Combined mean-field and full-field homogenization of porous elasto-plastic materials and composites under arbitrary stress triaxialities

Abstract

A predictive micromechanical approach is proposed for porous materials where the unreinforced or reinforced matrix phase is elasto-plastic with hardening. The cavities can be spheres, long or short cylinders. The approach is based on an alternative microstructure made of elasto-plastic inhomogeneities embedded in a homogenized porous matrix phase, and the volume fractions are determined from a maximum packing argument. The effective properties of single hollow solids are computed with an energy-based approach coupled with full-field finite element (FE) analyses. Next, the alternative microstructures are homogenized with mean-field (MF) models. For reinforced porous materials, a two-level method is adopted, where the proposed approach is used at the lower level to obtain a fictitious homogenized matrix, in which reinforcements are embedded at the upper level. The present work is restricted to monotonic and proportional loadings and to the secant formulation of isotropic or transversely isotropic elasto-plasticity. However, no constitutive models are supposed or identified. The predictions were verified against reference full-field FE results on the actual microstructures in 3D and 2D plane strain or stress, for arbitrary stress triaxialities, and good agreement was found in all cases.