Criticality and isostaticity in fibre networks

Disordered fibre networks are the basis of many man-made and natural materials, including structural components of living cells and tissue. The mechanical stability of such networks relies on the bending resistance of the fibres, in contrast to rubbers, which are governed by entropic stretching of polymer segments. Although it is known that fibre networks exhibit collective bending deformations, a fundamental understanding of such deformations and their effects on network mechanics has remained elusive. Here we introduce a lattice-based model of fibrous networks with variable connectivity to elucidate the roles of single-fibre elasticity and network structure. These networks exhibit both a low-connectivity rigidity threshold governed by fibre-bending elasticity and a high-connectivity threshold governed by fibre-stretching elasticity. Whereas the former determines the true onset of network rigidity, we show that the latter exhibits rich zero-temperature critical behaviour, including a crossover between various mechanical regimes along with diverging strain fluctuations and a concomitant diverging correlation length.