Dual domain material point method for nonequilibrium systems*

A multiscale numerical method is developed for materials undergoing a large deformation with a high strain rate. The continuum level equation of motion is solved using the dual domain material point method (DDMP) to avoid numerical difficulties caused by large deformations. In a DDMP calculation material points are used to carry the material deformation history, which is often important in thermodynamically nonequilibrium systems. The closure quantities, such as stress, are obtained from numerical simulations of small domains surrounding the material points considering the lower scale physics, such as the molecular dynamics (MD).

To preserve the deformation history, re-initialization of these MD systems is not allowed. New numerical schemes are needed to treat the large deformation of the simulation domain while ensuring the physical consistence between the calculations performed at different scales. These schemes are studied. Results from the combined DDMP-MD calculations are compared to a pure MD simulation. Although the size of the example problem is only a few hundred nanometers due to the limitation of the pure MD simulation, we show that the method of the combined simulation is applicable to macroscopic systems.