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The Affine-Nonaffine Transition in Anisotropic Semiflexible Networks

We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to non-affine cross-over controlled by the ratio of the filament length to the non-affinity length. Deep in the non-affine 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 generically more complex dependence of the shear modulus upon the direction of shear relative to the nematic director. We show that these features can be understood in terms of a generalized floppy modes analysis of the non-affine mechanics and a type of cooperative Euler buckling.