Stanifer Ethan, Manning M Lisa
Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA.
Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA.
Soft Matter. 2022 Mar 23;18(12):2394-2406. doi: 10.1039/d1sm01451j.
Under applied shear strain, granular and amorphous materials deform particle rearrangements, which can be small and localized or organized into system-spanning avalanches. While the statistical properties of avalanches under quasi-static shear are well-studied, the dynamics during avalanches is not. In numerical simulations of sheared soft spheres, we find that avalanches can be decomposed into bursts of localized deformations, which we identify using an extension of persistent homology methods. We also study the linear response of unstable systems during an avalanche, demonstrating that eigenvalue dynamics are highly complex during such events, and that the most unstable eigenvector is a poor predictor of avalanche dynamics. Instead, we modify existing tools that identify localized excitations in stable systems, and apply them to these unstable systems with non-positive definite Hessians, quantifying the evolution of such excitations during avalanches. We find that bursts of localized deformations in the avalanche almost always occur at localized excitations identified using the linear spectrum. These new tools will provide an improved framework for validating and extending mesoscale elastoplastic models that are commonly used to explain avalanche statistics in glasses and granular matter.
在施加剪切应变的情况下，颗粒材料和非晶材料会因颗粒重排而发生变形，这种重排可能是微小的局部变化，也可能组织成跨越整个系统的雪崩式变化。虽然准静态剪切下雪崩的统计特性已得到充分研究，但雪崩过程中的动力学情况却并非如此。在剪切软球的数值模拟中，我们发现雪崩可分解为局部变形的突发，我们使用持久同调方法的扩展来识别这些突发。我们还研究了雪崩期间不稳定系统的线性响应，证明在此类事件中特征值动力学非常复杂，而且最不稳定的特征向量并不能很好地预测雪崩动力学。相反，我们修改了用于识别稳定系统中局部激发的现有工具，并将其应用于这些具有非正定黑塞矩阵的不稳定系统，量化雪崩期间此类激发的演变。我们发现，雪崩中局部变形的突发几乎总是发生在使用线性谱识别出的局部激发处。这些新工具将为验证和扩展常用于解释玻璃和颗粒物质中雪崩统计的中尺度弹塑性模型提供一个改进的框架。
