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Athermal models of disordered fibrous networks are highly useful for studyingthe mechanics of elastic networks composed of stiff biopolymers. The underlyingnetwork architecture is a key aspect that can affect the elastic properties ofthese systems, which include rich linear and nonlinear elasticity. Existingcomputational approaches have focused on both lattice-based and off-latticenetworks obtained from the random placement of rods. It is not obvious, apriori, whether the two architectures have fundamentally similar or differentmechanics. If they are different, it is not clear which of these represents abetter model for biological networks. Here, we show that both approaches areessentially equivalent for the same network connectivity, provided the networksare sub-isostatic with respect to central force interactions. Moreover, for agiven sub-isostatic connectivity, we even find that lattice-based networks inboth 2D and 3D exhibit nearly identical nonlinear elastic response. We providea description of the linear mechanics for both architectures in terms of ascaling function. We also show that the nonlinear regime is dominated by fiberbending and that stiffening originates from the stabilization of sub-isostaticnetworks by stress. We propose a generalized relation for this regime in termsof the self-generated normal stresses that develop under deformation. Differentnetwork architectures have different susceptibilities to the normal stress, butessentially exhibit the same nonlinear mechanics. Such stiffening mechanism hasbeen shown to successfully capture the nonlinear mechanics of collagennetworks.

Elastic regimes of sub-isostatic athermal fiber networks