Dynamics of Random Packings in Granular Flow

Abstract

We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random packing undergo chain-like collective displacements in response to diffusing "spots" of influence, carrying a slight excess of interstitial free volume. We reconstruct the microscopic dynamics of particles from the "coarse grained" dynamics of spots by introducing a localized particle relaxation step after each spot-induced block displacement, simply to enforce packing constraints with a (fairly arbitrary) soft-core repulsion. To test the model, we study to what extent it can describe the dynamics of up to 135,000 frictional, viscoelastic spheres in granular drainage simulated by the discrete-element method (DEM). With only five fitting parameters (the radius, volume, diffusivity, drift velocity, and injection rate of spots), we find that the spot simulations are able to largely reproduce not only the mean flow and diffusion, but also some subtle statistics of the flowing packings, such as spatial velocity correlations and many-body structural correlations. The spot simulations run over 100 times faster than DEM and demonstrate the possibility of multiscale modeling for amorphous materials, whenever a suitable model can be devised for the coarse-grained spot dynamics.

8 pages, 7 figures

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• Modeling silo clogging with nonlocal granular rheology
• The stochastic flow rule: A multi-scale model for granular plasticity
• Flow of anisometric particles in a quasi-2D hopper
• Data-driven model order reduction for granular media
• Wide shear zones and the spot model: Implications from the split-bottom geometry
• On the interaction of dilatancy and friction in the behavior of fluid-saturated sheared granular materials: a coupled Computational Fluid Dynamics--Discrete Element Method study
• The Spot Model for random-packing dynamics
• Nonlinear elasto-plastic model for dense granular flow