Nonlinear Poisson effect in affine semiflexible polymer networks

TL;DR

This paper investigates the nonlinear Poisson effect in affine semiflexible polymer networks, revealing how filament properties influence volume reduction and filament alignment under strain, with implications for understanding their elastic behavior.

Contribution

The study provides a comprehensive characterization of the nonlinear Poisson effect in affine networks, linking filament properties to macroscopic nonlinear elastic responses.

Findings

Filament nonlinear force-extension causes asymmetric response to stretching and compression.

Volume reduction correlates with filament alignment along the strain axis.

Filament properties significantly influence the nonlinear elastic behavior.

Abstract

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.