Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials

TL;DR

This paper explores how hysteresis and nonlocal effects interact during flow initiation and arrest in granular materials, using an extended NGF model and DEM simulations to improve understanding and prediction of jamming behavior.

Contribution

It introduces a coupling of hysteresis and nonlocality into the NGF model and develops a new method to compare deterministic predictions with stochastic DEM results.

Findings

Both hysteresis and nonlocality are essential to explain flow transition features.

The extended NGF model can quantitatively predict flow behavior around jamming.

A new methodology links deterministic models with stochastic DEM simulations.

Abstract

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows. By artificially tuning the strength of nonlocal diffusion, we demonstrate that both ingredients are key to explaining certain features of the hysteretic transition between flow and arrest. Finally, we assess the ability of the NGF model to quantitatively predict material behavior both around the transition and in the flowing regime, through stress-driven discrete element method (DEM) simulations of flow onset and arrest in various geometries. Along the way, we develop a new methodology to compare deterministic model predictions with the stochastic behavior exhibited by the DEM simulations around the jamming transition.