Elliptic Inclusion in Orthotropic Medium

Abstract

The problems of circular and elliptic inclusions tending to undergo spontaneous dimensional changes in infinite isotropic elastic continuous unstressed or stressed material, the matrix, have been considered by the authors in previous papers. In these problems the elastic properties of the inclusion were taken to be different from those of the matrix. In this paper the exact analytical solution to such a problem when elliptic inclusion and matrix are of different orthotropic materials has been obtained. The solution has been obtained by the applications of the minimum strain energy principle first suggested by one of the authors (R.D.B.) coupled with a semi-inverse method and complex variable technique. Continuity of normal and shearing stresses at the interface is demonstrated, providing a useful check on the analysis.