The plane elasticity problem was considered for dislocations that were associated with an anisotropic elliptical inclusion in an unbounded anisotropic matrix. A general solution was obtained, for stresses and deformations throughout the entire domain, by applying the Stroh formalism and the method of analytical continuation. Because general solutions had not been published, comparisons were made with special cases for which analytical solutions existed. This showed that the present results were exact and universal. Continuity across the interface for the 3 different solution forms was ensured numerically by putting the dislocation on the interface. By incorporating the technique of numerical solution of singular integral equations, the present analytical solutions could be applied to treat problems such as a crack penetrating an inclusion, a crack lying around an interface, or any other crack/inclusion interaction problem. The Green's function for the inclusion problems could be obtained in a straightforward manner, from the present solutions, by exploiting an analogy between dislocations and point forces.

Dislocations Inside, Outside, or on the Interface of an Anisotropic Elliptical Inclusion. W.J.Yen, C.Hwu, Y.K.Liang: Journal of Applied Mechanics, 1995, 62[2], 306-11