Rheophysics of dense granular materials: Discrete simulation of plane shear flows

Frédéric da Cruz (1, 2) , Sacha Emam (1, 2) , Michaël Prochnow (2, 1) , Jean-Noël Roux (1, 2) , François Chevoir (1, 2)

1 navier umr 8205 - Laboratoire Navier
2 LMSGC - Laboratoire des matériaux et structures du génie civil

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 uniform, and become intermittent in the quasi-static regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasi-static 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. At the end, 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.

Domaines: Dynamique des Fluides [physics.flu-dyn]; Matière Molle [cond-mat.soft]

Frédéric da Cruz, Sacha Emam, Michaël Prochnow, Jean-Noël Roux, François Chevoir. Rheophysics of dense granular materials: Discrete simulation of plane shear flows. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2005, 72 (2), pp.021309. ⟨10.1103/PhysRevE.72.021309⟩. ⟨hal-01990685⟩