A High-order extended finite element method for extraction of mixed-mode strain energy release rates in arbitrary crack settings based on Irwin's integral

SUMMARY: An analytical formulation based on Irwin's integral and combined with the extended finite element method is proposed to extract mixed-mode components of strain energy release rates in linear elastic fracture mechanics. The proposed formulation extends our previous work to cracks in arbitrary orientations and is therefore suited for crack propagation problems. In essence, the approach employs high-order enrichment functions and evaluates Irwin's integral in closed form, once the linear system is solved and the algebraic degrees of freedom are determined.Several benchmark examples are investigated including off-center cracks, inclined cracks, and two crack growth problems. On all these problems, the method is shown to work well, giving accurate results. Moreover, because of its analytical nature, no special post-processing is required. Thus, we conclude that this method may provide a good and simple alternative to the popular J-integral method. In addition, it may circumvent some of the limitations of the J-integral in 3D modeling and in problems involving branching and coalescence of cracks.