Accuracy and robustness of stress intensity factor extraction methods for the generalized/eXtended Finite Element Method

This paper investigates the accuracy and robustness of three Stress Intensity Factor (SIF) extraction methods for the Generalized/eXtended Finite Element Method (G/XFEM): the Cutoff Function Method (CFM), the Contour Integral Method (CIM), and the Displacement Correlation Method (DCM). Challenges in SIF extraction from G/XFEM solutions using energy-based methods such as the CFM and the Interaction Integral Method are discussed. Numerical studies on problems with stress-free crack surfaces show that the CFM is path independent while the CIM is not. They also show that unless a proper enrichment scheme is adopted, SIFs extracted with the DCM are of low accuracy and sensitive to extraction parameters. Strategies to address both issues with the DCM are presented. This paper demonstrates that the DCM, with proper enrichment of the G/XFEM approximation, has an accuracy and robustness comparable to the CFM at a fraction of the computational cost. It is also shown that the DCM can be applied to problems where SIF extraction using domain integrals is not possible. Several problems aimed at investigating the applicability and accuracy of the various extraction methods are solved.