Explicit Solutions of Plane Elastostatics Problems in Heterogeneous Solids

Abstract

AbstractThe problem of two circular inclusions of arbitrary radii and of different elastic moduli, which are perfectly bonded to an infinite matrix subjected to arbitrary loading, is solved by the heterogenization technique. This implies that the solution of the heterogeneous problem can be readily obtained from that of the corresponding homogeneous problem by a simple algebraic substitution. Based on the method of successive approximations and the technique of analytical continuation, the solution is formulated in a manner which leads to an approximate, but arbitrary accuracy, result. The present derived solution can be also applied to the problem with straight boundaries. Both the problem of two circular inclusions embedded in an infinite matrix and the problem of a circular inclusion embedded in a half-plane matrix are considered as our examples to demonstrate the use of the present approach.