Solution for elliptic inclusion in an infinite plate with remote loading and Eshelby’s eigenstrain of polynomial type

Abstract

In this paper, a particular inhomogeneous inclusion problem is studied. In the problem, Eshelby’s eigenstrain takes the type [Formula: see text], where m+ n = 2, and the remote loadings [Formula: see text], [Formula: see text] are applied. In the solution, the complex variable method is used. The continuity conditions along the interface of the matrix and the inclusion are formulated exactly. Because the stress field is no longer uniform in inclusion in this case, the studied problem has an inherent difficulty. After some manipulation, the final result for stress components [Formula: see text], [Formula: see text] and [Formula: see text] in inclusion are obtainable. In the present study, [Formula: see text], [Formula: see text] and [Formula: see text] are no longer uniform.