A fast and exact computational method for crack propagation based on extended finite element method

This study presents a fast and exact computational method for crack propagation which is based on the extended finite element method (X-FEM). It is well known that the X-FEM has been developed to be an important numerical method for crack propagation. However, there are still some limitations on the computational cost due to the requirements of very refined meshes and very small iteration step length. Therefore, a highly efficient computational method termed decomposed updating reanalysis (DUR) is proposed to reduce the computational cost. Considering the characteristic of local change of stiffness matrix during X-FEM iterative procedure, the proposed X-FEM based reanalysis method can achieve the response of crack propagation more efficiently compared to the popular X-FEM. To further enhance the performance of X-FEM, a local updating stiffness matrix strategy is suggested. To verify the performance of the DUR method, several typical numerical examples have been analyzed and the results demonstrate that this method is a highly efficient method with high accuracy.