TWO STABLE-BY-HOMOGENIZATION MODELSIN SIMPLE SHEARING OF RATE-DEPENDENTNON-HOMOGENEOUS MATERIALS

摘要

In this paper we study two models, the viscoplastic model and the thermo-viscous model, of rate-dependent non-homogeneous materials with non-oscillating strain-rate sensitivity submitted to simple quasistatic shearing. We prove that the two models are stable by homogenization, i.e. that the equations in both the heterogeneous problems and the homogenized one have the same form, and we give explicit formulas for the ho-mogenized (effective) coefficients. These formulas depend on the initial conditions, but not on the boundary conditions. Our theoretical results are illustrated by a numerical example.