Simple and effective approach to modeling crack propagation in the framework of extended finite element method

In this study, the extended finite element method (XFEM) coupled with the hierarchical mesh adaptation method and direct method is developed to model crack propagation. First, we observe that crack tip stresses can be approximated with high accuracy by using the stress intensity factor (SIF) terms and T-stress term within 0.1% of the crack length away from the crack tip, without considering other high order terms of the crack-tip stresses. Next, based on the XFEM, the hierarchical mesh adaptation method is developed to obtain the stresses around the location which is very close to the crack tip. Then, the SIFs are derived directly from the crack-tip stresses based on the least square fitting without considering the special algorithms and procedures. Finally, the numerical results reveal that the proposed method can obtain SIFs accurately and it can predict a better crack trajectory for crack simulation. In addition, the proposed method has the advantage over the J-integral method and it is benefit for the simulation of large-scale engineering problems.