Inclusions in a two-phase elastic space—plane circular and rectangular inclusions

Abstract

This paper is concerned with the elastic field generated in two bonded isotropic half-planes containing either a circular or a rectangular inclusion, each having the same elastic properties as those of the surrounding half-plane. The circular inclusion undergoes a transformation which in the absence of the surrounding material would be an arbitrary uniform stress-free strain, while that imposed on the rectangular inclusion corresponds to a pure dilatation. The analysis is based upon the Papkovich-Neuber stress function approach. It is found that the elastic components in the composite plane can be derived from the corresponding components in the homogeneous plane by a set of relations, which are the same for both inclusion shapes, provided that each transformation corresponds to a stress-free dilatation.