Simulation of Impact and Fragmentation with the Material Point Method

The simulation of high-rate deformation and failure of metals is has traditionally been performed using Lagrangian finite element methods or Eulerian hydrocodes. Lagrangian mesh-based methods are limited by issues involving mesh entanglement under large deformation and considerable complexity in handling contact. On the other hand, Eulerian hydrocodes are prone to material diffusion. In the Material Point Method (MPM), the material state is defined on solid Lagrangian particles. The particles interact with other particles in the same body, with other solid bodies, or with fluids through a background mesh. Thus, some of the problems associated with finite element codes and hydrocodes are alleviated. Another attractive feature of the material point method is the ease with which large deformation, fully coupled, fluid-structure interaction problems can be handled. In this work, we present MPM simulations that involve large plastic deformations, contact, material failure and fragmentation, and fluid-structure interaction. The plastic deformation of metals is simulated using a hypoelastic-plastic stress update with radial return that assumes an additive decomposition of the rate of deformation tensor. The Johnson-Cook model and the Mechanical Threshold Stress model are used to determine the flow stress. The von Mises and GursonTvergaard-Needleman yield functions are used in conjunction with associated flow rules. Failure at individual material points is determined using porosity, damage and two bifurcation conditions the Drucker stability postulate and the acoustic tensor check for loss of hyperbolicity. Particles are converted into a new material with a different velocity field upon failure. Impact experiments have been simulated to validate these models using data from high strain rate impact experiments. Finally, results from simulations of the fragmentation of steel containers due to explosively expanding gases are presented. The results show that MPM can be used as an alternative method for simulating high strain-rate, large deformation impact, penetration, and fluid-structure interaction problems.