New solution for a screw dislocation in a multilayered laminate

Abstract

Using analytic continuation, we derive a new analytical solution for a screw dislocation in an N-phase laminate composed of N−2 intermediate elastic layers of equal thickness encased in two semi-infinite elastic media. The number of phases comprising the laminate can be arbitrarily large. The solution can be interpreted in terms of image screw dislocations, the magnitudes of which are determined by solving an algebraic equation of order N−2. We also obtain an elementary expression for the image force acting on the screw dislocation in terms of a single real function. Several specific examples are presented to demonstrate the solution. Analytic continuation is also applied to solve the related problem of a screw dislocation interacting with a multicoated circular elastic inhomogeneity.