Criticality and isostaticity in fiber networks

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 $ξ$, implying a breakdown of continuum elasticity in this simple mechanical system on length scales less than $ξ$.