An XFEM crack-tip enrichment for a crack terminating at a bi-material interface

Crack-tip enrichment functions are determined for a crack terminating at a bi-material interface. The stress and displacement components at the crack-tip are expressed considering plane elasticity solution based on Airy functions. The crack-tip characteristic exponents and the enrichment functions are determined using the problem boundary conditions. Single real, double real or complex characteristic exponents are found depending on the crack-angle and the relative mechanical properties of the considered bi-material. Crack-tip enrichment functions are determined for cases where the characteristic exponent is real and complex. To validate the efficiency of the enrichment functions at the crack-tip singularity, the eXtended Finite Element Method (XFEM) is used to solve a mode-I crack terminating at the bi-material interface. Thanks to two Level-set functions, the crack and the bi-material interface are located and the nodes belonging to elements cut by these discontinuities are enriched. The Stress Intensity Factors (SIF) are calculated for a crack perpendicular and terminating at the bi-material interface using the body force method (BFM). The implemented method was tested and good agreement is found when compared to other investigations in the literature.