Evolution of static to dynamic mechanical behavior in topological nonreciprocal robotic metamaterials

Mechanical metamaterials are those structures designed to convey force and motion in novel and desirable ways. Recently, Kane and Lubensky showed that lattices at the point of marginal mechanical stability (Maxwell lattices) possess a topological invariant that describes the distribution of floppy, zero-energy edge modes. Here, we show that applying force at a point in the bulk of these lattices generates a directional mechanical response, in which stress or strain is induced...

Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk-edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such surface modes can be used for various applications such as wave-guiding, vibration isolation, or the design of static properties such as stable floppy modes where parts of a system move freely. Here, we provide a classification scheme of top...

Circumventing the reciprocity invariance has posed an interesting challenge in the design of modern devices for wave engineering. In passive devices, operating the device in the nonlinear response regime is a common means for realizing nonreciprocity. Because mirror-symmetric systems are trivially reciprocal, breaking the mirror symmetry is a necessary requirement for nonreciprocal dynamics to exist in nonlinear systems. However, the response of an asymmetric nonlinear system...

In this work, we show that collisions of one type of nonlinear wave can lead to generation of a different kind of nonlinear wave. Specifically, we demonstrate the formation of topological solitons (or transition waves) via collisions of elastic vector solitons, another type of nonlinear wave, in a multi-stable mechanical system with coupling between translational and rotational degrees of freedom. We experimentally observe the nucleation of a phase transformation arising from...

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial -- comprised of coupled gyroscopes on a lattice -- that breaks time-reversal symmetry. The vibrational spectrum of these novel structures displays a sonic gap populated by topologically protected edge modes which propagate in only one dire...

Nonreciprocal nonhermitian systems provide an unconventional localization mechanism of topological zero modes via the nonhermitian skin effect. While fundamental theoretical characterizations of this effect involve the biorthogonal system of right and left eigenmodes, the recent demonstration of this effect for a zero mode in a robotic metamaterial (Ghatak et al., arXiv:1907.11619) is based on the direct experimental observation of the conventional right eigenvectors. Here I ...

We propose and verify experimentally a new concept for achieving strong nonlinear coupling between the electromagnetic and elastic properties in metamaterials. This coupling is provided through a novel degree of freedom in metamaterial design: internal rotation within structural elements. Our meta-atoms have high sensitivity to electromagnetic wave power, and the elastic and electromagnetic properties can be independently designed to optimise the response. We demonstrate a ri...

Maxwell lattice metamaterials possess a rich phase space with distinct topological states featuring mechanically polarized edge behaviors and strongly asymmetric acoustic responses. Until now, demonstrations of non-trivial topological behaviors from Maxwell lattices have been limited to either monoliths with locked configurations or reconfigurable mechanical linkages. This work introduces a transformable topological mechanical metamaterial (TTMM) made from a shape memory poly...

The complex behavior of highly deformable mechanical metamaterials can substantially enhance the performance of soft robots.

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 ar...