Meshfree Method Of Analyzing Interfacial Crack Problems

The widespread application of laminated plates in aircraft structures leads the interfacial crack problem into one of the research highlights. Accordingly, as an essential parameter in crack problems, the strain energy release rate has aroused extensive concern. Currently, typical methods of calculating the energy release rate in the interfacial crack problems are mostly based on the finite element method(FEM). Meshfree method is a new numerical method developed in recent years. Different from FEM, the meshfree method is superior in that it's independent of grids, simpler in pretreatment and more accurate.According to previous work, this paper extended the commonly used two-dimensional(2D) meshfree method into three-dimensional(3D) meshfree method, and then used the virtual crack closure technique(VCCT) to analyze the energy release rate of interfacial crack problems based on 3D meshfree method.On the other hand, in order to simplify the calculation of nodal force on the crack front which is necessary for VCCT, spring layer model was introduced into 3D meshfree method to simplify the nodal stress-displacement relationship on crack tip, and then the 3D meshfree formulation for interfacial crack problems was deduced.After theoretical analysis, this paper implemented several numerical examples through Mathematica software programming. Firstly, the statics analyses of a perfect cantilever beam and a perfect laminated plate were conducted respectively. The results were compared with solutions of FEM software Abaqus and analytical solutions and validated the correctness of the program and the high accuracy of the meshfree method. Then the statics analyses of models with interfacial crack were implemented by using the meshfree method together with the spring layer model. Finally, the energy release rates of a cantilever beam with interfacial crack and a laminated plate with interfacial crack were investigated by using the VCCT on the basis of the 3D meshfree method together with the spring layer model. Through comparison with the FEM results of Abaqus and the analytical solutions, the results of this paper demonstrated that this method was highly accurate and effective for solving interfacial crack problems.This study provides a new way for the investigation of both related theory and engineering practices.