Fracture propagation using the radial point interpolation method

This work presents a crack path prediction algorithm combined with the radial point interpolation method (RPIM), a meshless method. To allow easier implementation in existing structural analysis software, this algorithm is numerically compatible with finite element method (FEM) formulations. The proposed RPIM formulation uses the triangular elements of a FEM mesh as the background integration grid, allowing also to combine both formulations more easily. Thus, with the developed methodology, the RPIM can be integrated directly in a FEM software or use the same CAD tools to build the discretization meshes. Because the RPIM shape functions possess the delta Kronecker property, all the numerical techniques available for the FEM can be applied to enforce the natural and essential boundary conditions. The developed algorithm uses the maximum tangential stress criterion to determine the crack propagation direction, and the crack paths obtained with it corresponded well to previous research.