Revisiting integration in the material point method: a scheme for easier separation and less dissipation

The material point method (MPM) recently demonstrated its efficacy at simulating many materials and the coupling between them on a massive scale. However, in scenarios containing debris, MPM manifests more dissipation and numerical viscosity than traditional Lagrangian methods. We have two observations from carefully revisiting existing integration methods used in MPM. First, nearby particles would end up with smoothed velocities without recovering momentum for each particle during the particle-grid-particle transfers. Second, most existing integrators assume continuity in the entire domain and advect particles by directly interpolating the positions from deformed nodal positions, which would trap the particles and make them harder to separate. We propose an integration scheme that corrects particle positions at each time step. We demonstrate our method's effectiveness with several large-scale simulations involving brittle materials. Our approach effectively reduces diffusion and unphysical viscosity compared to traditional integrators.