Granular contact force density of states and entropy in a modified Edwards ensemble

TL;DR

This paper develops a first-principles method to analyze granular contact force distributions within Edwards' ensemble, successfully matching experimental and simulation data by considering key correlations and entropy maximization.

Contribution

It introduces a novel approach to derive granular contact force probability densities from first principles under Edwards' flat measure, highlighting the roles of grain and structure factors.

Findings

Excellent agreement with experimental data

Identification of grain and structure factors influencing force distributions

Numerical solution of a transport equation for force density

Abstract

A method has been found to analyze Edwards' granular contact force probability functional for a special case. As a result, the granular contact force probability density functions are obtained from first principles for this case. The results are in excellent agreement with the experimental and simulation data. The derivation assumes Edwards' flat measure -- a density of states that is uniform within the metastable regions of phase space. The enabling assumption, supported by physical arguments and empirical evidence, is that correlating information is not significantly recursive through loops in the packing. Maximizing a state-counting entropy results in a transport equation that can be solved numerically. For the present this has been done using the "mean structure approximation," projecting the density of states across all angular coordinates to more clearly identify its predominant non-uniformities. These features are: (1) the grain factor (Psi) related to grain stability and strong correlation between the contact forces on the same grain, and (2) the structure factor (Upsilon) related to Newton's third law and strong correlation between neighboring grains.