  When subject to applied strain, fiber networks exhibit nonlinear elastic
stiffening. Recent theory and experiements have shown that this phenomenon is
controlled by an underlying mechanical phase transition that is critical in
nature. Growing simulation evidence points to non-mean-field behavior for this
transition and a hyperscaling relation has been proposed to relate the
corresponding critical exponents. Here, we report simulations on two distinct
network structures in 3D. By performing finite-size scaling analysis, we test
hyperscaling and identify various critical exponents. From the apparent
validity of hyperscaling, as well as the non-mean-field exponents we observe,
our results suggest that the upper critical dimension for the strain-controlled
phase transition is above three, in contrast to the jamming transition that
represents another athermal, mechanical phase transition.
