First order rigidity transition and multiple stability regimes for random networks with internal stresses

TL;DR

This paper shows that internal stresses in disordered networks change the rigidity transition from continuous to first-order and reveal a new stability regime at low coordination numbers, with implications for understanding material stability.

Contribution

It introduces a theoretical framework demonstrating how internal stresses alter the nature of rigidity transitions and predicts a new stability regime in random networks.

Findings

Rigidity transition becomes first-order due to internal stresses.

Existence of a new stability regime at low coordination numbers.

Predictions are made for experimental verification.

Abstract

By applying effective medium-style calculations to random spring networks, we demonstrate that internal stresses fundamentally alter the nature of the rigidity transition in disordered materials, changing it from continuous to first-order and increasing the mean coordination number z at which rigidity first occurs. Furthermore, we predict the existence of a novel stability regime at low z when the distribution of stresses is asymmetric. Means of verifying these predictions are suggested.