X-FEM modeling of large plasticity deformation; a convergence study on various blending strategies for weak discontinuities

In the extended finite element method (FEM), the transition elements between the enriched and standard elements, which are generally referred as the blending, or partially enriched elements, are often crucial for a good performance of the local partition of unity enrichments. In these elements, the enrichment function cannot be reproduced exactly due to the lack of a partition of unity, and blending elements produce unwanted terms into the approximation that cannot be compensated by the standard finite element part of the approximation. In this paper, some optimal X-FEM-type methods reported in literature are employed to study the performance of blending elements in large plastic deformation problems with weak discontinuities. Several numerical examples are solved using the standard X-FEM, the X-FEM with modified enrichment function, the hierarchical X-FEM and the corrected X-FEM technique, and the results are compared with an alternative intrinsic enrichment strategy in large deformation problems.