Model of sheared granular material and application to surface-driven granular flows under gravity

Abstract

This work presents a novel model of sheared granular materials that consist of two-dimensional, slightly inelastic, circular disks. To capture the static and kinetic features of the granular flow involving different regimes, both the shear stress and pressure are superimposed by a rate-independent component ͑representing the static contribution͒ and a rate-dependent component ͑representing the kinetic contribution͒, as determined using granular kinetic theory. The dilatancy law is adopted to close the set of equations, and the constraint that static pressure is non-negative is utilized to determine the transition between the dense regime and the inertial regime. The balance equation of granular temperature incorporates the works done by both the static and kinetic components of shear stress. This enabled the proposed model to predict the hysteretic flow thresholds and the shear bands. Additionally, a thick, surface-driven granular flow under gravity is investigated using the proposed model. The predicted velocity, volume fraction, granular temperature, and stress are consistent with results obtained using the molecular dynamic method. This finding demonstrates the ability of the proposed model to simulate granular flow in which the quasistatic, dense, and kinetic regimes coexist simultaneously.

Kinetic-theory-based model of dense granular flows down inclined planes

“…(10), herein, includes the work done by both the static and kinetic components of shear stress, as in previous studies. 3,20,23 The hydrodynamic theory developed by Jenkins and Richman 31 ignores the spin effect too. To incorporate the effect of tangential contact in collisions, e in the constitutive relations is replaced by e eff , the effective restitution coefficient, as was suggested by Jenkins and Zhang 43 and Yoon and Jenkins.…”

From solid to granular gases: the steady state for granular materials

“…Γ q being the rate at which energy is dissipated in frictional, enduring contacts and Γ c the energy dissipated by collisions, the balance of energy for the simple, shear flow reduces to As suggested by several authors , we assume to subdivide the granular stresses into two contributions: Here and in what follows, the subscripts q (quasi‐static) and c (collisional) refer to quantities associated with enduring, frictional contacts of particles involved in force chains (soil skeleton) and nearly instantaneous collisions, respectively. By substituting Equation into Equation , we obtain Unlike suggested in other works , enduring contacts among particles in force chains cannot produce fluctuating energy. As a consequence, Equation reduces to …”

“…As suggested by several authors [9,[16][17][18][19], we assume to subdivide the granular stresses into two contributions:…”

A visco‐elasto‐plastic model for granular materials under simple shear conditions

“…The model hereafter illustrated can be interpreted as the extension to unsteady conditions of the model discussed in Berzi et al [39] and Vescovi et al [40]. The parallel scheme was already proposed by some authors [34,35,36,37,38], but the novelty of the approach introduced by Berzi et al [39] and Vescovi et al [40] concerns the role of critical state [41,42,43,44,28]: this is here interpreted as the limit for granular stationary flows, under simple shear conditions, when the granular temperature nullifies.…”

“…In contrast, the theoretical constitutive model hereafter presented, as in Johnson and Jackson [34,35], Savage [36], Louge [37], Lee and Huang [38], Berzi et al [39] and Vescovi et al [40], assumes a parallel scheme according to which the stress tensor is evaluated as the sum of two contributions: one "ratedependent" and another "rate-independent". The model hereafter illustrated can be interpreted as the extension to unsteady conditions of the model discussed in Berzi et al [39] and Vescovi et al [40].…”