Crack path prediction using the natural neighbour radial point interpolation method

One of the most challenging problems in computational mechanics is the prediction of the crack propagation path. In this work, the Natural Neighbour Radial Point Interpolation Method (NNRPIM), an efficient meshless method, is extended to the field of fracture mechanics. Since the NNRPIM relies on the Natural Neighbour mathematical concept to obtain the integration mesh and establish the nodal connectivity, the NNRPIM only requires a computational nodal distribution to fully discretise the problem domain. The Radial Point Interpolators (RPI) are used to construct the NNRPIM interpolation functions.Taking advantage of the unique features of the NNRPIM, in this work, the crack propagation path is numerically simulated using an adapted crack path opening algorithm, in which the crack is iteratively extended in line segments. In each iteration, using the obtained stress field, the crack propagation direction is determined using the maximum circumferential stress criterion. Due to the flexibility of the natural neighbour concept, the increase of the domain discontinuities do not represent a numerical difficulty. In the end, several crack opening path benchmark examples are solved in order to show the efficiency of the proposed numerical approach.