# Stress-stabilized sub-isostatic fiber networks in a rope-like limit

## TL;DR

This paper investigates how external stress stabilizes sub-isostatic fiber networks with rope-like interactions, revealing a power-law relationship between shear modulus and stress, and showing prestress effects on critical strain.

## Contribution

It demonstrates that external stress can stabilize sub-isostatic networks with tensile interactions, extending understanding of their mechanical phase behavior without bending rigidity.

## Key findings

- External stress stabilizes rope-like fiber networks.
- Shear modulus scales with stress via a non-mean-field power law.
- Prestress shifts the critical strain to lower values.

## Abstract

The mechanics of disordered fibrous networks such as those that make up the extracellular matrix are strongly dependent on the local connectivity or coordination number. For biopolymer networks this coordination number is typically between three and four. Such networks are sub-isostatic and linearly unstable to deformation with only central force interactions, but exhibit a mechanical phase transition between floppy and rigid states under strain. Introducing weak bending interactions stabilizes these networks and suppresses the critical signatures of this transition. We show that applying external stress can also stabilize sub-isostatic networks with only tensile central force interactions, i.e., a rope-like potential. Moreover, we find that the linear shear modulus shows a power law scaling with the external normal stress, with a non-mean-field exponent. For networks with finite bending rigidity, we find that the critical stain shifts to lower values under prestress.