The numerical simulation of crack propagation using radial point interpolation meshless methods

Abstract

In this work, a new crack propagation prediction algorithm is combined with two distinct meshless methods – the Radial Point Interpolation Method (RPIM) and the Natural Neighbor Radial Point Interpolation Method (NNRPIM). Both these advanced discretization numerical techniques construct the shape functions using the radial point interpolating technique, which allows to build shape functions possessing the delta Kronecker property. The RPIM requires a background integration grid to numerically integrate the partial differential equations ruling the physical phenomenon. Alternatively, the NNRPIM constructs the background integration points using only the information of the spatial position of the nodes.This work aims to present a new methodology to predict the crack propagation and, simultaneously, to compare the performance of both meshless techniques (for similar conditions). The developed algorithm advances the crack tip iteratively and uses the maximum tangential stress criterion to calculate the propagation direction. In the end, three benchmark tests were analyzed using the proposed algorithm. Accurate crack paths were obtained when compared to the solutions described in the literature.