Granular flows from grains to a continuum point of view

Pierre-Yves Lagree (University Paris 06)

Frank Adams 1, Alan Turing Building,

Granular matter (sand, rocks, gravels...) flows like a viscous fluid, but also resists  shear stress like a solid. It evolves from one state to the other over a typical distance of a few grain diameters. Here we adopt the fluid point of view and discribe granular matter as a continuum with the so called µ(I) rheology: a plastic rheology where the normal and shear stress are proportional (Coulomb friction law).

This non-Newtonian rheology is implemented in a 2D Navier-Stokes solver (Gerris). Moreover, comparison with Contact Dynamics simulations (the displacement of all the grains is computed) with Shallow-Water models and experiments show the reliability of the μ(I)-rheology when modeling complex flow of granular matter in cases of avalanche flows (Bagnold flow), collapse‌ of columns and flow in hourglass.

                                               Flow in a sand glass

                                               

   Discrete Contact Dynamics                                                Continuum Flow

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