da Cruz Frédéric, Emam Sacha, Prochnow Michaël, Roux Jean-Noël, Chevoir François
LMSGC, Institut Navier, 2 allée Kepler, 77 420 Champs sur Marne, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Aug;72(2 Pt 1):021309. doi: 10.1103/PhysRevE.72.021309. Epub 2005 Aug 31.
We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.
我们使用离散模拟并规定压力和剪切速率来研究耗散圆盘致密集合体的平面剪切流。这些剪切状态是稳定且均匀的，并且在准静态状态下会变得间歇性。在刚性颗粒的极限情况下，剪切状态由一个单一的无量纲数决定，称为惯性数(I)，它描述了惯性力与压力之比。(I)的小值对应于土力学的准静态临界状态，而(I)的大值对应于动力学理论的完全碰撞状态。当(I)在中等致密流状态下增加时，我们测量到固体分数从最大堆积值近似线性下降，有效摩擦系数从静态内摩擦值近似线性增加。从这些剪胀和摩擦定律中，我们推导出了致密颗粒流的本构定律，其中包含一个塑性库仑项和一个粘性巴格诺尔德项。颗粒的力学特性（恢复系数、摩擦系数和弹性）在致密流状态下影响较小。最后，我们表明相对速度涨落和接触力各向异性随(I)的演化对摩擦定律提供了一个简单解释。
