Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

Abstract

We perform molecular dynamics simulations of model granular systems undergoing boundarydriven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time t l required for the velocity profiles to become linear and find that t l increases as a power-law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.

Flow transitions in two-dimensional foams

“…In these flows, the rate of strain is discontinuous across the system, often at a transition from shear flow to rigid body type behavior. Discontinuous flows have not yet been observed in simulations, though a number of simulations exhibit continuous flow localization [20][21][22][23][24].…”

Strain localization in a shear transformation zone model for amorphous solids

“…On the smallest scales, molecular dynamics and quasi-static simulations generate a wealth of information about particle interactions and emergent macroscopic behavior -including shear banding [1,19,20] -but they are limited to smaller numbers of particles and time scales. On the largest scales, phenomenological models such as viscoelasticity and the Dieterich-Ruina friction law [21,22], which has been studied extensively in the context of rock mechanics, describe stress-strain step and frequency responses, but to date these laws have not been derived from microscopic dynamics.…”

Subdiffusive behavior in a two-dimensional granular assembly under shear

“…While for I < 0.1 the velocity profile has significant excursions above and below the linearity threshold indicating that the system is in the quasi-static region. These excursions around the linearity threshold have been observed by N. Xu et al, [11] for a Couette flow composed of frictionless beads.…”

“…Computer simulations highlighted the characteristic features of granular flows and revealed some intriguing features, namely: a) a nonlocality of the flow [10], b) a nonlinear behavior of the velocity profile for a planar shear granular flow [11], c) the presence of correlations in the force network [12]. The studies developed in [13] suggest that the granular temperature may be at the origin of the nonlocality.…”