Computational homogenization of composites experiencing plasticity, cracking and debonding phenomena

Aim of the present paper is the development of a homogenization technique able to determine the overall mechanical response of composite materials taking into account the cracking and plastic behavior of its constituents and the decohesion process among them. A representative volume element of a composite material is studied. The plastic effects in the constituents are considered introducing a plastic model with isotropic and kinematic hardening. The debonding between constituents and the cracking process are described introducing a cohesive damage interface model that takes into account also the unilateral contact and frictional effects. In particular, a new procedure based on the nonuniform Transformation Field Analysis is presented. The plastic strains in the constituents and the inelastic relative displacements along the interfaces are approximated as linear combinations of inelastic scalar modes that are functions of the spatial variables. The coefficients of the linear combinations are the internal variables of the problem that are computed solving the evolutive problem. Some numerical applications are carried out to verify the efficiency of the proposed homogenization approach in reproducing the overall mechanical response of composites characterized by cracking and plastic phenomena in the constituents and debonding between them. The homogenization results are compared with the solution obtained by micro-mechanical nonlinear finite element analyses.