Local mechanical response in semiflexible polymer networks subjected to an axisymmetric prestress

TL;DR

This study investigates how axisymmetric prestress influences the local mechanical response and anisotropy in semiflexible polymer networks, combining analytical and numerical methods to predict behavior relevant to microrheology.

Contribution

It introduces a framework for analyzing anisotropic responses in fiber networks under prestress, focusing on non-linear fiber force-extension behavior and providing testable expressions for experiments.

Findings

Prestress induces anisotropy in local mechanical response.

Numerical integration reveals stress distribution around force monopoles.

Results are applicable to various semiflexible polymer systems.

Abstract

Analytical and numerical calculations are presented for the mechanical response of fiber networks in a state of axisymmetric prestress, in the limit where geometric non-linearities such as fiber rotation are negligible. This allows us to focus on the anisotropy deriving purely from the non-linear force-extension curves of individual fibers. The number of independent elastic coefficients for isotropic, axisymmetric and fully anisotropic networks are enumerated, before deriving expressions for the response to a locally applied force that can be tested against e.g. microrheology experiments. Localised forces can generate anisotropy away from the point of application, so numerical integration of non-linear continuum equations is employed to determine the stress field, and induced mechanical anisotropy, at points located directly behind and in front of a force monopole. Results are presented for the wormlike chain model in normalised forms, allowing them to be easily mapped to a range of systems. Finally, the relevance of these findings to naturally occurring systems and directions for future investigation are discussed.