Micromechanical analysis of heterogeneous materials subjected to overall Cosserat strains

• A Cosserat and a Cauchy medium are coupled for a two-scale homogenization.
• A higher-order kinematic map is formulated depending on the Cosserat macro-strains.
• Unit cells made of heterogeneous periodic materials are analyzed.
• The displacement perturbation distribution in the heterogeneous medium is studied.
• Boundary conditions on the UC more complex than the classical periodic ones emerge.

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