The stochastic flow rule: A multi-scale model for granular plasticity

TL;DR

The paper introduces the Stochastic Flow Rule, a multi-scale, rate-independent model for granular plasticity that accurately predicts flow behaviors in various granular systems by modeling diffusing spots of fluidization.

Contribution

It presents the Stochastic Flow Rule as a novel, general constitutive law for granular flow, validated against DEM simulations across different flow geometries.

Findings

Good agreement between SFR predictions and DEM simulations.

SFR effectively models gravity-driven and shear-driven granular flows.

Parametric studies confirm robustness of the model.

Abstract

In spite of many attempts to model dense granular flow, there is still no general theory capable of describing different types of flows, such as gravity-driven drainage in silos and wall-driven shear flows in Couette cells. Here, we summarize our recent proposal of the Stochastic Flow Rule (SFR), which is able to describe these cases in good agreement with experiments, and we focus on testing the theory in more detail against brute-force simulations with the discrete-element method (DEM). The SFR is a general rate-independent constitutive law for plastic flow, based on diffusing spots of fluidization. In the case of quasi-2D granular materials, we assume limit-state stresses from Mohr-Coulomb plasticity and postulate that spots undergo biased random walks along slip-lines, driven by local stress imbalances. We compare analytical predictions of the SFR against DEM simulations for silos and Couette cells, carrying out several parametric studies in the latter case, and find good agreement.