A new finite element method for accurately modelling the displacement and stress fields produced by a dislocation was proposed. The methodology was based on a local enrichment of the finite element space by closed form solutions for dislocations in infinite media via local partitions of unity. This allows the treatment of both arbitrary boundary conditions and interfaces between materials. The method could readily be extended to arrays of dislocations, 3D problems, large strains and non-linear constitutive models. Results were given for an edge dislocation in a hollow cylinder and in an infinite medium, for the cases of a glide plane intersecting a rigid obstacle and an interface between 2 materials.

Dislocations by Partition of Unity. G.Ventura, B.Moran, T.Belytschko: International Journal for Numerical Methods in Engineering, 2005, 62[11], 1463-87