Homogenization of multi-phase composites based on a revisited formulation of the multi-coated inclusion problem

In this work, the effective elastic properties of composite materials with multi-coated reinforcements are estimated by a new formulation of the multi-inclusion model based on Green's functions technique and integral equation which gives the local strain and stress fields through strain concentration equations in each phase of the composite-inclusion. The effective behavior of multi-coated inclusion-reinforced material is determined within a ‘(N+1)-phase’ Generalized Self-Consistent Scheme. To assess the present model's reliability, some comparisons with other micromechanical models and exact solutions are presented. The model is applied to two-phase and three-phase materials and the results are compared to exact analytical solutions for the case of spherical inclusion and isotropic elastic behavior. Some results for three-phase materials are given regarding the influence of constituents’ volume fraction. Furthermore, the effects of the mechanical contrast between phases and the shape of inclusions are studied.