The emergence of Airy stress function in two-dimensional disordered packings of particles

TL;DR

This paper develops an analytical framework for understanding stress distributions in two-dimensional disordered particle packings, revealing the emergence of the Airy stress function in such systems.

Contribution

It introduces a stress probability functional and derives equations for stress tensor components, advancing the analytical understanding of stress in disordered packings.

Findings

Derivation of stress tensor equations in 2D disordered packings

Identification of the Airy stress function's role in these systems

Analytical approach to stress distribution in particle packings

Abstract

The packing of hard-core particles in contact with their neighbors offers the statically determinate problem which allows analytical investigation of the stress tensor distribution. We construct the stress probability functional and derive the complete set of equations for the tensor components in two-dimensions.