Abstract: Meshes are generated without taking account of existence of cracks in the extended finite element method. However, the enriched nodes and their enrichment types are determined by the interaction between the computational mesh and the locations of cracks. In general, the enriched nodes and their enrichment types are determined according to the enriched element types. To determine the enriched element types, the locations of cracks and the shapes of elements must be considered. The limitations judging the enriched element types with the nodal level set values only considering the locations of cracks are pointed out; and the improved method is proposed. For complex cracks, it is inconvenient to determine the enriched element types with the level set method. An effective method is proposed to determine the enriched element types, enriched nodes and their enrichment types, i.e. according to the intersection number between the cracks and element boundaries and the locations of crack inflection points, the enriched element types are determined; then the enriched nodes and their enrichment types are determined by the enriched element types. The detailed procedure of the method is presented. The case studies of numerical simulation show the correctness of the proposed method.

Key words: extended finite element method, crack, level set method, enriched element type, enriched node, enrichment type of node