Hierarchical, adaptive, material point method for dynamic energy release rate calculations

A crack-closure method was developed for use in material point method (MPM) calculations. The method can be used for calculation of the dynamic energy release rate in a variety of dynamic fracture mechanics problems. Most previous MPM analyses have used regular grids and a “lumped” mass matrix. For the most accurate energy release rate calculations, the regular grid had to be replaced by an adaptive grid that automatically refined the mesh around the crack tip and the lumped mass matrix had to be replaced by a full mass matrix. Using an adaptive mesh was more important to accuracy than was switching to a full mass matrix. Some sample calculations are given for energy release rate in a double cantilever beam specimen carried out by several different MPM methods.