Shock waves simulated using the dual domain material point method combined with molecular dynamics

Abstract

In this work we combine the dual domain material point method with molecular dynamics in an attempt to create a multiscale numerical method to simulate materials undergoing large deformations with high strain rates. In these types of problems, the material is often in a thermodynamically nonequilibrium state, and conventional constitutive relations or equations of state are often not available. In this method, the closure quantities, such as stress, at each material point are calculated from a molecular dynamics simulation of a group of atoms surrounding the material point. Rather than restricting the multiscale simulation in a small spatial region, such as phase interfaces, or crack tips, this multiscale method can be used to consider nonequilibrium thermodynamic effects in a macroscopic domain.This method takes the advantage that the material points only communicate with mesh nodes, not among themselves; therefore molecular dynamics simulations for material points can be performed independently in parallel. The dual domain material point method is chosen for this multiscale method because it can be used in history dependent problems with large deformation without generating numerical noise as material points move across cells, and also because of its convergence and conservation properties.To demonstrate the feasibility and accuracy of this method, we compare the results of a shock wave propagation in a cerium crystal calculated using the direct molecular dynamics simulation with the results from this combined multiscale calculation.