A stochastic flow rule for granular materials

TL;DR

This paper introduces a stochastic flow rule (SFR) for modeling dense granular flow, incorporating randomness and discreteness through diffusing spots, successfully predicting various flow profiles with minimal fitting parameters.

Contribution

The paper presents a novel stochastic flow rule that replaces classical plasticity principles, accounting for granular material features via biased random walks of fluidization spots.

Findings

Predicts flow profiles in silos, Couette cells, heaps, and plate dragging.

Operates with no fitting parameters in many cases.

Provides a multiscale framework linking continuum, meso, and microscopic models.

Abstract

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip-lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments -- with essentially no fitting parameters -- although it is only expected to function where material is at incipient failure and slip-lines are inadmissible. For special cases of admissible slip-lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, meso-scale spot random walks, and microscopic particle relaxation.