Averaging Models for Heterogeneous Viscoplastic and Elastic Viscoplastic Materials

Averaging models are proposed for viscoplastic and elastic-viscoplastic heterogeneous materials. The case of rigid viscoplastic materials is first discussed. Large deformations are considered. A first class of models is based on different linearizations of the nonlinear local response. A second class of models is obtained from approximate solutions of the nonlinear Eshelby problem. In this problem, an ellipsoid with uniform nonlinear properties is embedded in an infinite homogeneous matrix. An approximate solution is obtained by approaching the matrix behavior with an affine response. Using this solution of the nonlinear Eshelby problem, the average strain rate is calculated in each phase of the composite material, each phase being represented by an ellipsoid embedded in an infinite reference medium. By adequate choices of the reference medium, different averaging models are obtained (self-consistent scheme, nonlinear Mori Tanaka model…). Finally, elasticity is included in the modelling, but with a restriction to small deformations.