Nonlinear elasticity of disordered fiber networks

TL;DR

This paper investigates the nonlinear elastic behavior of disordered biopolymer gels, extending known linear scaling laws to the nonlinear regime through numerical tests on lattice models.

Contribution

It introduces a two-parameter scaling law for nonlinear elasticity in disordered fiber networks and validates it with numerical simulations.

Findings

Good scaling collapse for shear modulus in both regimes

Critical exponents computed for lattice models

Results applicable to real biopolymer gels

Abstract

Disordered biopolymer gels have striking mechanical properties including strong nonlinearities. In the case of athermal gels (such as collagen-I) the nonlinearity has long been associated with a crossover from a bending dominated to a stretching dominated regime of elasticity. The physics of this crossover is related to the existence of a central-force isostatic point and to the fact that for most gels the bending modulus is small. This crossover induces scaling behavior for the elastic moduli. In particular, for linear elasticity such a scaling law has been demonstrated [Broedersz et al. Nature Physics, 2011 7, 983]. In this work we generalize the scaling to the nonlinear regime with a two-parameter scaling law involving three critical exponents. We test the scaling law numerically for two disordered lattice models, and find a good scaling collapse for the shear modulus in both the linear and nonlinear regimes. We compute all the critical exponents for the two lattice models and discuss the applicability of our results to real systems.