Scaling theory for mechanical critical behavior in 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.
Keywords
Cite
@article{arxiv.1807.01205,
title = {Scaling theory for mechanical critical behavior in fiber networks},
author = {Jordan Shivers and Sadjad Arzash and Abhinav Sharma and Fred C. MacKintosh},
journal= {arXiv preprint arXiv:1807.01205},
year = {2019}
}