Appropriate extended functions for X-FEM simulation of plastic fracture mechanics

The extended finite element method (X-FEM) was used with success in the past few years for linear elastic fracture mechanics (LEFM). In the case of elastic–plastic fracture mechanics (EPFM), this method cannot be used without adequate asymptotic solutions to enrich the shape function basis. In this paper, we propose to use the well-known Hutchinson–Rice–Rosengren (HRR) fields to represent the singularities in EPFM. The analysis we are presenting is done in the context of confined plasticity, and shall be used to predict fatigue crack growth without remeshing. A Fourier analysis of the HRR fields is done in order to extract a proper elastic–plastic enrichment basis. Several strategies of enrichment, based on the Fourier analysis results, are compared and a six-enrichment-functions basis is proposed. This new tip enrichment basis is coupled with a Newton like iteration scheme and a radial return method for plastic flow. Numerical comparisons with and without unloading of fracture parameters are made with classical finite element results and show good agreements.