Nonlocal rheology of granular materials*

Granular materials are inherently heterogeneous, and it is therefore difficult to construct a continuum model that successfully spans all the way from creeping to well-developed flows. This deficiency has serious consequences for making predictions in geological and industrial flows, but also presents a very interesting challenge for physicists. Local rheologies, such as the μ(I) rheology, relate the local shear rate to the local stresses. However, they fail to describe creeping flows, non-trivial particle size scaling, and the influence of small vibrations on the flow. Recently, the development of nonlocal rheologies has made inroads into solving this problem by allowing the fluidity at any position in the flow to depend on a spatially-extended region. In my talk, I will describe several experiments on two-dimensional granular materials which bridge particle-scale, meso-scale, and continuum-scale approaches. We test the efficacy of local and nonlocal models for describing flows across various particle shapes, particle stiffness, packing fractions, shear rates, and geometries. Through a combination of photoelastic force measurements, boundary stress measurements, and particle-tracking, it is possible to both fully-characterize the flows and test the assumptions of nonlocal models. We find that a single set of material parameters is able to capture the rheology of a particular granular material under a variety of flow conditions. Our measurements confirm the prediction that there is a growing lengthscale at a finite yield stress ratio associated with a frictional yield criterion. Finally, we observe rearrangements of the force network extending into quasi-static regions of the flow where shear rates vanish, and propose connections between their dynamics and the mechanisms responsible for nonlocal behaviors.