Modeling the mechanical behaviour of heterogeneous multi-phase materials

Many materials of engineering interest have highly heterogeneous microstructures. To a first approximation, the response of multi-phase materials to external stimuli such as mechanical loading depends on global parameters such as average particle size or phase volume fraction. Most classical models of materials behaviour are based on such an assumption. It is clear however that an accurate description must include parameters that characterize the distribution of phases. Moreover, some processes that we wish to model are inherently stochastic in nature. This adds considerable complexity. First, the quantitative description of microstructure containing higher order moments is fraught with difficulties — both analytical and experimental. Second, the inclusion of clustering into analytical models is prone to assumptions and approximations. In this paper we will restrict ourselves to phenomena for which a continuum approach is adequate. For these, self-consistent approaches are especially valuable. The two examples that we discuss in some depth are related to (i) damage in porous, brittle films such as thermal barrier coatings and (ii) the simultaneous effects of damage and particle clustering on the elasto-plastic response of metal matrix composites.