Three-dimensional granular flow continuum modeling via material point method with hyperelastic nonlocal granular fluidity

TL;DR

This paper introduces a thermodynamically consistent 3D material point method for modeling granular flows using a nonlocal granular fluidity model, validated through experiments and comparisons with other models.

Contribution

It develops a novel numerical approach within a hyperelastic framework to implement the dynamical NGF model in 3D MPM for granular flow simulation.

Findings

Model accurately predicts flow geometry and forces.

Outperforms modified Drucker-Prager model in various configurations.

Validated with experimental data from robotic measurements.

Abstract

The accurate and efficient modeling of granular flows and their interactions with external bodies is an open research problem. Continuum methods can be used to capture complexities neglected by terramechanics models without the computational expense of discrete element methods. Constitutive models and numerical solvers are the two primary aspects of the continuum methods. The viscoplastic size-dependent non-local granular fluidity (NGF) constitutive model has successfully provided a quantitative description of experimental flows in many different configurations in literature. This research develops a numerical approach, within a hyperelasticity framework, for implementing the dynamical form of NGF in three-dimensional material point method (3D MPM, an appropriate numerical solver for granular flow modeling). This approach is thermodynamically consistent to conserve energy, and the dynamical form includes the nonlocal effect of flow cessation. Excavation data, both quantitative measurements and qualitative visualization, are collected experimentally via our robotic equipment to evaluate the model with respect to the flow geometry as well as interaction forces. The results are further compared with the results from a recent modified plastic Drucker-Prager constitutive model, and in other configurations including wheel-soil interactions, a gravity-driven silo, and Taylor-Couette flow.