Homogenization of elastic-viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes. (English) Zbl 1162.74037

Summary: This paper deals with the prediction of macroscopic behavior of a multiphase elastic-viscoplastic material. The proposed homogenization schemes are based on an interaction law postulated by A. Molinari et al. [Mech. Mater. 26, 43–62 (1997)]. 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 in the literature and predictions based on the interaction law are performed and have demonstrated the efficiency of the proposed homogenization schemes.


74Q15 Effective constitutive equations in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics
74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74E30 Composite and mixture properties
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