Topological Edge Floppy Modes in Disordered Fiber Networks

Abstract

Disordered fiber networks are ubiquitous in natural and manmade materials. The dilute nature of these networks permits floppy modes which only bend the fibers without changing their length, and these floppy modes govern mechanical response of the material. In this talk, we show that the geometry of the fiber network dictates the nature of these floppy modes. In particular, an ideal network in which all fibers are straight hosts bulk floppy modes, whereas perturbing the network geometry induces floppy modes exponentially localize on the edge of the network. Various activities present in fiber networks, such as active driving of motors in the cytoskeleton and actuators in manmade fiber networks, could lead to such edge floppy modes. We show that the localization of these edge floppy modes is protected by the topology of the phonon structure of the fiber networks, analogous to topological edge floppy modes in Maxwell lattices.