Nonlinear Poisson effect in critical mechanical networks

Fibrous networks of stiff athermal biopolymers such as collagen, a major structural component of the extracellular matrix, have been shown to exhibit anomalously large apparent Poisson ratios, i.e. significant transverse contraction under small applied longitudinal extension. Here we show that this effect can be understood in the context of a macroscopic mechanical phase transition from a bending-dominated regime to a stretching-dominated regime at a critical applied extension controlled by the network connectivity. We measure this effect using a variety of 2D and 3D model network structures and propose a phase diagram governing the transition as a function of connectivity and strain.