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Second-order computational homogenization of heterogeneous materials with periodic microstructure

Bacigalupo, Andrea and Gambarotta, Luigi Second-order computational homogenization of heterogeneous materials with periodic microstructure. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 90 (10-11). pp. 796-811. ISSN 0044-2267 (2010)

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A 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.

Item Type: Article
Identification Number: 10.1002/zamm.201000031
Uncontrolled Keywords: Second-order continuum, computational homogenization, periodic microstructure, boundary layer effect, material characteristic length.
Subjects: T Technology > TJ Mechanical engineering and machinery
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 20 Jan 2015 14:44
Last Modified: 20 Jan 2015 14:44
URI: http://eprints.imtlucca.it/id/eprint/2530

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