Homogenization of elastic-viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes

This paper deals with the prediction of the macroscopic behavior of a multiphase elastic-viscoplastic material. The proposed homogenization schemes are based on an interaction law postulated by Molinari et al. [Molinari, A., Ahzi, S., Kouddane, R. 1997. On the self-consistent modelling of elastic-plastic behavior of polycrystals. Mech. Mater., 26, 43-62]. Self-consistent schemes are developed to describe the behavior of disordered aggregates. The Mori-Tanaka approach is used to capture the behavior of composite materials, where one phase can be clearly identified as the matrix. The proposed schemes are developed within a general framework where compressible elasticity and anisotropy of the materials are taken into account. Inclusions can have various shapes and orientations. Illustrations of the homogenization procedure are given for a two-phase composite materials. Comparisons between results of the literature and predictions based on the interaction law are performed and have demonstrated the efficiency of the proposed homogenization schemes. (C) 2008 Elsevier Ltd. All rights reserved.