Fatigue crack propagation simulation method using XFEM with variable-node element

The extended finite element method (XFEM) with the local refinement technique using the variable-node element (VNE) is proposed to simulate the fatigue crack propagation under the cyclic loadings, in which the initially generated coarse mesh around the crack tip is refined after the crack propagation and the VNE is used to connect the refined elements and the adjacent elements. The local refine elements are used to improve the accuracy of stress near the crack tip and it is unnecessary to conform the discretization to the crack surfaces. The maximum tangential stress criterion is used to determine the crack propagation angle theta c and the fatigue life is estimated by the Paris law. With this method, the condition number of the global stiffness matrix is alleviated by using the only discontinuous branch enrichment function and the crack increment size can be set flexibly and small enough to reproduce true crack path. Because only the refined mesh around crack tip is updated at each increment step during crack propagation, the simulation cost is much less than that of the method in which global fine mesh is required. Numerical examples of the crack propagation under the monotonic and cyclic loadings are given out and it is demonstrated that the proposed method can calculate the stress intensity factors (SIFs) and predict the crack paths more accurately with the local refine elements near the each crack tip. The proposed method is also suitable to simulate the crack propagation of the functional graded materials under the thermal loadings in the future works, in which the material non-homogeneity near the crack tip requires accurate modeling.