  Networks with only central force interactions are floppy when their average
connectivity is below an isostatic threshold. Although such networks are
mechanically unstable, they can become rigid when strained. It was recently
shown that the transition from floppy to rigid states as a function of simple
shear strain is continuous, with hallmark signatures of criticality (Nat. Phys.
12, 584 (2016)). The nonlinear mechanical response of collagen networks was
shown to be quantitatively described within the framework of such mechanical
critical phenomenon. Here, we provide a more quantitative characterization of
critical behavior in subisostatic networks. Using finite size scaling we
demonstrate the divergence of strain fluctuations in the network at
well-defined critical strain. We show that the characteristic strain
corresponding to the onset of strain stiffening is distinct from but related to
this critical strain in a way that depends on critical exponents. We confirm
this prediction experimentally for collagen networks. Moreover, we find that
the apparent critical exponents are largely independent of the spatial
dimensionality. In a highly simplified computational model of network dynamics,
we also observe critical slowing down in the vicinity of the critical strain.
With subisostaticity as the only required condition, strain-driven criticality
is expected to be a general feature of biologically relevant fibrous networks.
