Numerical analysis of growing crack problems using particle discretization scheme

This paper presents the particle discretization scheme (PDS) to analyze brittle failure of solids. The scheme uses characteristic functions of Voronoi and Delaunay tessellations to discretize a function and its derivatives, respectively. A discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks, without making any extra computation to accommodate new displacement discontinuities. When the scheme is implemented to a finite element method (FEM), the resulting stiffness matrix coincides with the one that is obtained by using linear elements. The accuracy of computing a stress intensity factor at a crack tip is examined. It is shown that the accuracy is better than that of a FEM with linear elements when the rotational degree of freedom is included in discretizing displacement functions. Three three-dimensional growing crack problems are solved by means of the PDS and the results are presented.