Non-Uniform Eigenstrain Induced Stress Field in an Elliptic Inhomogeneity Embedded in Orthotropic Media with Purely Imaginary Roots

Complex analysis of anisotropic elasticity indicates that the degree of anisotropy is characterized by two complex parameters. A closed-form solution has been formulated for the stress field resulting from non-uniform eigenstrains in an elliptic inhomogeneity in elastic media with complex roots. In this paper, corresponding analytical solution for the induced stress field in elastic materials with pure imaginary roots is derived based on the polynomial conservation theorem and conformal transformation. The solution is verified by continuity conditions for stresses at the interface between the inhomogeneity and matrix. In addition, numerical examples are provided to present distributions of stresses and strains.