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Item Type: Publication × Author: Mao, Xiaoming ×

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Topological Edge Floppy Modes in Disordered Fiber Networks

2018-05-14 , Mao, Xiaoming

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.

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Fracturing of Marginally Stable Structures: Fiber Networks and Topological Metamaterials

2018-04-19 , Mao, Xiaoming

When conventional brittle materials break, long cracks form due to stress focusing at crack tips: a phenomenon explained by Griffith in the 1920s. In this talk, we will discuss two types of systems where the fracturing process is “unconventional”. The first type are fiber networks. Using simulations we found that stress concentration never occurs in these networks. Instead, the network enters a steady state where force chains break and reform, leading to a divergent length scale. The second type are Maxwell lattices with domain walls hosting topologically protected states of self stress. Our simulations showed that stress and bond breaking events are concentrated on these domain walls, even in presence of cracks and deep into the nonlinear process of fracturing. We discuss how these ideas can be used in designing metamaterials that are protected against crack formation.

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