The mechanics of disordered fibrous networks such as those that make up the
extracellular matrix are strongly dependent on the local connectivity or
coordination number. For biopolymer networks this coordination number is
typically between three and four. Such networks are sub-isostatic and linearly
unstable to deformation with only central force interactions, but exhibit a
mechanical phase transition between floppy and rigid states under strain.
Introducing weak bending interactions stabilizes these networks and suppresses
the critical signatures of this transition. We show that applying external
stress can also stabilize sub-isostatic networks with only tensile central
force interactions, i.e., a rope-like potential. Moreover, we find that the
linear shear modulus shows a power law scaling with the external normal stress,
with a non-mean-field exponent. For networks with finite bending rigidity, we
find that the critical stain shifts to lower values under prestress