Entropy maximization in the force network ensemble for granular solids

TL;DR

This paper demonstrates that in two-dimensional granular solids, entropy maximization under the constraint of reciprocal tiling area conservation predicts a Gaussian tail in the force distribution, aligning well with numerical results.

Contribution

It shows that conservation of reciprocal tiling area is essential for accurately predicting force distributions in granular media, resolving a long-standing debate.

Findings

Force distribution has a Gaussian tail when tiling area is conserved.

Entropy maximization with tiling area constraint matches numerical data.

Results hold for frictional and frictionless contact networks.

Abstract

A long-standing issue in the area of granular media is the tail of the force distribution, in particular whether this is exponential, Gaussian, or even some other form. Here we resolve the issue for the case of the force network ensemble in two dimensions. We demonstrate that conservation of the total area of a reciprocal tiling, a direct consequence of local force balance, is crucial for predicting the local stress distribution. Maximizing entropy while conserving the tiling area and total pressure leads to a distribution of local pressures with a generically Gaussian tail that is in excellent agreement with numerics, both with and without friction and for two different contact networks.