A stochastic flow rule for granular materials

Abstract

There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along slip-lines with a drift direction determined by the stress imbalance upon a local switch from static to dynamic friction. In the continuum limit (based on a Fokker-Planck equation for the spot concentration), this simple model is able to predict a variety of granular flow profiles in flat-bottom silos, annular Couette cells, flowing heaps, and plate-dragging experiments -- with essentially no fitting parameters -- although it is only expected to function where material is at incipient failure and slip-lines are inadmissible. For special cases of admissible slip-lines, such as plate dragging under a heavy load or flow down an inclined plane, we postulate a transition to rate-dependent Bagnold rheology, where flow occurs by sliding shear planes. With different yield criteria, the SFR provides a general framework for multiscale modeling of plasticity in amorphous materials, cycling between continuum limit-state stress calculations, meso-scale spot random walks, and microscopic particle relaxation.

References in corpus (5)

• Analysis of Granular Flow in a Pebble-Bed Nuclear Reactor
• Diffusion and mixing in gravity-driven dense granular flows
• Velocity profile of granular flows inside silos and hoppers
• Friction of a slider on a granular layer: Non-monotonic thickness dependence and effect of boundary conditions
• Dynamics of Random Packings in Granular Flow

Cited by in corpus (12)

• Numerical simulations of granular dynamics. I. Hard-sphere discrete element method and tests
• Orientation, Flow, and Clogging in a Two-Dimensional Hopper: Ellipses vs. Disks
• Granular Flows in Split-Bottom Geometries
• Modeling silo clogging with nonlocal granular rheology
• Continuum theory of memory effect in crack patterns of drying pastes
• Modelling the Microstructure and Stress in Dense Suspensions Under Inhomogeneous Flow
• Flow of anisometric particles in a quasi-2D hopper
• Wide shear zones and the spot model: Implications from the split-bottom geometry
• Kinematic flow patterns in slow deformation of a dense granular material
• Sediment creep triggered by porous flow
• Microfluidic velocimetry reveals spatial cooperativity in soft glassy flows
• Nonlinear elasto-plastic model for dense granular flow