Using molecular dynamics simulations, we calculate fluctuations and responses for steadily sheared hard spheres over a wide range of packing fractions $\phi$ and shear strain rates $\dot{\gamma }$, 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 $T_{\mathrm{eff}}$ that is equal to or larger than the kinetic temperature $T_{\mathrm{kin}}$. We find a crossover in the relationship between the relaxation time $\tau$ and the the nondimensionalized effective temperature $T_{\mathrm{eff}}/p{\sigma }^3$, where $p$ is the pressure and $\sigma$ is the sphere diameter. In the solid response regime, the behavior at a fixed packing fraction satisfies $\tau \dot{\gamma }\propto \exp (-cp{\sigma }^3/T_{\mathrm{eff}})$, where $c$ depends weakly on $\phi$, 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 $T_{\mathrm{eff}}/p{\sigma }^3$ as it depends on $T_{\mathrm{kin}}/p{\sigma }^3$ in equilibrium. This regime includes both near-equilibrium conditions where $T_{\mathrm{eff}}\simeq T_{\mathrm{kin}}$ and far-from-equilibrium conditions where $T_{\mathrm{eff}}\ne T_{\mathrm{kin}}$. We discuss the implications of our results for systems with soft repulsive interactions.

• Received 27 October 2011

DOI:https://doi.org/10.1103/PhysRevE.85.011503