High-order stable generalized/eXtended finite element approximations for accurate stress intensity factors

Abstract

This paper investigates the accuracy and robustness of stress intensity factor (SIF) extraction using the p-Hierarchical Discontinuous Interpolant Stable Generalized Finite Element Method (pFEM-DSGFEM). This method is well-conditioned and optimally convergent for fracture mechanics problems if a proper enrichment strategy and mesh refinement are used. The method performs well when calculating global quantities such as strain energy, but its ability to capture local quantities such as SIFs has not yet been explored. pFEM-DSGFEM spaces are used to solve a variety of fracture mechanics problems and their solutions are used to extract SIFs with the Displacement Correlation Method (DCM). These numerical experiments show that pFEM-DSGFEM spaces provide highly accurate SIFs, even better than standard GFEM spaces, while being well-conditioned.