Numerical simulation of 2-D weak and strong discontinuities by a novel approach based on XFEM with local mesh refinement

The present paper is concerned with numerical simulation of two-dimensional (2-D) cracks and material interfaces by an effective computational approach. A local mesh refinement in terms of extended finite element method is thus described. The new approach combines a posteriori error estimation algorithm, a local non-conformal mesh connection strategy, and local enrichment. An error estimator based on recovery strain for adaptivity is used; allowing the mesh where it is needed is subsequently refined. Unlike preceding local refined methods, variable-node elements are integrated into the present formulation instead, which aims to treat mismatching problem induced by different scale-meshes in an effective way. The discontinuity and singularity of cracks or material interfaces are captured by local enrichments in terms of partition of unity. Due to existence of different types of elements in the model, a special technique is thus proposed for appropriately and accurately treating numerical integration. We address the developed methodology, assessing its numerical properties and performance through several numerical examples. In particular, discontinuity problems with material interfaces, multiple inclusions, single and multiple cracks are analyzed. The obtained results indicate a high accuracy, low cost and good performance of the proposed method in simulation of 2-D cracks and material interfaces.