On the general treatment of multiple inclusions in antiplane elastostatics

Abstract

This article provides an explicit general solution of an infinitely extended plate containing any number of circular inclusions under antiplane deformation. The derived solution of the present heterogeneous problem associated with multiple inclusions is obtained in terms of the corresponding homogeneous solution by a simple algebraic substitution. This is accomplished by the technique of analytical continuation and the method of successive approximations. A rapidly convergent series solution either in the matrix or in the inclusions, which is expressed in terms of an explicit general term involving the complex potential of the corresponding homogeneous problem, is derived in an elegant form. The present derived solution can also be applied to the inclusion problem with straight boundaries. Numerical examples of three circular inclusions embedded in an infinite matrix, in a half-plane matrix, and in a strip are discussed in detail and displayed in graphic form. Interaction of a crack with multiple circular inclusions is also considered.