Stress relaxation in dense and slow granular flows

In a dense granular system, particles interact in networks containing many particles and interaction times are long compared with the particle binary collision time. In these systems, the streaming part of the granular stress is negligible. We only consider the collisional stress in this paper. The average behavior of particle contacts is studied. By following the statisti cal method developed recently by the authors [Zhang and Rauenzahn, J. Rheol . 41, 1275 (1997)], we derive an evolution equation for the collisional str ess. This equation provides guidance to collateral numerical simulations, w hich show that the probability distribution of particle contact times is ex ponential for long contact times. This can be explained by network interact ions in a dense granular system. In general, the relaxation of the collisio nal stress is a combined effect of the decay of the contact time probabilit y and the relaxation of collisional forces among particles. In the numerica l simulations, the normal force between a pair of particles is modeled as p arallel connect of a spring and a dashpot. In this case, the relaxation of the force magnitude conditionally averaged given a specific contact time is negligible, and the major contribution to the stress relaxation is from th e exponential decay of the contact time probability. We also note that the probability decay rate is proportional to the imposed strain rate. Conseque ntly, in a simple shear flow with a constant particle volume fraction, as t he shear rate approaches zero, the shear stress approaches a finite value. This value is the yield stress for that particle volume fraction. Hence, th e evolution equation of the collisional stress predicts viscoplasticity of dense granular systems. (C) 2000 The Society of Rheology. [S0148-6055(00)00 105-X].