A Hybrid Material Point and Discrete Element Method for Granular Media Modeling

Capturing the propagation of microscale physics to macroscale phenomena for many systems is intractable. Granular media simulation is especially susceptible to this issue, wherein two extremes are often taken. In one, grains are modeled as continuum elements, lowering the degrees of freedom but ignoring inherent length scales. In discrete element methods (DEM), every grain and the interactions between them are simulated. DEM is accurate but solve time scales poorly with large grain numbers. A hybrid scheme which bridges these two approaches is presented.

A mass of granular media is partitioned into three domains: continuum using the material point method (MPM), discrete grains using DEM, and a transition zone of both MPM and DEM that are coupled via kinematic constraints. An “oracle” determines which areas of the domain are MPM and which are DEM, and converts between the two. In the canonical example of silo flow, the hybrid method captures a Beverloo curve. Flow with a sufficiently small orifice jams, resolving length scale dependent effects. Collapse of granular columns modeled with the hybrid method compare well quantitatively with pure discrete simulation and experiments in literature. A speedup is seen with the hybrid method over a similar domain of pure discrete grains.