Ratio of effective temperature to pressure controls the mobility of sheared hard spheres

Abstract

Using molecular dynamics simulation, we calculate fluctuations and response for steadily sheared hard spheres over a wide range of packing fractions $\varphi$ and shear strain rates $\gamma$, using two different methods to dissipate energy. To a good approximation, shear stress and density fluctuations are related to their associated response functions by a single effective temperature $T_{eff}$ that is equal to or larger than the kinetic temperature $T_{kin}$. We find a crossover in the relationship between the relaxation time $\tau$ and the the nondimensionalized effective temperature $T_{eff}/p{\sigma }^3$, where $p$ is the pressure and $\sigma$ is the sphere diameter. In the solid response regime, the behavior at fixed packing fraction satisfies $\tau \gamma \propto \exp (-cp{\sigma }^3/T_{eff})$, where $c$ depends weakly on $\varphi$, suggesting that the average local yield strain is controlled by the effective temperature in a way that is consistent with shear transformation zone theory. In the fluid response regime, the relaxation time depends on $T_{eff}/p{\sigma }^3$ as it depends on $T_{kin}/p{\sigma }^3$ in equilibrium. This regime includes both near-equilibrium conditions where $T_{eff}{T}_{kin}$ and far-from-equilibrium conditions where $T_{eff}\ne T_{kin}$. We discuss the implications of our results for systems with soft repulsive interactions.

9 pages, 6 figures. Major revision: added results and analysis for sheared inelastic hard spheres to complement the previous results for sheared thermostatted hard spheres, increasing the available range of $T_{eff}$ and strengthening the conclusions; added discussion of results relative to the jamming phase diagram

References in corpus (8)

• Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
• Excitations are localized and relaxation is hierarchical in glass-forming liquids
• Nonlinear rheology of colloidal dispersions
• Rheological properties of the soft-disk model of two-dimensional foams
• Mapping the glassy dynamics of soft spheres onto hard-sphere behavior
• Particle dynamics and effective temperature of jammed granular matter in a slowly sheared 3D Couette cell
• Universal Jamming Phase Diagram in the Hard-Sphere Limit
• Effective temperatures of a driven, strongly anisotropic Brownian system

Cited by in corpus (8)

• Mapping the glassy dynamics of soft spheres onto hard-sphere behavior
• Stick-slip instabilities in sheared granular flow: the role of friction and acoustic vibrations
• Non-equilibrium thermodynamics in sheared hard-sphere materials
• Grain fragmentation in sheared granular flow: weakening effects, energy dissipation, and strain localization
• Athermal Jamming vs Thermalized Glassiness in Sheared Frictionless Particles
• Shear flow of angular grains: acoustic effects and non-monotonic rate dependence of volume
• Glass Dynamics at High Strain Rates
• Temperature-pressure scaling for air-fluidized grains on approaches to Point J