Walker David M, Tordesillas Antoinette, Froyland Gary
Department of Mathematics and Statistics, University of Melbourne, Parkville, VIC 3010, Australia.
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032205. doi: 10.1103/PhysRevE.89.032205. Epub 2014 Mar 21.
Recent advances in high-resolution measurements means it is now possible to identify and track the local "fabric" or contact topology of individual grains in a deforming sand throughout loading history. These provide compelling impetus to the development of methods for inferring changes in the contact forces and energies at multiple spatiotemporal scales, using information on grain contacts alone. Here we develop a surrogate measure of the fluctuating kinetic energy based on changes in the local contact topology of individual grains. We demonstrate the method for dense granular materials under quasistatic biaxial shear. In these systems, the initially stable and solidlike response eventually gives way to liquidlike behavior and global failure. This crossover in mechanical behavior, akin to a phase transition, is marked by bursts of kinetic energy and frictional dissipation. Mechanisms underlying this release of energy include the buckling of major load-bearing structures known as force chains. These columns of grains represent major repositories for stored strain energy. Stored energy initially accumulates at all of the contacts along the force chain, but is released collectively when the chain overloads and buckles. The exact quantification of the buildup and release of energy in force chains, and the manner in which force chain buckling propagates in the sample (i.e., diffuse and systemwide versus localized into shear bands), requires detailed knowledge of contact forces. To date, however, the forces at grain contacts continue to elude measurement in natural granular materials like sand. Here, using data from computer simulations, we show that a proxy for the fluctuating kinetic energy in dense granular materials can be suitably constructed solely from the evolving properties of the grain's local contact topology. Our approach directly relates the evolution of fabric to energy flux and makes possible research into the propagation of failure from measurements of grain contacts in real granular materials.
高分辨率测量技术的最新进展意味着现在有可能在整个加载历史过程中识别并追踪变形砂中单个颗粒的局部“结构”或接触拓扑。这些进展为开发利用仅关于颗粒接触的信息来推断多个时空尺度下接触力和能量变化的方法提供了有力的推动。在此，我们基于单个颗粒局部接触拓扑的变化开发了一种波动动能的替代度量。我们展示了该方法在准静态双轴剪切下的致密颗粒材料中的应用。在这些系统中，最初稳定且类似固体的响应最终会转变为类似液体的行为和全局破坏。这种力学行为的转变类似于相变，其特征是动能和摩擦耗散的突发。能量释放背后的机制包括被称为力链的主要承载结构的屈曲。这些颗粒柱代表了储存应变能的主要场所。储存的能量最初沿着力链在所有接触点积累，但当链过载并屈曲时会集体释放。要准确量化力链中能量的积累和释放，以及力链屈曲在样品中传播的方式（即扩散到整个系统还是局部化为剪切带），需要详细了解接触力。然而，迄今为止，在像沙子这样的天然颗粒材料中，颗粒接触处的力仍然难以测量。在此，利用计算机模拟数据，我们表明致密颗粒材料中波动动能的一个替代指标可以仅根据颗粒局部接触拓扑的演化特性适当地构建。我们的方法直接将结构的演化与能量通量联系起来，并使得从实际颗粒材料中颗粒接触的测量来研究破坏的传播成为可能。
