Micromechanical analysis of heterogeneous materials subjected to overall Cosserat strains

tIn the framework of the computational homogenization procedures, the problem of coupling a Cosseratcontinuum at the macroscopic level and a Cauchy medium at the microscopic level, where a hetero-geneous periodic material is considered, is addressed. In particular, non-homogeneous higher-orderboundary conditions are defined on the basis of a kinematic map, properly formulated for taking intoaccount all the Cosserat deformation components and for satisfying all the governing equations at themicro-level in the case of a homogenized elastic material. Furthermore, the distribution of the pertur-bation fields, arising when the actual heterogeneous nature of the material is taken into account, isinvestigated. Contrary to the case of the first-order homogenization where periodic fluctuations arise, inthe analyzed problem more complex distributions emerge.