The Affine-Nonaffine Transition in Anisotropic Semiflexible Networks

TL;DR

This paper investigates the transition from affine to non-affine mechanics in nematically ordered semiflexible networks, revealing complex directional dependence and vanishing linear response in highly ordered regimes, explained through floppy modes and buckling analysis.

Contribution

It introduces a detailed analysis of the affine-nonaffine transition in anisotropic networks, highlighting complex mechanical behaviors and their underlying mechanisms.

Findings

Transition controlled by filament length to non-affinity length ratio

Vanishing linear response in highly ordered networks

Direction-dependent shear modulus behavior

Abstract

We study the mechanics of nematically ordered semiflexible networks showing that they, like isotropic networks, undergo an affine to non-affine cross-over controlled by the ratio of the filament length to the non-affinity length. Deep in the non-affine regime, however, these anisotropic networks exhibit a much more complex mechanical response characterized by a vanishing linear response regime for highly ordered networks and a generically more complex dependence of the shear modulus upon the direction of shear relative to the nematic director. We show that these features can be understood in terms of a generalized floppy modes analysis of the non-affine mechanics and a type of cooperative Euler buckling.