On the Cosserat-Cauchy homogenization procedure for heterogeneous periodic media

In the present paper the homogenization problem of periodic composites is investigated, in the case of a Cosserat continuum at the macro-level and a Cauchy continuum at the micro-level. In the framework of a strain-driven approach, the two levels are linked by a kinematic map based on a third order polynomial expansion. The determination of the displacement perturbation ¯elds in the Unit Cell (UC), arising when second or third order polynomial boundary conditions are imposed, is investigated. A new micromechanical approach, based on the decomposition of the perturbation ¯elds in terms of functions which depend on the macroscopic strain components, is proposed. The identi¯cation of the linear elastic 2D Cosserat constitutive parameters is performed, by using a Hill-Mandel-type macrohomogeneity condition. The in°uence of the selection of the UC is analyzed and some critical issues are outlined. Numerical examples referred to a speci¯c composite with cubic symmetry are shown.