An effective fracture analysis method based on the virtual crack closure-integral technique implemented in CS-FEM

摘要

In this work, the virtual crack closure integral technique (VCCT) is formulated in the framework of cell-based smoothed finite element (CS-FEM) for evaluating stress intensity factors and for modeling the crack propagation in solids. In the present CS-FEM, the strain smoothing technique is operated over the smoothing domains which are constructed based on elements, and each element is further subdivided into several smoothing cells. The smoothed strain is then obtained by a boundary integral along the boundaries of the smoothing cells. Only shape function itself is involved in computing the strains and no derivatives of the shape functions or coordinate transformation is required for the computation of the discretized stiffness matrix, and thus ideal for fracture mechanics problems to evaluate the stress intensity factors, we utilize the one-step-analysis approach of the VCCT based on the assumption that an infinitesimal perturbation of crack-tip location shall not significantly affect the stress/displacement field. The significant feature of the present CS-FEM method equipped with VCCT is that it requires no domain integration in the analysis of fracture mechanics problems. Several numerical examples are presented to validate the effectiveness of the present method. It uses only the information for displacement openings behind the crack-tip and the nodal forces at the crack-tip for stress intensity factor evaluation. The comparison study has shown that is as accuracy as the FEM-Q4 that need domain integrations for both stiffness matrix computation and interaction integral methods for stress intensity factor evaluation. The present method is further used to successfully predict the crack growth trajectory with excellent agreement between numerical results and the experimental observations.