Abstract

Granular packings are disordered, athermal, driven materials that defy description with conventional statistical mechanics. In this talk, I will introduce the stress ensemble, based on conservation laws for packings in mechanical equilibrium. Adapting the fundamental derivation of the thermal canonical ensemble, we arrive at a description with a granular density of states, closely linked to the entropy, and a tensorial inverse temperature equivalent. The idea of the ensemble has been tested numerically in frictionless packings, and experimentally in frictional packings, including an adaptation of the SGR formalism. I will briefly sketch these.

The complex interactions between stress and contact degrees of freedom allow only limited direct calculations. I will present the results of a field theory based on the Airy stress function (2 dimensional), and a full mean field description.