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.

中文翻译：

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颗粒材料流动开始和停止期间滞后和非定域性之间的相互作用

众所周知，颗粒材料中的堵塞转变会表现出滞后现象，其中触发流动所需的剪切应力水平大于流动停止所需的剪切应力水平。虽然这种行为通常被建模为一个简单的非单调流动规则，但由于颗粒尺度上的协同性，颗粒材料的流变学也是非局部的，例如，随着系统尺寸的减小，流动阈值的增强会增加。我们通过将流动规则的非单调性纳入非局部颗粒流动性 (NGF) 模型（一种用于颗粒流动的非局部本构模型）来研究这两种效应（滞后和非局部性）如何相互耦合。通过人为调整非局部扩散的强度，我们证明这两种成分都是解释流动和停顿之间滞后过渡的某些特征的关键。最后，我们通过应力驱动离散元方法 (DEM) 模拟各种几何形状的流动开始和停止，评估 NGF 模型定量预测过渡和流动状态中材料行为的能力。在此过程中，我们开发了一种新方法来比较确定性模型预测与围绕干扰过渡的 DEM 模拟所展示的随机行为。