Particle difference method for dynamic crack propagation

• We present a novel particle difference method (PDM) for solving dynamic crack propagation problems based on the strongly formulated meshfree method.
• The PDM takes advantage of fast computation speed owing to the exemption of numerical integration and the full differentiation of the approximation.
• The Newmark method and the central difference method are effectively modified for complete explicit and implicit time integrations of the discrete equations.
• The crack propagation simulation is successfully conducted by simple nodal topology change such as addition and deletion of nodes.

This paper presents a novel particle difference method (PDM) for solving dynamic crack propagation problems. The PDM is based on the strong formulation that directly discretizes the governing partial differential equations for space and takes advantage of fast computation speed owing to the exemption of numerical integration and the full differentiation of the approximation by using the Taylor polynomial expanded by the moving least squares method. It also differentiates the discrete equations for time through both explicit and implicit algorithms; specifically, the Newmark method (NM) is effectively modified for complete explicit and implicit time integrations. Nodal topology change due to the crack propagation modeling is easily conducted by simple addition and deletion of nodes. Dynamic fracture simulation is successfully performed by the help of the visibility criterion and dynamic energy release rate evaluation. Robustness and effectiveness of the PDM are thoroughly verified through various numerical experiments.