Abstract
The classification of materials into insulators and conductors has been shaken up by the discovery of topological insulators that conduct robustly at the edge but not in the bulk. In mechanics, designating a material as insulating or conducting amounts to asking if it is rigid or floppy. Although mechanical structures that display topological floppy modes have been proposed, they are all vulnerable to global collapse. Here, we design and build mechanical metamaterials that are stable and yet capable of harboring protected edge and bulk modes, analogous to those in electronic topological insulators and Weyl semimetals. To do so, we exploit gear assemblies that, unlike point masses connected by springs, incorporate both translational and rotational degrees of freedom. Global structural stability is achieved by eliminating geometrical frustration of collective gear rotations extending through the assembly. The topological robustness of the mechanical modes makes them appealing across scales from engineered macrostructures to networks of toothed microrotors of potential use in micromachines.
- Received 17 March 2016
DOI:https://doi.org/10.1103/PhysRevX.6.041029
Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
Metamaterials are artificial structures whose properties derive from the geometry and arrangement of their building blocks. Developing new structures with useful properties is an outstanding theoretical challenge in metamaterials research. Here, we design and build periodic gear assemblies that harbor topological floppy modes, which are free mechanical motions in otherwise rigid structures. Topological floppy modes have been proposed in structures based on spring networks, but these structures were susceptible to global collapse and had to be pinned down to a rigid substrate to isolate the topological response. Our structures use collective rotations of engaged gears to avoid such collapse, making them elastically stable without relying on pinning or other additional constraints.
We consider metal gear assemblies incorporating both translational and rotational degrees of freedom. Each gear has 3 degrees of freedom: displacements in two directions and rotation. We show that the modes of such assemblies are mechanical analogues of protected electronic states in topological insulators and Weyl semimetals. We are able to tune mechanical rigidity locally as well as globally in a manner that is robust against imperfections and disorder, a potentially useful feature for the design of metamaterials. Besides imparting stability, our use of gears as building blocks extends the application of topological ideas to mechanical structures beyond spring networks.
We envision that our findings will inform other investigations of topological phenomena in structures with even more complex building blocks, such as colloidal or supramolecular assemblies, which would pave the way for topological mechanical metamaterials on all scales.
