A coupled meshless-finite element method for fracture analysis of cracks

This paper presents a coupling technique for integrating the element-free Galerkin method (EFGM) with the traditional finite element method (FEM) for analyzing linear-elastic cracked structures subject to mode-I and mixed-mode loading conditions. The EFGM was used to model material behavior close to cracks and the FEM in areas away from cracks. In the interface region, the resulting shape function, which comprises both EFGM and FEM shape functions, satisfies the consistency condition thus ensuring convergence of the method. The proposed method was applied to calculate mode-I and mode-II stress–intensity factors (SIFs) in a number of two-dimensional cracked structures. The SIFs predicted by this method compare very well with the existing solutions obtained by all-FEM or all-EFGM analyses. A significant saving of computational effort can be achieved due to coupling in the proposed method when compared with the existing meshless methods. Furthermore, the coupled EFGM–FEM method was applied to model crack propagation under mixed-mode loading condition. Since the method is partly meshless, a structured mesh is not required in the vicinity of the cracks. Only a scattered set of nodal points is required in the domain of interest. A growing crack can be modeled by simply extending the free surfaces, which correspond to a crack. By sidestepping remeshing requirements, crack-propagation analysis can be dramatically simplified. A number of mixed-mode problems were studied to simulate crack propagation. The agreement between the predicted crack trajectories with those obtained from existing numerical simulation and experiments are excellent.