Physics of Granular Flows

Title

Constructing and verifying a three-dimensional nonlocal granular rheology

Abstract

We begin by reviewing the 3D inertial flow law for steady, dense granular flow, where plastic flow vanishes within a friction-like (i.e. Drucker-Prager) yield envelope. Beyond this limit the material is modeled to flow more rapidly the larger the stress state is above static yield. This relation appears to function well for very rapid flows, however experimental and DEM results can often differ from the predictions in regions of slower flow. While certain descriptors of the steady flow (e.g. packing fraction) are relatively well-described by local modeling, the velocity profile loses qualitative agreement with model predictions in the quasi-static regime.

We have been able to attribute much of this disagreement to nonlocal effects stemming from the finite-ness of the grain size. To correct for this, we first consider the addition of a simple nonlocal term to the rheology in a fashion similar to recent nonlocal flow models in the emulsions community. This model encompasses the notion that flow events can cause nonlocal stress perturbations on the scale of the grains, which then can induce other flow events. The spatial extent of nonlocality depends on the distance to the "standard" yield surface consistent with notions of critical scaling about the jamming point. The results of this extended model are compared against many DEM steady-flow simulations in three different, albeit simple, 2D geometries. Quantitative agreement is found for all geometries and over various geometrical/loading parameters.

By natural extension, the nonlocal model is then converted to three dimensions with minimal changes, and is implemented numerically as a customized User-Element within the Abaqus software package. We show that a single calibration of the 3D model quantitatively predicts hundreds of experimental flows in different geometries, including, for the first time, the wide-shear zones observed in the split-bottom annular couette cell, a geometry made infamous for resisting a theoretical treatment for a decade.