A new method to describe dislocations within the framework of the element-free Galerkin method was presented. Based upon the Peierls–Nabarro concept of balancing the elastic energy with an inter-planar potential, the method naturally led to dislocation core spreading on the glide planes. A weak formulation compatible with the time-dependent Ginzburg–Landau relaxation mechanism was presented and its implementation analyzed. As an example, modeling of the complex core structure of a screw dislocation in Ta by using 15 glide planes was presented and its Peierls stress calculated.

Modeling Dislocation by Coupling Peierls–Nabarro and Element-Free Galerkin Methods. C.Denoual: Computer Methods in Applied Mechanics and Engineering, 2007, 196[13-16], 1915-23