Non-equilibrium thermodynamics in sheared hard-sphere materials

TL;DR

This paper integrates shear-transformation-zone theory with Edwards' statistical approach to model shear flow in disordered, thermalized hard-sphere systems, providing a thermodynamic framework that links jamming and glass transitions.

Contribution

It develops a novel thermodynamic model combining STZ theory with Edwards' statistical mechanics for hard spheres, predicting flow behavior near jamming.

Findings

Predicted strain rate as a function of shear stress and pressure.

Interpreted numerical simulations to gain insights into jamming and glass transitions.

Identified the role of compactivity in the internal state of disorder.

Abstract

We combine the shear-transformation-zone (STZ) theory of amorphous plasticity with Edwards' statistical theory of granular materials to describe shear flow in a disordered system of thermalized hard spheres. The equations of motion for this system are developed within a statistical thermodynamic framework analogous to that which has been used in the analysis of molecular glasses. For hard spheres, the system volume $V$ replaces the internal energy $U$ as a function of entropy $S$ in conventional statistical mechanics. In place of the effective temperature, the compactivity $X = \partial V / \partial S$ characterizes the internal state of disorder. We derive the STZ equations of motion for a granular material accordingly, and predict the strain rate as a function of the ratio of the shear stress to the pressure for different values of a dimensionless, temperature-like variable near a jamming transition. We use a simplified version of our theory to interpret numerical simulations by Haxton, Schmiedeberg and Liu, and in this way are able to obtain useful insights about internal rate factors and relations between jamming and glass transitions.