Integral formulation and self-consistent modelling of elastoviscoplastic behavior of heterogeneous materials

Based on projection operators, an integral formulation is proposed for elas toviscoplastic heterogeneous materials. The problem requires a complete mec hanical formulation, including the static equilibrium property concerning t he known field sigma, in addition to the classical field equations concerni ng the unknown fields (epsilon) over dot and (sigma) over dot. The formulat ion leads to an integral equation, in which elasticity and viscoplasticity effects interact through an homogeneous elastoviscoplastic medium with elas tic moduli C and viscoplastic moduli B. To approximate the integral equation, the self-consistent scheme is followe d. In order to obtain consistent approximation conditions, we introduce flu ctuations of elastic and viscoplastic strain rate fields with respect to kn own kinematically compatible fields. It results in a strain rate concentrat ion relation connecting the strain rate at each point to the macroscopic lo ading conditions and the local stress held. The results are presented and c ompared with other models and with experimental data in the case of a two-p hase material.