Size-dependence of the flow threshold in dense granular materials

The flow threshold in dense granular materials is typically modeled by local, stress-based criteria. However, grain-scale cooperativity leads to size effects that cannot be captured with local conditions. In a widely studied example, flows of thin layers of grains down an inclined surface exhibit a size effect whereby thinner layers require more tilt to flow. In this paper, we consider the question of whether the size-dependence of the flow threshold observed in inclined plane flow is configurationally general. Specifically, we consider three different examples of inhomogeneous flow - planar shear flow with gravity, annular shear flow, and vertical chute flow - using two-dimensional discrete-element method calculations and show that the flow threshold is indeed size-dependent in these flow configurations, displaying additional strengthening as the system size is reduced. We then show that the nonlocal granular fluidity model - a nonlocal continuum model for dense granular flow - is capable of quantitatively capturing the observed size-dependent strengthening in all three flow configurations.