Rheological Transitions in Two- and Three-Dimensional Granular Media

Abstract

The planar shearing of dense systems of bidisperse as well as polydisperse, non-cohesive, hard, round, dissipative and frictional particles is simulated in two and three dimensions using Contact Dynamics. The system is sheared by smooth, frictional walls at constant shear velocities, subject to a constant normal force. Depending on the shear velocity, the system behavior belongs to one of the three different regimes (from high to low shear velocities): a) a fluid like state with almost homogeneous shearing, b) a block like state with symmetric velocity profiles and fluidization only at the walls, c) a state of broken symmetry, where a block moves essentially with one wall while possessing a shear zone at the other. The two shear velocities separating theses regimes do not depend on the distance between the walls.

Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region

“…Our system size analysis shows a discontinuous transition from regime B to regime C, at V BC ≃0.10 and a continuous transition between regimes A and B completed at V AB ≃0.50 [19][20][21]. V BC and V AB are system size independent.…”

“…However, with rough walls the homogeneous shear regime persists down to very low velocities, in spite of increasing fluctuations. The smooth walls of our system, allowing for slip and rotation at the walls, are responsible for the more complex behavior [19][20][21].…”

“…6) the profiles fluctuate very strongly and the top/bottom symmetry is broken. The shear strain strongly localizes at one wall, while the rest of the system, the bulk region and the opposite wall, moves like one single solid object [19][20][21]. This is the slow shear or one-shear band regime (regime C).…”

“…In this work we use grain-level discrete numerical simulation to investigate the behavior of a model granular material in plane shear between smooth parallel walls, a simple setup which has already been observed to produce [19][20][21], depending on the control parameters, several possible flow patterns, with either bulk shear flow, or localization of gradients at one or both walls. We extract a boundary layer constitutive law similar to the one applying to the bulk material.…”

Minimal dissipation theory and shear bands in biaxial tests

“…The latter parameter can be determined e.g. from simple shear simulations [14] and it was found to be µ w ≃0.12. The result of numerical minimization at different aspect ra- tios match prefectly the simulation data as shown on Fig.…”