Normal stress anisotropy and marginal stability in athermal elastic networks

TL;DR

This paper investigates how normal stress anisotropy and marginal stability manifest in athermal elastic networks, revealing deviations from affine deformation driven by a strain-dependent rigidity transition.

Contribution

It introduces a numerical study of normal stresses in anisotropic, athermal semiflexible networks, highlighting the role of a rigidity transition in stress behavior under shear.

Findings

Networks show strong deviations from affine deformation.

Normal stress anomalies are controlled by a strain-dependent rigidity transition.

The behavior differs from isotropic viscoelastic materials.

Abstract

Hydrogels of semiflexible biopolymers such as collagen have been shown to contract axially under shear strain, in contrast to the axial dilation observed for most elastic materials. Recent work has shown that this behavior can be understood in terms of the porous, two-component nature and consequent time-dependent compressibility of hydrogels. The apparent normal stress measured by a torsional rheometer reflects only the tensile contribution of the axial component $\sigma_{zz}$ on long (compressible) timescales, crossing over to the first normal stress difference, $N_1 = \sigma_{xx}-\sigma_{zz}$ at short (incompressible) times. While the behavior of $N_1$ is well understood for isotropic viscoelastic materials undergoing affine shear deformation, biopolymer networks are often anisotropic and deform nonaffinely. Here, we numerically study the normal stresses that arise under shear in subisostatic, athermal semiflexible polymer networks. We show that such systems exhibit strong deviations from affine behavior and that these anomalies are controlled by a rigidity transition as a function of strain.