Maxwell Lattices and Topological Mechanics

This is a review on the emergent field of topological mechanics, where concepts from electronic topological states of matter are applied to mechanics. We focus on the subcategory of topological mechanics of Maxwell lattices, which are mechanical frames having average coordination numbers equal to tw...

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Bibliographic Details
Published in:Annual review of condensed matter physics 2018-03, Vol.9 (1), p.413-433
Main Authors: Mao, Xiaoming, Lubensky, Tom C
Format: Article
Language:English
Subjects:
continuum elasticity
mechanical metamaterials
mechanics of frames
surface mode
zero modes
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Summary:This is a review on the emergent field of topological mechanics, where concepts from electronic topological states of matter are applied to mechanics. We focus on the subcategory of topological mechanics of Maxwell lattices, which are mechanical frames having average coordination numbers equal to twice their spatial dimension, 〈 z 〉=2 d , leaving them on the verge of mechanical instability. We start by introducing examples of Maxwell lattices, describing their elastic properties, and discussing their general classification. We then focus on topological phonon modes of these lattices by reviewing recent theoretical progress on one-dimensional chains and two-dimensional lattices that exhibit topologically protected zero-frequency phonon modes on edges and domain walls. We also propose metamaterials based on Maxwell lattices with unusual topologically protected mechanical properties.
ISSN:1947-5454
1947-5462
DOI:10.1146/annurev-conmatphys-033117-054235