A new finite-element method for the modelling of dislocations was improved by adding adjustments in the neighbourhood of the dislocation core. In this method, the dislocation was modelled as a line or surface of discontinuity in two or three dimensions. The method was applicable to non-linear and anisotropic materials, large deformations and complicated geometries. Two separate adjustments were considered: these were a discontinuous jump adjustment and a singular adjustment based upon closed-form infinite-domain solutions for the dislocation core. Examples were presented for dislocations constrained in layered materials in 2 dimensions and 3 dimensions in order to illustrate the applicability of the method to interface problems.

On a New Extended Finite Element Method for Dislocations-Core Enrichment and Nonlinear Formulation. R.Gracie, J.Oswald, T.Belytschko: Journal of the Mechanics and Physics of Solids, 2008, 56[1], 200-14