Mechanics of fiber networks under a bulk strain

TL;DR

This paper investigates the critical mechanical behavior of biopolymer fiber networks under bulk strain, revealing phase transition characteristics and differing exponents compared to shear deformation.

Contribution

It extends understanding of fiber network mechanics by analyzing bulk strain effects and identifying unique critical exponents and hyperscaling relations.

Findings

Bulk modulus exhibits critical behavior near a critical strain.

Different non-mean-field exponents are observed for bulk versus shear.

Hyperscaling relations similar to shear are confirmed.

Abstract

Biopolymer networks are common in biological systems from the cytoskeleton of individual cells to collagen in the extracellular matrix. The mechanics of these systems under applied strain can be explained in some cases by a phase transition from soft to rigid states. For collagen networks, it has been shown that this transition is critical in nature and it is predicted to exhibit diverging fluctuations near a critical strain that depends on the network's connectivity and structure. Whereas prior work focused mostly on shear deformation that is more accessible experimentally, here we study the mechanics of such networks under an applied bulk or isotropic extension. We confirm that the bulk modulus of subisostatic fiber networks exhibits similar critical behavior as a function of bulk strain. We find different non-mean-field exponents for bulk as opposed to shear. We also confirm a similar hyperscaling relation to what previously found for shear.