An Extended Finite Element Method For Modeling Crack Propagation In Quasi Brittle Material

The extended finite element method is an effective numerical analysis method to solve the discontinuous problems. Its basic principle is based on the thought of the mesh division, where some strengthen functions are incorporated in the displacement mode of the conventional finite element method to reflect the discontinuity. The geometrical or physical interface is independent of each other. The extended finite element method can easily simulate discontinuous problems, especially the discontinuous boundary problem of evolution. The large commercial software Abaqus can be used to mimic the crack propagation, however, the crack tip strengthening function is not enriched in Abaqus, so the crack tip field cannot be accurately simulated. In this paper, an extended finite element program is written to simulate the crack propagation based on the Matlab platform. The specific work is as follows:The matrix expression of the whole process of linear elastic fracture and elastic-plastic fracture is derived. Two kinds of stiffness matrix of the ultimate stiffness matrix are obtained respectively. The schemes of the integrals are determined.In the linear elastic fracture model, the crack tip strengthening function is introduced, and the stress intensity factor is calculated by interaction integral method. Three factors affecting the stress intensity factor are considered, namely, mesh division, crack length and crack tip strengthening area. At the same time, a square crack tip strengthening region is proposed, and the number of the mixed units is reduced relative to the circular crack tip region. It can effectively improve the accuracy of calculation. The results are more stable.The numerical simulation of the pure I fracture in a simple supported beam with the pre-existed crack is carried out. In the process of crack propagation, there is no need to reconstruct the mesh. The limitation is independent on element type.Considering the fracture process zone, the failure process of concrete three point bending beam is simulated by using the virtual crack model. The p-δ curve of the fracture process is calculated. The crack tip strengthening function is introduced. The crack tip stay position is not limited, and the results are more precise and more flexible.