  We develop a continuum theory for equilibrium elasticity of a network of
crosslinked semiflexible filaments, spanning the full range between flexible
entropy-driven chains to stiff athermal rods. We choose the 3-chain
constitutive model over several plausible candidates, and derive analytical
expressions for the elastic energy at arbitrary strain, with the corresponding
stress-strain relationship. The theory fits well to a wide range of
experimental data on simple shear in different filament networks,
quantitatively matching the differential shear modulus variation with stress,
with only two adjustable parameters (which represent the filament stiffness and
pre-tension in the network, respectively). The general theory accurately
describes the crossover between the positive and negative Poynting effect
(normal stress on imposed shear) on increasing the stiffness of filaments
forming the network.
