A study was made of the interaction of a screw dislocation with a multi-layered interphase between a circularly cylindrical inclusion and a matrix. The layers were coaxial cylinders of annular cross-sections with arbitrary radii and different shear moduli. The number of layers could also be arbitrary. Continuity of traction and displacement across all interfaces was assumed. The solution of Honein et alia for circularly cylindrical layered media in anti-plane elastostatics was extended to the case where all of the singularities resided within the inclusion core. The solution to this heterogeneous problem was given explicitly for arbitrary singularities as a rapidly convergent Laurent series. The coefficients of the latter were expressed in terms of those of the complex potential of a corresponding homogeneous problem having the same singularities. Two particular cases of a screw dislocation were then considered where, in the first instance, the dislocation resided inside the matrix. In the second instance, it was located within the inclusion core. In both cases, the Peach–Koehler force which acted on the dislocation was calculated explicitly as a rapidly convergent series.

The Material Force Acting on a Screw Dislocation in the Presence of a Multi-Layered Circular Inclusion. E.Honein, H.Rai, M.I.Najjar: International Journal of Solids and Structures, 2006, 43[7-8], 2422-40