Cross-linked networks of stiff filaments exhibit negative normal stress

Motivated by recent experiments showing that a variety of stiff biopolymer gels exhibit highly unusual negative normal elastic stresses, we simulate networks of elastic rods over a wide range of concentrations and bending stiffness. In all cases, we find that sheared networks develop significant negative normal stresses that coincide with other elastic nonlinearities, including shear stiffening and compressive bucking. The threshold strain for normal stress in these athermal networks increases with both concentration and stiffness, in contrast with prior predictions for thermal networks. This may provide an experimental test for entropic vs enthalpic effects in such networks.