Simulating fracture propagation in brittle materials using a meshless approach

In the present work, a meshless method is combined with a crack growth algorithm, considering a linear elastic model to simulate the propagation of cracks in brittle materials. The proposed methodology is automatic, which means that it does not require the user intervention. In this study, the meshless method used is the Natural Neighbour Radial Point Interpolation Method (NNRPIM), an efficient discrete numeric method. Being a truly meshless method, the NNRPIM only requires an unstructured nodal distribution to fully discretize the problem domain. With the coordinates of the nodes, the NNRPIM formulation is autonomously capable: to define the nodal connectivity; to build the background integration mesh; and to construct the shape functions. The crack propagation algorithm here proposed simulates the crack growth by displacing iteratively the crack tip. Updating the crack tip location requires a local remeshing, which does not represent a numeric difficulty for the NNRPIM. The updated position of the crack tip depends on the estimated stress field in the vicinity of the crack tip. Thus, in each iteration, the stress field in the vicinity of the crack tip is estimated, and then, the direction of the crack propagation is calculated using the maximum circumferential stress criterion.