Identification of a universal data collapse in the rheology of granular media

We propose a reduced description of nonlocal phenomena in dense granular flows where the shear stress ratio μ is not locally determined by the inertial number (dimensionless shear rate) I. The nonlocal granular fluidity (NGF) model has been proposed to describe nonlocality by introducing an implicit “fluidity” field and its diffusion. A recent study found the fluidity can be roughly expressed by two physical quantities: the particle velocity fluctuations δv and packing fraction. Here, we reduce the number of quantities from two to one revealing that only δv is needed to explain nonlocality. We perform DEM simulations in many geometries using 3D spheres and 2D discs with various surface frictions. For each granular material, we show there exists a clear constitutive equation that works across geometries, which directly relates three local dimensionless variables: μ, I, and the dimensionless granular temperature (dimensionless δv²) Θ. It allows us to consider the nonlocal phenomena as the result of various spatial distributions of the granular temperature, a field that is generated, diffuses, and dissipates similar to the implied behavior of the fluidity field in the NGF model. We also demonstrate how this μ-I-Θ relation can be applied in continuum simulations of granular flows.