  The jamming transition in granular materials is well-known for exhibiting
hysteresis, wherein the level of shear stress required to trigger flow is
larger than that below which flow stops. Although such behavior is typically
modeled as a simple non-monotonic flow rule, the rheology of granular materials
is also nonlocal due to cooperativity at the grain scale, leading for instance
to increased strengthening of the flow threshold as system size is reduced. We
investigate how these two effects - hysteresis and nonlocality - couple with
each other by incorporating non-monotonicity of the flow rule into the nonlocal
granular fluidity (NGF) model, a nonlocal constitutive model for granular
flows. By artificially tuning the strength of nonlocal diffusion, we
demonstrate that both ingredients are key to explaining certain features of the
hysteretic transition between flow and arrest. Finally, we assess the ability
of the NGF model to quantitatively predict material behavior both around the
transition and in the flowing regime, through stress-driven discrete element
method (DEM) simulations of flow onset and arrest in various geometries. Along
the way, we develop a new methodology to compare deterministic model
predictions with the stochastic behavior exhibited by the DEM simulations
around the jamming transition.
