Rheophysics of dense granular materials: discrete simulation of plane shear flows.

By F. Da Cruz, Sacha Emam, Michaël Prochnow, J. Roux, F. Chevoir. Physical review. E, Statistical, nonlinear, and soft matter physics, 2005

1,183 citations recorded by the source corpus.

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.

Subfields: Biomedical Engineering, Computational Mechanics, Management, Monitoring, Policy and Law

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Citations in the corpus

Continuum modelling and simulation of granular flows through their many phases (2014, methodology): “Reasonable codirectionality (with rotations of the principal axes only a handful of degrees apart) between D0 and σ0 in dense granular flow has been observed in DEM simulations by da Cruz et al. (2005); Silbert et al. (2001); Koval et al.”
Flows of Dense Granular Media (2008, methodology): “Investigators have made several attempts to connect the rheology to the evolution of the distribution of contacts within the granular assembly (Ancey et al. 1999, da Cruz et al. 2005, Lois et al. 2006).”
Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions (2014, background): “This perspective can be incorporated in a dimensionless inertial number I ≡ γ̇d √ ρ/Π [da Cruz et al. 2005], where d is the diameter of the solid particles, ρ their density, and Π the particle pressure.”
Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory (2010, background): “Numerical simulations of homogeneous, steady shearing flows of granular materials [17,18] indicate that the presence of friction does have an influence on the tractions necessary to maintain a shearing flow at a given solids fraction.”
Local determination of the constitutive law of a dense suspension of noncolloidal particles through magnetic resonance imaging (2005, background): “…expect the criterion for starting and stopping (as localization is perfectly reversible) the flow to be a frictional Coulomb criterion: τ/σN ≤ µs(φ) in the jammed material (for a discussion on the φ dependence of the friction coefficient µs near the jamming transition, see da Cruz et al. (2005)).”
Exploring the relationship between critical state and particle shape for granular materials (2015, methodology): “Several studies have examined the effect of μs on the shear behavior (e.g., Thornton, 2000; Dai et al., 2015) and the granular flow (da Cruz et al., 2005; Kamrin and Koval, 2014) by using the discrete element method (DEM).”