A direct analytical method to extract mixed-mode components of strain energy release rates from Irwin's integral using extended finite element method

A new analytical approach, within the extended finite element framework, is proposed to compute mixed-mode components of strain energy release rates directly from Irwin's integral. Crack tip enrichment functions in extended FEM allow for evaluation of integral quantities in closed form (for some crack configurations studied) and therefore resulting in a simple and accurate method.Several benchmark examples on pure and mixed-mode problems are studied. In particular, we analyze the effects of high-order enrichments, mesh refinement, and the integration limits of Irwin's integral. The results indicate that high-order enrichment functions have significant effect on the convergence, in particular when the integral limits are finite. When the integral limits tend to zero, simpler strain energy release rate expressions are obtained, and high-order terms vanish. Nonetheless, these terms contribute indirectly via coefficients of first-order terms.The numerical results show that high accuracy can be achieved with high-order enrichment terms and mesh refinement. However, the effect of the integral limits remains an open question, with finite integration intervals chosen as h/2 tending to give more accurate results.