New micromechanical approach of the coated inclusion problem: Exact solution and applications

In this work, a new micromechanical model for the solution of the problem of coated inclusion embedded in an infinite homogeneous medium is presented. The method is based on the Green functions technique and the concept of the interior and exterior-point Eshelby tensors for an ellipsoidal inclusion. The proposed formulation is general and can be successfully applied to ellipsoidal coated inclusion in the case of anisotropic elasticity. For the particular case of spherical coated inclusion and isotropic behaviour, the exact analytic solution in terms of strain localisation tensors inside inclusion and in the coating is obtained. Using the generalized self-consistent scheme, we determine the effective elastic properties of a material containing spherical inclusions. The provided results are compared with the exact solution and other models and also with experimental data in the case of a two-phase material.