Topological modes in disordered fiber networks under active driving*

Disordered fiber networks are ubiquitous in a broad range of natural (e.g., cytoskeleton) and manmade (e.g. aerogels) materials. The dilute nature of these fiber network structures permits floppy modes which only bend the fibers without changing their length, and these floppy modes govern mechanical response of the material, such as strain stiffening. 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 floppy modes that extend through the bulk, whereas perturbing the geometry from this ideal state and bending the fibers induce floppy modes exponentially localize on the edge of the network, leading to asymmetric edge stiffness. Various activities present in fiber networks, such as active driving of motors in the cytoskeleton, active pulling of cells in the extracellular matrix, and actuators in manmade fiber networks, could lead to such perturbed geometry and thus interesting consequences in the mechanical properties. 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 recently studied in topological mechanics. We also discuss our numerical results showing how such modes are generated by active driving, the resulting mechanical properties, and relevance for experimental systems in biology and engineering [1].
[1] Di Zhou, Leyou Zhang, Xiaoming Mao, arXiv:1708.03935 [cond-mat.soft].