Maximum Entropy and the Stress Distribution in Soft Disk Packings Above Jamming

TL;DR

This paper demonstrates that the maximum entropy hypothesis, incorporating stress and force-tile area, effectively explains stress distributions in disordered soft disk packings above jamming, highlighting the role of force-tile area as a key constraint.

Contribution

It introduces the inclusion of Maxwell-Cremona force-tile area as a critical variable in maximum entropy models for stress distributions in jammed packings.

Findings

Maximum entropy accurately predicts stress distributions.

Force-tile area is essential for modeling stress in 2D packings.

Results extend understanding of force networks above jamming.

Abstract

We show that the maximum entropy hypothesis can successfully explain the distribution of stresses on compact clusters of particles within disordered mechanically stable packings of soft, isotropically stressed, frictionless disks above the jamming transition. We show that, in our two dimensional case, it becomes necessary to consider not only the stress but also the Maxwell-Cremona force-tile area, as a constraining variable that determines the stress distribution. The importance of the force-tile area had been suggested by earlier computations on an idealized force-network ensemble.