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

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 mater...

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Bibliographic Details
Published in:Soft matter 2021-08, Vol.17 (31), p.7359-7375
Main Authors: Mowlavi, Saviz, Kamrin, Ken
Format: Article
Language:English
Subjects:
Constitutive models
Discrete element method
Flow
Fluidity
Granular materials
Hysteresis
Jamming
Mathematical models
Nerve growth factor
Rheological properties
Rheology
Shear stress
Stochasticity
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Summary: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. Using continuum modeling as well as discrete-element simulations, we investigate how velocity-weakening and nonlocality explain characteristic features of the solid-like to liquid-like transition in granular materials.
ISSN:1744-683X
1744-6848
DOI:10.1039/d1sm00659b