A meshless method with enriched weight functions for three-dimensional crack propagation

The propagation of cracks in three dimensions is analyzed by a meshless method. The cracks are modeled by a set of triangles that are added when the propagation occurs. Since the method is meshless, no remeshing of the domain is necessary during the propagation. To avoid using a large number of degrees of freedom, the stress singularity along the front of the cracks is taken into account by an enrichment of the shape functions of the meshless method by means of appropriate weight functions. This enrichment technique is an extension of the technique that proved to be successful in two dimensions in a previous paper. Several algorithms for efficiently implementing the meshless method in three dimensions are detailed. The accuracy of the enrichment is first assessed on simple examples and some results of non-planar propagation of multiple cracks are then presented. Key-words: meshless method; crack propagation; near-tip enrichment