Homogenization of elasto-plastic composites coupled with a nonlinear finite element analysis of the equivalent inclusion problem

Abstract

This paper deals with the micromechanical modeling of particle reinforced elasto-plastic composites under general non-monotonic loading histories. Incremental mean-field (MF) homogenization models offer an excellent cost-effective solution, however there are cases where their predictions are inaccurate. Here, we assess the applicability of the equivalent inclusion representation, which sustains many homogenization schemes. To this end, MF models are fully coupled with a finite element (FE) solution of the equivalent inclusion problem (EIP). Consequently, Eshelby’s tensor is not used and most (but not all) approximations involved in the generalization of MF models from linear elasticity to the nonlinear regime are avoided. The proposal is implemented for Mori-Tanaka (M-T) and dilute inclusion models and applied to several composite systems with elasto-plastic matrix and spherical or ellipsoidal particles, subjected to various loadings (tension, plane strain, cyclic tension/compression). The predictions are verified against reference full-field FE simulations of multiparticle cells. Results show that the M-T model coupled with the nonlinear FE solution of the EIP is very accurate at the macro level up to 25% volume fraction of reinforcement, while the phase averages remain accurate as long as the volume fraction does not exceed 15%. The strain concentration tensor computed almost exactly from single inclusion FE analysis is compared against approximate expressions assumed by classical MF models. Implications for the development of advanced MF homogenization models are discussed.