Rigidity Loss in Disordered Systems: Three Scenarios

TL;DR

This paper compares the rigidity transitions in three types of disordered networks, revealing distinct behaviors and the influence of global self-organization on their mechanical properties.

Contribution

It identifies qualitative differences in rigidity loss among randomly diluted, jammed, and stress-relieved networks, highlighting the role of global self-organization.

Findings

Jammed and stress-relieved networks are globally isostatic at the marginal state.

Randomly diluted networks exhibit both overconstrained and underconstrained regions.

Adding or removing a bond affects jammed networks globally, but only locally in stress-relieved networks.

Abstract

We reveal significant qualitative differences in the rigidity transition of three types of disordered network materials: randomly diluted spring networks, jammed sphere packings, and stress-relieved networks that are diluted using a protocol that avoids the appearance of floppy regions. The marginal state of jammed and stress-relieved networks are globally isostatic, while marginal randomly diluted networks show both overconstrained and underconstrained regions. When a single bond is added to or removed from these isostatic systems, jammed networks become globally overconstrained or floppy, whereas the effect on stress-relieved networks is more local and limited. These differences are also reflected in the linear elastic properties and point to the highly effective and unusual role of global self-organization in jammed sphere packings.