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 contribution) and a rate-dependent component (representing the kinetic contribution), 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.