Solutions were provided for various dislocation-inclusion interaction problems. Each was posed as a plane elasticity problem for an infinite elastic region (matrix) which contained a 2-phase elliptical inclusion with elastic properties that differed from those of the infinite region. An edge dislocation acted at an arbitrary point; either in the matrix or in the inclusion. The problem was expressed in terms of Muskhelishvili complex potentials and was simplified by using a conformal mapping which transformed the confocal elliptical contours into concentric circles. It was noted that continuity of traction and displacement was required at all material interfaces. An iterative solution technique was developed for the case where the dislocation was in the outermost or innermost region.

Edge Dislocation Interacting with an Elliptical Inclusion Surrounded by an Interfacial Zone. M.T.Qaissaunee, M.H.Santare: Quarterly Journal of Mechanics and Applied Mathematics, 199, 48[3], 465-82