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

In the present paper, we derive a solution for two circular elastic inclusions that are perfectly bonded to an elastic medium (matrix) of infinite extent under in-plane deformation. These two inclusions have different radii, central points, and elasticities. The matrix is subjected to arbitrary loading by, for example, uniform stresses, as well as to a concentrated force at an arbitrary point. In this paper, we present a solution under uniform stresses at infinity as an example. The solution is obtained through iterations of the Mö bius transformation as a series with an explicit general term involving the complex potential of the corresponding homogeneous problem. This procedure is referred to as heterogenization. Using these solutions, several numerical examples are presented graphically.