What determines static force chains in stressed granular media?

TL;DR

This paper introduces a new formalism to compute inter-particle forces in stressed granular media using external forces and contact orientations, revealing that force chains are determined by an eigenfunction expansion.

Contribution

The paper presents a novel formalism for calculating inter-particle forces based on external forces and contact orientations, advancing understanding of force chain formation.

Findings

Force chains are determined by an eigenfunction expansion.

The formalism effectively computes all inter-particle forces.

The approach applies to particles of any size.

Abstract

The determination of the normal and transverse (frictional) inter-particle forces within a granular medium is a long standing, taunting, and yet unresolved problem. We present a new formalism which employs the knowledge of the external forces and the orientations of contacts between particles (of any given sizes), to compute all the inter-particle forces. Having solved this problem we exemplify the efficacy of the formalism showing that the force chains in such systems are determined by an expansion in the eigenfunctions of a newly defined operator.