Modeling dislocation by coupling Peierls–Nabarro and element-free Galerkin methods

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