Continuum and continuum-atomistic models of dislocations and cracks using the extended finite element method

Several new numerical methods for the simulation of dislocations are described and the numerical properties of these methods are studied. First, a continuum mesoscale dislocation model is presented which is based on the Extended Finite Element Method (XFEM). The method is applicable to problems with nonlinear anisotropic material models, large deformation problems and applications with material interfaces. The computation of the Peach-Koehler force is also described. We also describe a multiscale continuum atomistic model for dislocations and cracks. The multiscale method combines the XFEM mesoscale model with a molecular statics model using the Bridging Domain Method. The atomistic model is used to model the core region where the continuum model breaks down. Simulations of dislocations in graphene show that the multiscale method can accurately capture the behaviour of dislocation cores with substantially fewer degrees of freedom than a fully atomistic model.;We also address the issue of blending in XFEM. We decompose the simulation domain into patches which are independently discretized and enriched. A Discontinuous Galerkin (DG) formulation is used to enforce compatibility between the patches. It is shown that the DG-XFEM framework improves the accuracy of the XFEM in problems involving cracks, dislocations and material interfaces. In addition, the DG-XFEM converges optimally even when the standard XFEM model does not (which occurs in some XFEM models of dislocations).