi-parametric methods have been applied with success to model predictive control (MPC) schemes. In this paper we propose a novel method for linear systems to obtain the explicit description of the control law that is based on dynamic programming and exploits the structure of the MPC formulation.David Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho2011-07-27T08:47:40Z2011-08-05T13:54:55Zhttp://eprints.imtlucca.it/id/eprint/565This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5652011-07-27T08:47:40ZRobust explicit MPC based on approximate multi-parametric convex programmingMany robust model predictive control (MPC) schemes require the online solution of a convex program, which can be computationally demanding. For deterministic MPC schemes, multi-parametric programming was successfully applied to move most computations offline. In this paper we adopt a general approximate multi-parametric algorithm recently suggested for convex problems and propose to apply it to a classical robust WC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded set.David Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T08:47:36Z2011-08-05T13:54:10Zhttp://eprints.imtlucca.it/id/eprint/521This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5212011-07-27T08:47:36ZStabilization conditions for model predictive control of constrained PWA systemsModel predictive control (MPC) has recently been applied to several relevant classes of hybrid systems with promising results. These developments generated an increasing interest towards issues such as stability and computational problems that arise in hybrid MPC. Stability aspects have been addressed only marginally. In this paper we present an extension of the terminal cost and constraint set method for guaranteeing stability in MPC to the class of constrained piecewise affine systems. Semidefinite programming is used to calculate the employed terminal weight matrix that ensures stability for quadratic cost based MPC. A procedure for computing a robust positively invariant set for piecewise linear systems is also developed. The implementation of the proposed method is illustrated by an example.Mircea LazarW.P.M.H. HeemelsSiep WeilandAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:47:24Z2011-08-05T13:52:14Zhttp://eprints.imtlucca.it/id/eprint/526This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5262011-07-27T08:47:24ZInfinity norms as Lyapunov functions for model predictive control of constrained PWA systemsIn this paper we develop a priori stabilization conditions for infinity norm based hybrid MPC in the terminal cost and constraint set fashion. Closed-loop stability is achieved using infinity norm inequalities that guarantee that the value function corresponding to the MPC cost is a Lyapunov function of the controlled system. We show that Lyapunov asymptotic stability can be achieved even though the MPC value function may be discontinuous. One of the advantages of this hybrid MPC scheme is that the terminal constraint set can be directly obtained as a sublevel set of the calculated terminal cost, which is also a local piecewise linear Lyapunov function. This yields a new method to obtain positively invariant sets for PWA systems. Mircea LazarW.P.M.H. HeemelsSiep WeilandAlberto Bemporadalberto.bemporad@imtlucca.itOctavian Pastravanu2011-07-27T08:47:22Z2011-08-05T13:51:39Zhttp://eprints.imtlucca.it/id/eprint/530This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5302011-07-27T08:47:22ZOn the stability and robustness of non-smooth nonlinear MPCThis paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with Model Predictive
Controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in
the Lyapunov sense and robust stability, while allowing for both the system dynamics and the value function of the MPC cost (the usual candidate Lyapunov function in MPC) to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear systems. As an application of the general theory, it is shown that Lyapunov stability is achieved in hybrid MPC. For a particular class of piecewise affine systems, a modified MPC set-up is proposed, which is proven to be robust to small additive disturbances via an input-to-state stability argument.Mircea LazarW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.itSiep Weiland2011-07-27T08:45:02Z2011-08-05T13:50:39Zhttp://eprints.imtlucca.it/id/eprint/531This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5312011-07-27T08:45:02ZModel predictive control of hybrid systems with applications to supply chain managementHybrid systems are dynamical systems whose behavior is determined by the interaction of continuous and discrete dynamics. Such systems arise in many real contexts, including automotive systems, chemical processes, communication networks, and supply chain management. A supply chain, whose goal is to transform ideas and raw materials into delivered products and services, is an example of a heterogeneous interconnection between continuous dynamics (inventory levels, material flows, etc.) and discrete dynamics (connection graphs, precedences, priorities, etc.). In general, in order to maximize a certain benefit or minimize certain costs, we have to optimally control all the heterogeneous components of the hybrid system. Model predictive control (MPC) is a well-known technique used in industry to (sub)optimally control dynamical processes, and is usually based on linear models.
This paper presents an overview of MPC techniques for hybrid systems. After giving a brief introduction to hybrid system models, model predictive control, and standard computation techniques, the paper summarizes recent results in using symbolic techniques and event-based formulations that exploit the particular structure of the hybrid process to come up with improved numerical computation schemes. The
concepts are illustrated through application examples in centralized management of supply chains.Alberto Bemporadalberto.bemporad@imtlucca.itStefano Di CairanoNicolò Giorgetti2011-07-27T08:44:00Z2011-08-05T13:44:03Zhttp://eprints.imtlucca.it/id/eprint/537This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5372011-07-27T08:44:00ZFeedback min-max model predictive control based on a quadratic cost functionFeedback min-max model predictive control based on a quadratic cost function is addressed in this paper. The main contribution is an algorithm for solving the min-max quadratic MPC problem with an arbitrary degree of approximation. The paper also introduces the "recourse horizon", which allows one to obtain a trade-off between computational complexity and performance of the control law. The results are illustrated by means of a simulation of a quadruple-tank processDavid Muñoz de la PeñaTeodoro AlamoAlberto Bemporadalberto.bemporad@imtlucca.itEduardo F. Camacho2011-07-27T08:43:58Z2016-04-06T10:27:04Zhttp://eprints.imtlucca.it/id/eprint/488This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4882011-07-27T08:43:58ZHybrid model predictive control application towards optimal semi-active suspensionThe optimal control problem of a quarter-car semi-active suspension has been studied in the past. Considering that a quarter-car semi-active suspension can either be modelled as a linear system with state dependent constraint on control (of actuator force) input, or a bi-linear system with a control (of variable damping coefficient) saturation, the seemingly simple problem poses several interesting questions and challenges. Does the saturated version of the optimal control law derived from the corresponding un-constrained system, i.e. “clipped-optimal”, remain optimal for the constrained case as suggested in some previous publications? Or should the optimal deviate from the “clipped-optimal” as suggested in other publications? If the optimal control law of the constrained system does deviate from its unconstrained counter-part, how different are they? What is the structure of the optimal control law? Does it retain the linear state feedback form (as the unconstrained case)? In this paper, we attempt to answer some of the above questions by utilizing the recent development in model predictive control (MPC) of hybrid dynamical systems.
The constrained quarter-car semi-active suspension is modelled as a switching affine system, where the switching is determined by the activation of passivity constraints, force saturation, and maximum power dissipation limits. Theoretically, over an infinite prediction horizon the MPC controller corresponds to the exact optimal controller. The performance of different finite-horizon hybrid MPC controllers is tested in simulation using mixed-integer quadratic programming. Then, for short-horizon MPC controllers, we derive the explicit optimal control law and show that the optimal control is piecewise affine in state. In the process, we show that for horizon equal to one the explicit MPC control law corresponds to clipped LQR as expected. We also compare the derived optimal control law to various semi-active control laws in the literature including the well-known “clipped-optimal”. We evaluate their corresponding performances for both a deterministic shock input case and a stochastic random disturbances case through simulations.Nicolò GiorgettiAlberto Bemporadalberto.bemporad@imtlucca.itH. E. TsengDavor Hrovat2011-07-27T08:43:56Z2011-08-05T13:43:06Zhttp://eprints.imtlucca.it/id/eprint/491This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4912011-07-27T08:43:56ZHybrid model predictive control of direct injection stratified charge enginesThis paper illustrates the application of hybrid modeling and model predictive control techniques to the management of air-to-fuel ratio and torque in advanced technology gasoline direct-injection stratified-charge (DISC) engines. A DISC engine is an example of a constrained hybrid dynamical system, because it can operate in two distinct modes (stratified and homogeneous) and because the mode-dependent constraints on the air-to-fuel ratio and on the spark timing need to be enforced during its operation to avoid misfire, knock, and high combustion variability. In this paper, we approximate the DISC engine dynamics as a two-mode discrete-time switched affine system. Using this approximation, we tune a hybrid model predictive controller with integral action based on online mixed-integer quadratic optimization, and show the effectiveness of the approach through simulations. Then, using an offline multiparametric optimization procedure, we convert the controller into an equivalent explicit piecewise affine form that is easily implementable in an automotive microcontroller through a lookup table of linear gainsNicolò GiorgettiGiulio RipaccioliAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat2011-07-27T08:43:52Z2011-08-05T13:42:05Zhttp://eprints.imtlucca.it/id/eprint/539This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5392011-07-27T08:43:52ZModel predictive control of nonlinear mechatronic systems: an application to a magnetically actuated mass spring damperMechatronic systems in the automotive applications are characterized by significant nonlinearities and tight performance specifications further exacerbated by state and input constraints. Model Predictive Control (MPC) in conjunction with hybrid modeling can be an attractive and systematic methodology to handle these challenging control problems. In this paper, we focus on a mass spring damper system actuated by an electromagnet, which is one of the most common elements in the automotive actuators, with fuel injectors representing a concrete example. We present two designs which are based, respectively, on a linear MPC approach in cascade with a nonlinear state-dependent saturation, and on a hybrid MPC approach. The performance and the complexity of the two MPC controllers are compared.Stefano Di CairanoAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat2011-07-27T08:43:50Z2011-08-04T07:29:07Zhttp://eprints.imtlucca.it/id/eprint/498This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4982011-07-27T08:43:50ZEvent-based model predictive control and verification of integral continuous-time hybrid automataThis paper proposes an event-driven model predictive control scheme with guaranteed closed-loop convergence properties for the class of integral continuous-time hybrid automata (icHA). After converting icHA to a corresponding event-driven representation that allows one to compute the model predictive control action by mixed integer programming, sufficient conditions ensuring event-asymptotic and time-asymptotic convergence are proven. The paper also shows how the same modeling methodology can be employed to efficiently solve problems of verification of safety properties. Alberto BemporadStefano Di CairanoJorge Júlvez2011-07-27T08:43:46Z2011-08-05T13:40:55Zhttp://eprints.imtlucca.it/id/eprint/454This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4542011-07-27T08:43:46ZAn MPC/hybrid system approach to traction controlThis paper describes a hybrid model and a model predictive control (MPC) strategy for solving a traction control problem. The problem is tackled in a systematic way from modeling to control synthesis and implementation. The model is described first in the Hybrid Systems Description Language to obtain a mixed-logical dynamical (MLD) hybrid model of the open-loop system. For the resulting MLD model, we design a receding horizon finite-time optimal controller. The resulting optimal controller is converted to its equivalent piecewise affine form by employing multiparametric programming techniques, and finally experimentally tested on a car prototype. Experiments show that good and robust performance is achieved in a limited development time by avoiding the design of ad hoc supervisory and logical constructs usually required by controllers developed according to standard techniques.Francesco BorrelliAlberto Bemporadalberto.bemporad@imtlucca.itMichael FodorDavor Hrovat2011-07-27T08:43:40Z2011-08-05T13:37:53Zhttp://eprints.imtlucca.it/id/eprint/543This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5432011-07-27T08:43:40ZConvex Polyhedral Invariant Sets for Closed-Loop Linear MPC Systems Given an asymptotically stabilizing linear MPC controller, this paper proposes an algorithm to construct invariant polyhedral sets for the closed-loop system. Rather than exploiting an explicit form of the MPC controller, the approach exploits a recently developed DC (Difference of Convex functions) programming technique developed by the authors to construct a polyhedral set in between two convex sets. Here, the inner convex set is any given level set V(x) les gamma of the MPC value function (implicitly defined by the quadratic programming problem associated with MPC or explicitly computed via multiparametric quadratic programming), while the outer convex set is the level set of a the value function of a modified multiparametric quadratic program (implicitly or explicitly defined). The level gamma acts as a tuning parameter for deciding the size of the polyhedral invariant containing the inner set, ranging from the origin (gamma = 0) to the maximum invariant set around the origin where the solution to the unconstrained MPC problem remains feasible, up to the whole domain of definition of the controller (possibly the whole state space Ropfn) (gamma = inf). Potential applications of the technique include reachability analysis of MPC systems and generation of constraints to supervisory decision algorithms on top of MPC loopsAlessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.itW.P.M.H. HeemelsMircea Lazar2011-07-27T08:40:49Z2011-08-04T07:29:07Zhttp://eprints.imtlucca.it/id/eprint/544This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5442011-07-27T08:40:49ZModel predictive control Design: New Trends and Tools Model-based design is well recognized in industry as a systematic approach to the development, evaluation, and implementation of feedback controllers. Model predictive control (MPC) is a particular branch of model-based design: a dynamical model of the open-loop process is explicitly used to construct an optimization problem aimed at achieving the prescribed system's performance under specified restrictions on input and output variables. The solution of the optimization problem provides the feedback control action, and can be either computed by embedding a numerical solver in the real-time control code, or pre-computed off-line and evaluated through a lookup table of linear feedback gains. This paper reviews the basic ideas of MPC design, from the traditional linear MPC setup based on quadratic programming to more a advanced explicit and hybrid MPC, and highlights available software tools for the design, evaluation, code generation, and deployment of MPC controllers in real-time hardware platformsAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:40:43Z2012-03-30T10:34:59Zhttp://eprints.imtlucca.it/id/eprint/495This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4952011-07-27T08:40:43ZLogic-based solution methods for optimal control of hybrid systemsCombinatorial optimization over continuous and integer variables is a useful tool for solving complex optimal control problems of hybrid dynamical systems formulated in discrete-time. Current approaches are based on mixed-integer linear (or quadratic) programming (MIP), which provides the solution after solving a sequence of relaxed linear (or quadratic) programs. MIP formulations require the translation of the discrete/logic part of the hybrid problem into mixed-integer inequalities. Although this operation can be done automatically, most of the original symbolic structure of the problem (e.g., transition functions of finite state machines, logic constraints, symbolic variables, etc.) is lost during the conversion, with a consequent loss of computational performance. In this paper, we attempt to overcome such a difficulty by combining numerical techniques for solving convex programming problems with symbolic techniques for solving constraint satisfaction problems (CSP). The resulting "hybrid" solver proposed here takes advantage of CSP solvers for dealing with satisfiability of logic constraints very efficiently. We propose a suitable model of the hybrid dynamics and a class of optimal control problems that embrace both symbolic and continuous variables/functions, and that are tailored to the use of the new hybrid solver. The superiority in terms of computational performance with respect to commercial MIP solvers is shown on a centralized supply chain management problem with uncertain forecast demand.Alberto Bemporadalberto.bemporad@imtlucca.itNicolò Giorgetti2011-07-27T08:40:40Z2011-08-05T13:20:31Zhttp://eprints.imtlucca.it/id/eprint/489This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4892011-07-27T08:40:40ZRobust explicit MPC based on approximate multi-parametric convex programmingMany robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded setDavid Muñoz de la PeñaAlberto Bemporadalberto.bemporad@imtlucca.itCarlo Filippi2011-07-27T08:40:33Z2011-08-05T13:19:18Zhttp://eprints.imtlucca.it/id/eprint/493This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4932011-07-27T08:40:33ZStabilizing model predictive control of hybrid systemsIn this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, infin-norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theoryMircea LazarW.P.M.H. HeemelsSiep WeilandAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:40:30Z2011-08-05T13:15:12Zhttp://eprints.imtlucca.it/id/eprint/505This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5052011-07-27T08:40:30ZModel predictive control of magnetic automotive actuatorsMagnetically actuated mass-spring-damper systems are common in automotive systems as components of various actuation mechanisms. They are characterized by nonlinear dynamics, tight performance specifications and physical constraints. Due to these reasons, model predictive control (MPC) is an appealing control framework for such systems. In this paper we describe different MPC approaches to control the magnetically actuated mass-spring-damper system. The MPC controller based on the complete system model achieves very good performance, yet it may be too complex to be implemented in standard automotive microcontrollers. Hence, we consider the possibility of decoupling the electromagnetic subsystem from the mechanical subsystem, assuming that the electromagnetic dynamics, controlled by an inner-loop controller, are much faster than the mechanical dynamics. Based on a previous feasibility study, we implement a control architecture in which the MPC optimizes only the dynamics of the mechanical subsystem, and we test it in closed-loop simulations with the nonlinear system. The resulting control system achieves lower performance, but it is simple enough to be implemented in an automotive microcontroller.Stefano Di CairanoAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat2011-07-27T08:39:28Z2011-08-05T13:18:09Zhttp://eprints.imtlucca.it/id/eprint/527This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5272011-07-27T08:39:28ZOn hybrid model predictive control of sewer networksReal-time control (RTC) of sewer-network systems plays an important role in meeting increasingly restrictive environmental regulations to reduce release of untreated wastewater to the environment. This chapter presents the application of hybrid model predictive control (HMPC) on sewer systems. It is known from the literature that HMPC has a computational complexity growing exponentially with the size of the system to be controlled. However, the average solution time of modern mixed integer program (MIP) solvers is often much better than the predicted worst-case-solution time. The problem is to know when the worst-case computational complexity appears. In addition to presenting the application, a secondary aim of the chapter is to discuss the limits of applicability due to real-time constraints on computation time when HMPC is applied on large-scale systems such as sewer networks. By using a case study of a portion of the Barcelona sewer system, it is demonstrated how the computational complexity of HMPC appears for certain state and disturbance combinations. Carlos Ocampo-MartinezAlberto Bemporadalberto.bemporad@imtlucca.itAri IngimundarsonVincenç Puig Cayuela2011-07-27T08:39:18Z2011-08-05T13:17:43Zhttp://eprints.imtlucca.it/id/eprint/516This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5162011-07-27T08:39:18ZDiscrete-time non-smooth nonlinear MPC: Stability and robustnessThis paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with model predictive controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in the Lyapunov sense and input-to-state stability (ISS), while allowing for both the system dynamics and the value function of the MPC cost to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear. For a particular class of discontinuous piecewise affine systems, a new MPC set-up based on infinity norms is proposed, which is proven to be ISS to bounded additive disturbances. This ISS result does not require continuity of the system dynamics nor of the MPC value function. Mircea LazarW.P.M.H. HeemelsAlberto Bemporadalberto.bemporad@imtlucca.itSiep Weiland2011-07-27T08:39:11Z2011-08-05T13:16:49Zhttp://eprints.imtlucca.it/id/eprint/508This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5082011-07-27T08:39:11ZSuboptimal model predictive control of hybrid systems based on mode-switching constraintsModel predictive control (MPC) is recognized as a very versatile and effective way of controlling constrained hybrid dynamical systems in closed-loop. The main drawback of hybrid MPC is the heavy computation burden of the associated on-line mixed-integer optimization. Explicit MPC solutions overcome such a problem by rewriting the control law in piecewise affine form, but are limited to relatively simple hybrid control problem setups. This paper presents an alternative approach for reducing the complexity of computations by suitably constraining the mode sequence over the prediction horizon, so that on-line optimization is solved more quickly. While tracking performance of the feedback loop may be affected because of the suboptimality of the approach, closed- loop stability is guaranteed. The effectiveness of the method is demonstrated by an example.Ari IngimundarsonCarlos Ocampo-MartinezAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:39:08Z2011-08-04T07:29:07Zhttp://eprints.imtlucca.it/id/eprint/545This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5452011-07-27T08:39:08ZA wireless magneto-resistive sensor network for real-time vehicle detectionThis works describes a prototype wireless sensor network for vehicle detection developed at the University of Siena in collaboration with the Italian highways society Autostrade S.p.A. Each wireless sensor node is composed by an in-house designed electronic board driving a 2-axis Honeywell HMC1002 magneto-resistive sensor interfaced to a Telos rev.b (Moteiv Corporation) mote, and by a Matlab/Simulink interface for collecting and processing sensor data in (soft) real-time.Alberto Bemporadalberto.bemporad@imtlucca.itF. GentileA. MecocciFrancesco MolendiF. Rossi2011-07-27T08:39:05Z2011-08-05T13:15:39Zhttp://eprints.imtlucca.it/id/eprint/484This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4842011-07-27T08:39:05ZModel predictive control of magnetically actuated mass spring dampers for automotive applicationsMechatronic systems such as those arising in automotive applications are characterized by significant non-linearities, tight performance specifications as well as by state and input constraints which need to be enforced during system operation. This paper takes a view that model predictive control (MPC) and hybrid models can be an attractive and systematic methodology to handle these challenging control problems, even when the underlying process is not hybrid. In addition, the piecewise affine (PWA) explicit form of MPC solutions avoids on-line optimization and can make this approach computationally viable even in situations with rather constrained computational resources. To illustrate the MPC design procedure and the underlying issues, we focus on a specific non-linear process example of a mass spring damper system actuated by an electromagnet. Such a system is one of the most common elements of mechatronic systems in automotive systems, with fuel injectors representing a concrete example. We first consider a linear MPC design for the mechanical part of the system. The approach accounts for all the constraints in the system but one, which is subsequently enforced via a state-dependent saturation element. Second, a hybrid MPC approach for the mechanical subsystem is analysed that can handle all the constraints by design and achieves better performance, at the price of a higher complexity of the controller. Finally, a hybrid MPC design that also takes into account the electrical dynamics of the system is considered.Stefano Di CairanoAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat2011-07-27T08:39:04Z2011-08-04T07:29:06Zhttp://eprints.imtlucca.it/id/eprint/509This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5092011-07-27T08:39:04ZHybrid modeling and control of a multibody magnetic actuator for automotive applicationsThis paper investigates model predictive control (MPC) techniques based on hybrid models for a multi-mass magnetic actuator. The actuator has four operating modes depending on the mutual interaction of two moving masses and is modeled as a hybrid dynamical system. The control law optimizes a performance index and enforces several types of constraints: soft-landing during collisions to reduce mechanical wear, current limits and consequent position-dependent nonlinear bounds on the available magnetic force, and restrictions on the positions of the moving masses. Two different approaches are considered: (i) a hybrid MPC design based on the full two- mass model, and (ii) a switched MPC control design, which switches between two simpler hybrid MPC controllers, one for the case in which the masses are moving in contact, and the other case where the masses are decoupled, commanded by a simple switching logic. Simulation results and performance comparisons of the two control schemes are discussed.Alberto Bemporadalberto.bemporad@imtlucca.itStefano Di CairanoIlya KolmanovskyDavor Hrovat2011-07-27T08:36:41Z2014-01-20T15:22:08Zhttp://eprints.imtlucca.it/id/eprint/507This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/5072011-07-27T08:36:41ZDecentralized model predictive control of constrained linear systemsAlessandro AlessioAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:36:32Z2011-08-05T12:59:33Zhttp://eprints.imtlucca.it/id/eprint/478This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4782011-07-27T08:36:32ZHybrid model predictive control of a solar air conditioning plantThis paper describes the development and experimental validation ofamulti-layerhybrid controller for optimizing energy management inasolar air conditioning plant. The hybrid nature of the process is due to its multi-mode structure: the refrigeration circuit can be fed by flat solar collectors,astorage system, by an auxiliary gas heater, or byacombination of them. The selection of the operating mode is obtained by switching electrovalves, pumps, and three-way mixing valves. The proposed multi-layer hybrid controller consists ofahigh-level supervisor that decides on-line the optimal operating mode throughahybrid model predictive control strategy,astatic lower-level controller defining proper set-points for the chosen mode, and existing standard low-levelc on trollers that ensure robust tracking of such set-points. The overall controller was designed in Matlab/Simulink using the Hybrid Toolbox, and then tested experimentallyareal process, showing the effectiveness of the approach. P. MenchinelliAlberto Bemporadalberto.bemporad@imtlucca.it2011-07-27T08:34:14Z2014-07-02T14:30:10Zhttp://eprints.imtlucca.it/id/eprint/433This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4332011-07-27T08:34:14ZModel predictive control for systems with time delay: an application to air-fuel ratio control in automotive enginesTo meet increasingly stringent emission regulations modern internal combustion engines require highly accurate control of the air-to-fuel ratio. The performance of the conventional air-to-fuel ratio feedback loop is limited by the combustion delay between fuel injection and engine exhaust, and by the transport delay for the exhaust gas to propagate to the air-to-fuel ratio sensor location. The combined delay is variable, since it depends on engine speed and airflow. Drivability, fuel economy and emission requirements result in constraints on the deviations of the air-to-fuel ratio, stored oxygen in the three-way catalyst, and fuel injection. This paper proposes an approach for air-to-fuel ratio control based on Model Predictive Control (MPC). The approach systematically handles both variable time delays and pointwise-in-time constraints. A delay-free model is considered first, which takes into account the dynamic relations between the injected fuel and the air-to-fuel ratio and the dynamics of the oxygen stored in the catalyst. For the delay-free model, the explicit MPC law is computed. Delay compensation is obtained by estimating the delay online from engine operating conditions, and feeding the MPC law with the state predicted ahead over the time interval of the estimated delay. The predicted state is computed by combining measurement filtering with forward iterations of the nonlinear dynamic equations of the model. The achieved performance in tracking the air-to-fuel ratio and the oxygen storage setpoints while enforcing the constraints is demonstrated in simulation using real data profiles.Sergio TrimboliStefano Di CairanoAlberto Bemporadalberto.bemporad@imtlucca.itIlya Kolmanovsky2011-07-27T08:31:52Z2011-08-05T12:34:42Zhttp://eprints.imtlucca.it/id/eprint/431This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/4312011-07-27T08:31:52ZDecentralized model predictive control of dynamically-coupled linear systems: tracking under packet lossFor large-scale processes whose dynamics can be represented as the interaction of several dynamically-coupled linear subsystems, this paper proposes a decentralized model predictive control (MPC) design approach for set-point tracking under input constraints and possible loss of information packets. Following earlier results in (Alessio and Bemporad, 2007 and 2008), the global model of the process is approximated as the decomposition of several (possibly overlapping) smaller models used for local predictions. We present sufficient criteria for asymptotic tracking of output set-points and rejection of constant measured disturbances when the overall process is in closed loop with the set of decentralized MPC controllers, under possible intermittent lack of communication of measurement data between controllers. The effectiveness of the approach is shown in a simulation example on distributed temperature control in the passenger area of a railcar.Davide BarcelliAlberto Bemporadalberto.bemporad@imtlucca.it2011-06-21T10:13:44Z2011-08-05T12:57:37Zhttp://eprints.imtlucca.it/id/eprint/615This item is in the repository with the URL: http://eprints.imtlucca.it/id/eprint/6152011-06-21T10:13:44ZAn MPC design flow for automotive control and applications to idle speed regulationThis paper describes the steps of a model predictive control (MPC) design procedure developed for a broad class of control problems in automotive engineering. The design flow starts by deriving a linearized discrete-time prediction model from an existing simulation model, augmenting it with integral action or output disturbance models to ensure offset-free steady-state properties, and tuning the resulting MPC controller in simulation. Explicit MPC tools are employed to synthesize the controller to quickly assess controller complexity, local stability of the closed-loop dynamics, and for rapid prototype testing. Then, the controller is fine-tuned by refining the linear prediction model through identification from experimental data, and by adjusting from observed experimental performance the values of weights and noise covariances for filter design. The idle speed control (ISC) problem is used in this paper to exemplify the design flow and our vehicle implementation results are reported.Stefano Di CairanoDiana YanakievAlberto Bemporadalberto.bemporad@imtlucca.itIlya KolmanovskyDavor Hrovat