Affine-nonaffine transition in networks of nematically ordered semiflexible polymers

We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to nonaffine crossover controlled by the ratio of the filament length to the nonaffinity length. Deep in the nonaffine regime, however, these anisotropic networks exhibit a much more complex mechanical response characterized by a vanishing linear-response regime for highly ordered networks and a dependence of the shear modulus on shear direction at both small (linear) and finite (nonlinear) strains that is different from the affine prediction of orthotropic continuum linear elasticity. We show that these features can be understood in terms of a generalized floppy modes analysis of the nonaffine mechanics and a type of cooperative Euler buckling.