Calculating dislocation displacements on the surface of a volume

Abstract

In this paper we propose a new method for calculating the displacement field produced by an arbitrary dislocation structure on the surface of a finite convex volume. The algorithm is designed for use in 3D nodal based discrete dislocation dynamics codes, when coupling with the finite element method using the superposition principle. Starting from Barnett's solution for the displacement field generated by a triangular dislocation loop, we outline a method for evaluating the displacement field of an arbitrary dislocation structure. The algorithm can handle both internal and exited segments and does not require storing any history information. The displacement field is evaluated segment wise, in an analogous way to the stress field, allowing for easy parallelisation.