Dense granular materials display a complicated set of flow properties, which differentiate them from ordinary fluids. Despite their ubiquity, no model has been developed that captures or predicts the complexities of granular flow, posing an obstacle in industrial and geophysical applications. Here we propose a 3D constitutive model for well-developed, dense granular flows aimed at filling this need. The key ingredient of the theory is a grain-size-dependent nonlocal rheology-inspired by efforts for emulsions-in which flow at a point is affected by the local stress as well as the flow in neighboring material. The microscopic physical basis for this approach borrows from recent principles in soft glassy rheology. The sizedependence is captured using a single material parameter, and the resulting model is able to quantitatively describe dense granular flows in an array of different geometries. Of particular importance, it passes the stringent test of capturing all aspects of the highly nontrivial flows observed in split-bottom cells-a geometry that has resisted modeling efforts for nearly a decade. A key benefit of the model is its simple-to-implement and highly predictive final form, as needed for many real-world applications. G ranular materials are ubiquitous in day-to-day life, as well as central to important industries, such as geotechnical, energy, pharmaceutical, and food processing. In fact, granular matter is second only to water as the most handled industrial material (1), but unlike water, dense granular flows are substantially more complex (2-10). In particular, slowly flowing granular media form clear, experimentally robust features, most notably, shear bands, which can have a variety of possible widths and decay nontrivially into the surrounding quasi-rigid material. However, these behaviors remain poorly understood and have not been rationalized with a universal continuum model, posing a costly problem in industry. Quantitatively describing and predicting dense, well-developed granular flows with a constitutive model that may be applied in arbitrary configurations remains a major open challenge.For many years, mechanicians and materials engineers have approached granular materials modeling from a soil mechanics perspective, grounded in the principles of continuum solid mechanics, invoking various yield criteria and plastic flow relations (11, 12). In contrast, over the past two decades, a resurgence of interest in granular media has arisen among physicists, primarily drawing upon statistical and fluid dynamical approaches (13,14). More recently, drawing upon both schools of thought, granular rheologists have made progress combining a fluid-like, ratedependent flow approach with an appropriate yield criterion. Backed by numerous experiments and a coherent dimensional argument, the key result is the dimensionless relation μ = μ(I), consistent with the seminal work of Bagnold (15), which has become a well-regarded basis for modeling well-developed granular flows in simple shear (9, 16), where μ = τ/P fo...

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Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused on driven steady-flow problems. For layers thicker than the stopping height, the theoretical flow profiles display a thickness-dependent shape whose features are in agreement with previous discrete particle simulations. We also address the issue of the Froude number of the flows, which has been shown experimentally to collapse as a function of the ratio of layer thickness to stopping height. While the collapse is not obvious, two explanations emerge leading to a revisiting of the history of inertial rheology, which the nonlocal model references for its homogeneous flow response.