Effective Yield Surfaces for Anisotropic Composite Materials

Abstract

This work deals with the development of effective yield surfaces for two-phase composite materials made of homogeneous, isotropic, rigid/perfectly plastic constituents. For our purposes, a composite is a heterogeneous material with two distinct length scales: a macroscopic one, L ~ O(1), characterizing the overall dimensions of the specimen and the scale of variation of the applied loading conditions, and a microscopic one, l << L, characterizing the size of the typical heterogeneity (e.g., an inclusion). By effective properties, we mean the relation between the averages of the local stress and strain-rate fields within the composite. We consider the special class of microstructures consisting of aligned, self-similar, ellipsoidal inclusions distributed according to “ellipsoidal” two-point correlation functions in a matrix of another phase. Estimates of the Hashin-Shtrikman [6] type for the effective behaviour of linearly viscous (mathematically analogous to linear elastic) composites with this class of particulate microstructures were developed by Willis [14], [15]. They will be used here to generate corresponding estimates for the effective yield functions of the rigid/perfectly plastic composites by means of the variational procedure of Ponte Castaneda [7], [8].