Fiber networks below the isostatic point: fracture without stress concentration

TL;DR

This paper demonstrates through simulations that certain diluted fiber networks below the isostatic point exhibit a critical phase where stress does not concentrate, damage is diffuse, and catastrophic failure is prevented.

Contribution

It introduces a new critical phase in fiber networks below the isostatic point, showing stress distribution and damage behavior differ from traditional failure mechanisms.

Findings

Stress never concentrates in the critical phase.

Damage occurs over a divergent length scale.

Catastrophic failure is avoided in these networks.

Abstract

Crack nucleation is a ubiquitous phenomena during materials failure, because stress focuses on crack tips. It is known that exceptions to this general rule arise in the limit of strong disorder or vanishing mechanical stability, where stress distributes over a divergent length scale and the material displays diffusive damage. Here we show, using simulations, that a class of diluted lattices displays a new critical phase when they are below isostaticity, where stress never concentrates, damage always occurs over a divergent length scale, and catastrophic failure is avoided.