  Hydrogels of semiflexible biopolymers such as collagen have been shown to
contract axially under shear strain, in contrast to the axial dilation observed
for most elastic materials. Recent work has shown that this behavior can be
understood in terms of the porous, two-component nature and consequent
time-dependent compressibility of hydrogels. The apparent normal stress
measured by a torsional rheometer reflects only the tensile contribution of the
axial component $\sigma_{zz}$ on long (compressible) timescales, crossing over
to the first normal stress difference, $N_1 = \sigma_{xx}-\sigma_{zz}$ at short
(incompressible) times. While the behavior of $N_1$ is well understood for
isotropic viscoelastic materials undergoing affine shear deformation,
biopolymer networks are often anisotropic and deform nonaffinely. Here, we
numerically study the normal stresses that arise under shear in subisostatic,
athermal semiflexible polymer networks. We show that such systems exhibit
strong deviations from affine behavior and that these anomalies are controlled
by a rigidity transition as a function of strain.
