Stress transmission and isostatic states of non-rigid particulate systems

TL;DR

This paper extends isostaticity theory to non-rigid particles, demonstrating that macroscopic stress states can be accurately modeled by equivalent rigid assemblies, with errors diminishing as system size increases.

Contribution

It introduces a framework for applying isostaticity theory to non-rigid particles, showing the validity of stress transmission models beyond perfectly rigid systems.

Findings

Stress field errors decay as a power law with system size.

Isostatic states are achievable in non-rigid particles in 2D and 3D.

Equivalent rigid particle assemblies support the same stress fields.

Abstract

The isostaticity theory for stress transmission in macroscopic planar particulate assemblies is extended here to non-rigid particles. It is shown that, provided that the mean coordination number in $d$ dimensions is $d+1$, macroscopic systems can be mapped onto equivalent assemblies of perectly rigid particles that support the same stress field. The error in the stress field that the compliance introduces for finite systems is shown to decay with size as a power law. This leads to the conclusion that the isostatic state is not limited to infinitely rigid particles both in two and in three dimensions, and paves the way to an application of isostaticity theory to more general systems.