Scaling theory for mechanical critical behavior in fiber networks

TL;DR

This paper develops a scaling theory for the strain-controlled rigidity transition in fiber networks, linking critical exponents and validating predictions through simulations of different network models.

Contribution

It introduces a real-space renormalization approach to derive relations between critical exponents for the strain-induced transition in fiber networks.

Findings

Critical exponents are related through the developed scaling theory.

Numerical simulations confirm the theoretical predictions.

The theory applies to both lattice-based and packing-derived fiber networks.

Abstract

As a function of connectivity, spring networks exhibit a critical transition between floppy and rigid phases at an isostatic threshold. For connectivity below this threshold, fiber networks were recently shown theoretically to exhibit a rigidity transition with corresponding critical signatures as a function of strain. Experimental collagen networks were also shown to be consistent with these predictions. We develop a scaling theory for this strain-controlled transition. Using a real-space renormalization approach, we determine relations between the critical exponents governing the transition, which we verify for the strain-controlled transition using numerical simulations of both triangular lattice-based and packing-derived fiber networks.