Three-Dimensional Dynamic Fracture Analysis Using the Material Point Method

This paper describes algorithms for threedimensional dynamic stress and fracture analysis using the material point method (MPM). By allowing dual velocity fields at background grid nodes, the method provides exact numerical implementation of explicit cracks in a predominantly meshless method. Crack contact schemes were included for automatically preventing crack surfaces from interpenetration. Crack-tip parameters, dynamic J-integral vector and mode I, II, and III stress intensity factor, were calculated from the dynamic stress analysis solution. Comparisons to finite difference method (FDM), finite element method (FEM), and boundary element method (BEM), as well as to static theories have shown that MPM can efficiently and accurately solve three-dimensional dynamic fracture problems. Since the crack description is independent of the object description, MPM could be useful for simulation of three-dimensional dynamic crack propagation in arbitrary directions. keyword: Material point method, MPM. threedimensional dynamic fracture, cracks, dynamic J-integral, dynamic stress intensity, contact, mode I, mode II, mode III.