Predicting stress fluctuations in granular media under steady-state shear loading is crucial for applications ranging from geophysical processes to construction engineering. Stress fluctuations emerge from particle rearrangement, usually enabled by frictional slip and force-chain buckling. Existing models used to predict stress fluctuations are largely phenomenological, often accounting for the force chain phenomena implicitly through the introduction of internal variables, or explicitly through assumptions of force chain mechanics. Improper consideration of particle mechanics or mesoscale effects can lead to inaccurate predictions of shear strength and instability, making it difficult to predict the onset of yielding, shear band formation, and other instabilities. Furthermore, while recent advancements in machine learning methods have established links between microscale behavior and macroscopic stress drops in granular fault gouges, their predictive capabilities are limited due to their black-box nature. To gain a deeper understanding of stress fluctuations, and ultimately predict them in a physics-informed manner, it is necessary to examine how system energetics change with stress fluctuations. In this paper, we analyze stress fluctuations in a 2D granular fault gouge loaded under quasistatic, steady-state shear. We track the flow of potential energy between force networks and understand how energy and force networks vary with stress rises and drops. We derive an analytical, dynamic force chain model from first principles to illustrate how interactions between force networks lead to the emergence of localized instability phenomena. Finally, we offer insights into how these localized instabilities ultimately enable shear stress fluctuations at the continuum scale.

中文翻译：

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二维颗粒状断层凿孔中的不稳定性：颗粒动力学和应力波动


预测稳态剪切载荷下颗粒介质的应力波动对于从地球物理过程到建筑工程的各种应用至关重要。应力波动是由颗粒重排引起的，通常是由摩擦滑移和力链屈曲引起的。用于预测应力波动的现有模型在很大程度上是现象学的，通常通过引入内部变量隐含地解释力链现象，或者通过力链力学的假设来明确解释力链现象。对粒子力学或中尺度效应的不当考虑会导致对剪切强度和不稳定性的预测不准确，从而难以预测屈服、剪切带形成和其他不稳定因素的开始。此外，虽然机器学习方法的最新进展已经在微观行为和颗粒断层凿孔中的宏观应力下降之间建立了联系，但由于其黑盒性质，它们的预测能力受到限制。为了更深入地了解应力波动，并最终以物理学的方式预测它们，有必要研究系统能量如何随应力波动而变化。在本文中，我们分析了在准静态稳态剪切下加载的 2D 颗粒状断层凿孔中的应力波动。我们跟踪力网络之间的势能流动，并了解能量和力网络如何随应力的上升和下降而变化。我们从第一性原理中推导出一个分析性的动态力链模型，以说明力网络之间的相互作用如何导致局部不稳定现象的出现。最后，我们提供了关于这些局部不稳定性如何最终导致连续体尺度上的剪切应力波动的见解。