Saitoh Kuniyasu, Mizuno Hideyuki
Faculty of Engineering Technology, MESA+, University of Twente, Drienerlolaan 5, 7522 NB, Enschede, The Netherlands.
Soft Matter. 2016 Feb 7;12(5):1360-7. doi: 10.1039/c5sm02760h. Epub 2015 Dec 23.
By using molecular dynamics (MD) simulations of dense granular particles in two dimensions, we study turbulent-like structures of their non-affine velocities under simple shear deformations. We find that the spectrum of non-affine velocities, introduced as an analog of the energy spectrum for turbulent flows, exhibits the power-law decay if the system is yielding in a quasi-static regime, where large-scale collective motions and inelastic interactions of granular particles are crucial for the anomalous cascade of kinetic energy. Based on hydrodynamic equations of dense granular materials, which include both kinetic and contact contributions in constitutive relations, we derive a theoretical expression for the spectrum, where a good agreement between the result of MD simulations and theoretical prediction is established over a wide range of length scales.
通过对二维致密颗粒进行分子动力学（MD）模拟，我们研究了在简单剪切变形下其非仿射速度的类湍流结构。我们发现，作为湍流能量谱的类似物引入的非仿射速度谱，如果系统在准静态状态下屈服，则呈现幂律衰减，其中颗粒的大规模集体运动和非弹性相互作用对于动能的反常级联至关重要。基于致密颗粒材料的流体动力学方程，该方程在本构关系中同时包含动力学和接触贡献，我们推导了该谱的理论表达式，在很宽的长度尺度范围内，MD模拟结果与理论预测之间建立了良好的一致性。
