Fluctuations in Shear-Jammed States: A Statistical Ensemble Approach

TL;DR

This paper demonstrates that a stress ensemble framework effectively describes fluctuations in shear-jammed granular states, highlighting the role of angoricity as an analog to temperature and revealing correlations absent in isotropic jamming.

Contribution

It applies the stress ensemble approach to shear-jammed states, showing its effectiveness in capturing stress fluctuations and correlations in non-equilibrium granular solids.

Findings

Stress fluctuations are governed by angoricity, acting as a temperature analog.

Stress correlations are significant and distinct from isotropic jammed states.

The stress ensemble accurately predicts experimental fluctuation data.

Abstract

Granular matter exists out of thermal equilibrium, i.e. it is athermal. While conventional equilibrium statistical mechanics is not useful for characterizing granular materials, the idea of constructing a statistical ensemble analogous to its equilibrium counterpart to describe static granular matter was proposed by Edwards and Oakshott more than two decades ago. Recent years have seen several implementations of this idea. One of these is the stress ensemble, which is based on properties of the force moment tensor, and applies to frictional and frictionless grains. We demonstrate the full utility of this statistical framework in shear jammed (SJ) experimental states [1,2], a special class of granular solids created by pure shear, which is a strictly non-equilbrium protocol for creating solids. We demonstrate that the stress ensemble provides an excellent quantitative description of fluctuations in experimental SJ states. We show that the stress fluctuations are controlled by a single tensorial quantity: the angoricity of the system, which is a direct analog of the thermodynamic temperature. SJ states exhibit significant correlations in local stresses and are thus inherently different from density-driven, isotropically jammed (IJ) states.