Continuum modelling and simulation of granular flows through their many phases

TL;DR

This paper introduces a comprehensive continuum model for granular flows that captures transitions between solid-like and fluid-like phases, implemented via a Material Point Method for accurate simulation of large deformations.

Contribution

A novel constitutive framework enabling simulation of granular media through multiple phases using MPM, validated against known results.

Findings

Successfully models phase transitions in granular flows.

Capable of simulating large strains and nonlinear deformations.

Validated predictions align with established experimental data.

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 $\mu(I)$ 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. 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 known results.