  Stretching an elastic material along one axis typically induces contraction
along the transverse axes, a phenomenon known as the Poisson effect. From these
strains, one can compute the specific volume, which generally either increases
or, in the incompressible limit, remains constant as the material is stretched.
However, in networks of semiflexible or stiff polymers, which are typically
highly compressible yet stiffen significantly when stretched, one instead sees
a significant reduction in specific volume under finite strains. This volume
reduction is accompanied by increasing alignment of filaments along the strain
axis and a nonlinear elastic response, with stiffening of the apparent Young's
modulus. For semiflexible networks, in which entropic bending elasticity
governs the linear elastic regime, the nonlinear Poisson effect is caused by
the nonlinear force-extension relationship of the constituent filaments, which
produces a highly asymmetric response of the constituent polymers to stretching
and compression. The details of this relationship depend on the geometric and
elastic properties of the underlying filaments, which can vary greatly in
experimental systems. Here, we provide a comprehensive characterization of the
nonlinear Poisson effect in an affine network model and explore the influence
of filament properties on essential features of the macroscopic response,
including strain-driven alignment and volume reduction.
