The overall response of composite materials with inclusions

Abstract

The elastic field of composite materials with inclusions is presented in terms of the integrals of Green's functions. After averaging the strain and stress fields and performing some manipulations and approximations, we obtain the corresponding effective elastic moduli which are related to the integrals of the two-point correlation function. From the expressions obtained, it can be found that the effective elastic moduli of composite materials with inclusions depend on the moduli of two components, the volume fraction of inclusions, as well as the shape, size and distribution of inclusions, and interactions between them. In contrast to previous works, e.g., the self-consistent method, the differential scheme, the Mori-Tanaka method and the generalized selfconsistent method, the present method can analyze the effect of the distribution of inclusions on the overall elastic moduli of composite materials, providing that composite materials have periodic microstructures. Finally, some analyses for the effect of the shape, size and distribution of inclusions on the effective elastic moduli of composite materials are given and comparisons with existing methods and experimental results are also considered and discussed.