The challenge of predicting the flow behavior of a collection of grains has proven to be a difficult one, from both computational and theoretical perspectives. Unlike Newtonian fluids or linear elastic solids, a continuum model representing the effect of millions of particles interacting through dissipative, frictional contacts has remained a largely open endeavor since it was first considered by Coulomb in the late 1700's. Brute force grain-by-grain discrete element methods can be used, but these approaches become computationally unrealistic for large bodies of material and long times.
In this talk we propose a new, nonlocal continuum relation for granular matter, which is shown to predict granular flow and stress fields in hundreds of different geometries. The model is constructed in a step-by-step fashion. First a local, elasto-visoplastic flow relation is derived based on the principle of inertial scaling. The clearest missing ingredient is shown to be the lack of an intrinsic length-scale to represent the cooperativity that a finite grain size asserts on the flow. We account for this with a carefully justified implicit-nonlocal term, which introduces a single new material parameter, and converts the flow rule into a separate PDE that couples directly with the momentum balance PDE. The model is numerically implemented with a custom finite-element scheme. Under a single parameter calibration, the nonlocal model quantitatively predicts the flow and stress data from ~200 experiments of spherical bead systems in several different families of geometries. Moreover, it is the first model to accurately predict all features of flows in "split-bottom cells", a decade-long open problem in the field. We show that the same model also reconciles other "unusual" features of granular media, such as the observation that thinner granular layers behave as if they are stronger, and the motion-induced quicksand effect wherein flow at one location eliminates the yield stress everywhere.