Force distributions and force chains in random stiff fiber networks

TL;DR

This paper investigates the force transmission mechanisms in random stiff fiber networks, revealing that forces are predominantly stretching dominated and form localized force chains, contrasting with the bending-dominated elastic energy.

Contribution

It uncovers the dual nature of force transmission, showing that forces larger than a threshold form localized chains, a novel insight into fiber network mechanics.

Findings

Forces larger than a threshold are heterogeneously distributed.

Force chains resemble those in granular media.

Elastic forces are mainly stretching dominated despite bending-dominated energy.

Abstract

We study the elasticity of random stiff fiber networks. The elastic response of the fibers is characterized by a central force stretching stiffness as well as a bending stiffness that acts transverse to the fiber contour. Previous studies have shown that this model displays an anomalous elastic regime where the stretching mode is fully frozen out and the elastic energy is completely dominated by the bending mode. We demonstrate by simulations and scaling arguments that, in contrast to the bending dominated \emph{elastic energy}, the equally important \emph{elastic forces} are to a large extent stretching dominated. By characterizing these forces on microscopic, mesoscopic and macroscopic scales we find two mechanisms of how forces are transmitted in the network. While forces smaller than a threshold $F_c$ are effectively balanced by a homogeneous background medium, forces larger than $F_c$ are found to be heterogeneously distributed throughout the sample, giving rise to highly localized force-chains known from granular media.