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Abstract

Disordered filamentous networks with compliant crosslinks exhibit a low linear elastic shear modulus at
small strains, but stiffen dramatically at high strains. Experiments have shown that the elastic modulus
can increase by up to three orders of magnitude while the networks withstand relatively large stresses
without rupturing. Here, we perform an analytical and numerical study on model networks in three
dimensions. Our model consists of a collection of randomly oriented rigid filaments connected by
flexible crosslinks that are modeled as wormlike chains. Due to zero probability of filament intersection
in three dimensions, our model networks are by construction prestressed in terms of initial tension in the
crosslinks. We demonstrate how the linear elastic modulus can be related to the prestress in these
networks. Under the assumption of affine deformations in the limit of infinite crosslink density, we show
analytically that the nonlinear elastic regime in 1- and 2-dimensional networks is characterized by
power-law scaling of the elastic modulus with the stress. In contrast, 3-dimensional networks show an
exponential dependence of the modulus on stress. Independent of dimensionality, if the crosslink density
is finite, we show that the only persistent scaling exponent is that of the single wormlike chain. We
further show that there is no qualitative change in the stiffening behavior of filamentous networks even if
the filaments are bending-compliant. Consequently, unlike suggested in prior work, the model system
studied here cannot provide an explanation for the experimentally observed linear scaling of the
modulus with the stress in filamentous networks.