Elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity existing in orthotropic media under uniform tension at infinity

This paper presents an analytical solution for the elastic fields induced by non-elastic eigenstrains in a plane elliptical inhomogeneity embedded in the orthotropic matrix under tension at infinity and inclined at any angle. The conformal transformation and complex function method for the anisotropic elastic material were used to determine the strain energies in the inhomogeneity and matrix, which were expressed by four undetermined coefficients characterizing the equilibrium boundary of the inhomogeneity due to the acting eigenstrains and external load. The use of the principle of the minimum potential energy led to analytical expressions for these coefficients and thus generated a closed-form solution for the elastic strain/stress fields. The resulting stress field in the inhomogeneity was examined and verified by checking the continuity conditions for the normal and shear stresses on the interior boundary of the matrix.