  Under extensional strain, fiber networks can exhibit an anomalously large and
nonlinear Poisson effect accompanied by a dramatic transverse contraction and
volume reduction for applied strains as small as a few percent. We demonstrate
that this phenomenon is controlled by a collective mechanical phase transition
that occurs at a critical uniaxial strain that depends on network connectivity.
This transition is punctuated by an anomalous peak in the apparent Poisson's
ratio and other critical signatures such as diverging nonaffine strain
fluctuations.
