@incollection{eprints2514,
            note = {8th World congress on computational mechanics, WCCM8 - 5th European congress on computational methods in applied sciences and engineering, ECCOMAS 2008, held in Venice (Italy), 30 June - 4 July 2008},
       publisher = {CIMNE},
           pages = {1--2},
       booktitle = {  Cover image  Title     8th World congress on computational mechanics, WCCM8 - 5th European congress on computational methods in applied sciences and engineering, ECCOMAS 2008},
          author = {Andrea Bacigalupo and Luigi Gambarotta},
            year = {2008},
           title = {Cosserat homogenization of elastic periodic blocky masonry},
             url = {http://eprints.imtlucca.it/2514/},
        abstract = {In 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.},
        keywords = {Homogenization, Masonry, Micropolar elasticity, Multiscale models}
}