Continuum modelling and simulation of granular flows through their many phases

Abstract

We propose and numerically implement a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process. When dense, the material is treated as a pressure-sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic flow rule given by the ${\it\mu}(I)$ inertial rheology of granular materials. When the free volume exceeds a critical level, the material is deemed to separate and is treated as disconnected, stress-free media. A material point method (MPM) procedure is written for the simulation of this model and many demonstrations are provided in different geometries, which highlight the ability of the numerical model to handle transitions through dense and disconnected states. By using the MPM framework, extremely large strains and nonlinear deformations, which are common in granular flows, are representable. The method is verified numerically and its physical predictions are validated against many known experimental phenomena, such as Beverloo’s scaling in silo flows, jointed power-law scaling of the run-out distance in granular-column-collapse problems, and various known behaviours in inclined chute flows.