The problem of elastic inclusions at finite concentration

This paper is aimed at determining the overall properties and the local stresses of a composite material. The material is constituted of elastic ellipsoidal inclusions suspended in a homogeneous elastic matrix. An analytical approximate method is proposed to account for the interaction between the inclusions at finite concentration. This approach is based on a formulation of the problem of heterogeneous elasticity proposed by Zeller, R. and Dederichs, P. H. (1973). Elastic constant of polycrystals, Phys. Status Solidi B 55, 831-842. The zero order approximation of our scheme, coincides with the MO&Tanaka method when the inclusions are spherical, but improves significantly this method when higher order approximations are considered. The morphological and spatial distribution of the inclusions is accounted for in our scheme. Through different examples, it is shown how our results compare to existing analytical or numerical solutions. Copyright 0 1996 Published by Elsevier Science Ltd