Coupling of the meshfree and finite element methods for determination of the crack tip fields

This paper develops a new concurrent simulation technique to couple the meshfree method with the finite element method (FEM) for the analysis of crack tip fields. In the sub-domain around a crack tip, we applied a weak-form based meshfree method using the moving least squares approximation augmented with the enriched basis functions, but in the other subdomains far away from the crack tip, we employed the finite element method. The transition from the meshfree to the finite element (FE) domains was realized by a transition (or bridge region) that can be discretized by transition particles, which are independent of both the meshfree nodes and the FE nodes. A Lagrange multiplier method was used to ensure the compatibility of displacements and their gradients in the transition region. Numerical examples showed that the present method is very accurate and stable, and has a promising potential for the analyses of more complicated cracking problems, as this numerical technique can take advantages of both the meshfree method and FEM but at the same time can overcome their shortcomings.