A screw dislocation located outside, inside or on the interface of a parabolic elastic inhomogeneity

Using conformal mapping techniques, superposition and analytic continuation, we derive analytic solutions to the problem of a screw dislocation interacting with a parabolic elastic inhomogeneity. The screw dislocation can be located anywhere either in the surrounding matrix or in the parabolic inhomogeneity or simply on the parabolic interface itself. We obtain explicit expressions for the two analytic functions in the image plane characterizing the elastic fields describing displacement and stresses in the two-phase composite. Using the Peach-Koehler formula, we also obtain the image force acting on the screw dislocation. The analytic function defined in the parabolic inhomogeneity in the physical plane can be interpreted in terms of real and image screw dislocations for any location of the real screw dislocation.