Fluctuations in shear-jammed states: A statistical ensemble approach

¹ Department of Physics, Syracuse University - Syracuse, NY 13244, USA
² Institute of Natural Sciences and Department of Physics, Shanghai Jiao Tong University - Shanghai 200240, China
³ Department of Physics, Duke University - Durham, NC 27708, USA
⁴ Martin Fisher School of Physics, Brandeis University - Waltham, MA 02454, USA

Received: 27 February 2013
Accepted: 30 April 2013

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, a special class of granular solids created by pure shear, which is a strictly non-equilibrium 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.