Criticality and isostaticity in fiber networks

TL;DR

This paper investigates the mechanical behavior of disordered fibrous networks, revealing a crossover from stretching to bending dominance and identifying critical phenomena near the isostatic point that challenge continuum elasticity assumptions.

Contribution

It provides new insights into how bending constraints influence network rigidity and characterizes the critical behavior near the isostatic threshold in fibrous networks.

Findings

Power-law dependence of shear modulus on bending and stretching rigidities

Divergent strain fluctuations at the isostatic point

Breakdown of continuum elasticity below a correlation length 

Abstract

The rigidity of elastic networks depends sensitively on their internal connectivity and the nature of the interactions between constituents. Particles interacting via central forces undergo a zero-temperature rigidity-percolation transition near the isostatic threshold, where the constraints and internal degrees of freedom are equal in number. Fibrous networks, such as those that form the cellular cytoskeleton, become rigid at a lower threshold due to additional bending constraints. However, the degree to which bending governs network mechanics remains a subject of considerable debate. We study disordered fibrous networks with variable coordination number, both above and below the central-force isostatic point. This point controls a broad crossover from stretching- to bending-dominated elasticity. Strikingly, this crossover exhibits an anomalous power-law dependence of the shear modulus on both stretching and bending rigidities. At the central-force isostatic point---well above the rigidity threshold---we find divergent strain fluctuations together with a divergent correlation length $\xi$, implying a breakdown of continuum elasticity in this simple mechanical system on length scales less than $\xi$.