Non-locality in Granular Flow: Phenomenology and Modeling Approaches

Abstract

This paper reviews the emergence of non-local flow phenomena in granular materials and discusses a range of models that have been proposed to integrate an intrinsic length-scale into granular rheology. The frameworks discussed include micro-polar modeling, kinetic theory, three particular order-parameter-based models, and strongly non-local integral-based models. An extensive commentary is included discussing the current capabilities of these existing models as well as their implementational ease, physical motivation, and breadth of predictive ability.

Microscopic Origin of Nonlocal Rheology in Dense Granular Materials

“…To account for such nonlocal effects, the concept of granular fluidity was introduced [12][13][14][15][16], and continuum constitutive laws extending the inertial granular rheology to the quasistatic regime were proposed [14,[17][18][19]. Recently, using discrete element simulations in plane shear, gravitational and chute flows, a relation between granular fluidity and velocity fluctuations was exhibited [20].…”

Microscopic Picture of Erosion and Sedimentation Processes in Dense Granular Flows

“…This approach consists in a semi-empirical description of granular matter, through an effective friction coefficient µ, that is a function of an inertial number I directly related to the flow velocity [2]. Extensions of this µ(I) rheology have been proposed by several authors to address spatial heterogeneities and non-local effects [3][4][5][6][7]. For instance, the yield stress increases as the thickness of the flow region reduces, which manifests itself through a thickness-dependent stop angle in granular flows down inclined planes [8].…”

“…For instance, the yield stress increases as the thickness of the flow region reduces, which manifests itself through a thickness-dependent stop angle in granular flows down inclined planes [8]. Another example deals with heap flows, where creep appears through a spatial exponential decay of the velocity over a few grains [7]. In parallel, semi-empirical models have been developed to describe the dynamics of avalanches, defined as dense granular flows atop static granular solids.…”

“…With the above expressions for N sol and N flu , the evolutions of θ sed and θ ero can be computed by solving numerically Eqs. (6) and (7). There are five relevant dimensionless parameters in the model: µ eff , ϕ sol , a, ξ, and D. The coefficient a was estimated to be close to 0.5 [17], while the effective friction coefficient is fixed to µ eff = tan(20 • ), and ϕ sol spans the range [23…”

Nonlocality in granular complex networks: Linking topology, kinematics and forces

“…Alongside these micromechanical studies, it was recognized that standard continuum theories failed to capture nonlocal effects [41,42]. As a result, two major families of theories have emerged: enhanced continua [43] and nonlocal theories [44]. Enhanced (or weakly nonlocal [45]) continua depart from the standard Cauchy assumption of affine deformation, by introducing higher-order kinematics and their conjugate kinetics.…”