Analysis of In-Plane Problems for an Isotropic Elastic Medium with Many Circular Elastic Inclusions

Abstract

This paper presents general solutions for problems involving many circular elastic inclusions that are perfectly bonded to an elastic medium(matrix) of infinite extent under in-plane deformation. These many elastic inclusions may have different radii, central points and possess different elastic properties. The matrix is assumed to be subjected to arbitrary loading, for example, by uniform stresses at infinity. The solutions were obtained through iterations of the Möbius transformation as series with an explicit general term involving the complex potential functions of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.