Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method

Abstract

We present a new approach based on local partition of unity extended meshfree Galerkin method for modeling quasi-static crack growth in two-dimensional (2D) elastic solids. The approach utilizing the local partition of unity as a priori knowledge on the solutions of the boundary value problems that can be added into the approximation spaces of the numerical solutions. It thus allows for extending the standard basis functions by enriching the asymptotic near crack-tip fields to accurately capture the singularities at crack-tips, and using a jump step function for the displacement discontinuity along the crack-faces. The radial point interpolation method is used here for generating the shape functions. The representation of the crack topology is treated by the aid of the vector level set technique, which handles only the nodal data to describe the crack. We employ the domain-form of the interaction integral in conjunction with the asymptotic near crack-tip field to extract the fracture parameters, while crack growth is controlled by utilizing the maximum circumferential stress criterion for the determination of its propagating direction. The proposed method is accurate and efficient in modeling crack growths, which is demonstrated by several numerical examples with mixed-mode crack propagation and complex configurations.