Floppy modes and non-affine deformations in random fiber networks

TL;DR

This paper investigates the elastic properties of random fiber networks by linking microscopic non-affine deformations and floppy modes to macroscopic elastic behavior, using scaling and effective medium theories.

Contribution

It introduces a detailed theoretical framework connecting non-affine deformations and floppy modes to the elastic moduli of fibrous networks.

Findings

Non-affine deformations are related to low-energy floppy modes.

Theoretical models accurately predict the elastic moduli.

Non-affinity significantly influences the network's elasticity.

Abstract

We study the elasticity of random fiber networks. Starting from a microscopic picture of the non-affine deformation fields we calculate the macroscopic elastic moduli both in a scaling theory and a self-consistent effective medium theory. By relating non-affinity to the low-energy excitations of the network (``floppy-modes'') we achieve a detailed characterization of the non-affine deformations present in fibrous networks.