A constitutive law for dense granular flows

By P. Jop, Yoël Forterre, Olivier Pouliquen. Nature, 2006

1,838 citations recorded by the source corpus.

A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

Subfields: Civil and Structural Engineering, Computational Mechanics, Management, Monitoring, Policy and Law

View Paper: https://www.semanticscholar.org/paper/9c54005cea4d37f85a416fc98c873122eeaf2811

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Citations in the corpus

A coupled FEM/DEM approach for hierarchical multiscale modelling of granular media (2014, background): “The strain rate for each RVE P D p P " W P " is determined from the inertia number [42]”
Continuum modelling and simulation of granular flows through their many phases (2014, methodology): “The plastic flow parameters correspond approximately to the glass bead parameters in Jop et al. (2006). Unlike the verification tests of the prior section, the elastic modulus E is increased to 1 GPa in all following simulations.”
A three-dimensional numerical model for incompressible two-phase flow of a granular bed submitted to a laminar shearing flow (2010, positive): “…p I + τ p (9) In the frame of the three-dimensional model we express the Coulomb friction model in tensorial form following the idea of Jop et al. [22] : τ p = η p ( ˙ γ p , p p ) ˙ γ p , (10) 4 with η p ( ˙ γ p , p p ) = µ p p ˙ γ p , (11) where the rate of strain tensor ˙ γ p is defined as ˙ γ…”
Granular solid hydrodynamics (2008, background): “In the denser liquid phase, say in chute flows, there is less kinetic energy, more durable deformation, and a rich rheology that has been scrutinized recently [11–13].”
Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming (2013, methodology): “the Pouliquen rheology (Boyer et al., 2011) have been developed for constant normal force boundary conditions, such relations have not yet been applied to model DST systems.”
Viscoplastic modeling of granular column collapse with pressure-dependent rheology (2015, methodology): “As proposed by [31], we introduce variable friction”
Granular and particle-laden flows: from laboratory experiments to field observations (2017, background): “7 An alternative: discrete approach Developed in the late 70’s (Cundall and Strack (1979)), Discrete Element Modeling (DEM) may be seen as an outgrowth of molecular dynamics simulations used in statistical physics.”
Flows of Dense Granular Media (2008, methodology): “…limit of dense systems, the constitutive law of the granular liquid takes the form of a visco-plastic law, in which the stress tensor is given by ( Jop et al. 2006) σi j = −Pδi j + τi j , (5) where P is the isotropic pressure, τi j = ηγ̇i j , with η = μ(I )P|γ̇ | , (6) where |γ̇ | is second…”
The Physics of Sediment Transport Initiation, Cessation, and Entrainment Across Aeolian and Fluvial Environments (2020, methodology): “Experimental measurements of rapid, dense flow in several geometries show good agreement with the local rheology [MiDi, 2004; Jop et al., 2005, 2006].”
Temperature in and out of equilibrium: A review of concepts, tools and attempts (2017, background): “mayonnaise, which is characterised by the presence of a yield - or threshold - stress), or Herschel-Bulkeley models, which are fully non-linear in the strain/shear rate, or to more recent friction-like theories [261, 262, 263, 264, 265].”