Topological Mechanical Metamaterials Research Articles

Uncovering and Experimental Realization of Multimodal 3D Topological Metamaterials for Low-Frequency and Multiband Elastic Wave Control.

Topological mechanical metamaterials unlock confined and robust elastic wave control. Recent breakthroughs have precipitated the development of 3D topological metamaterials, which facilitate extraordinary wave manipulation along 2D planar and layer-dependent waveguides. The 3D topological metamaterials studied thus far are constrained to function in single-frequency bandwidths that are typically in a high-frequency regime, and a comprehensive experimental investigation remains elusive. In this paper, these research gaps are addressed and the state of the art is advanced through the synthesis and experimental realization of a 3D topological metamaterial that exploits multimodal local resonance to enable low-frequency elastic wave control over multiple distinct frequency bands. The proposed metamaterial is geometrically configured to create multimodal local resonators whose frequency characteristics govern the emergence of four unique low-frequency topological states. Numerical simulations uncover how these topological states can be employed to achieve polarization-, frequency-, and layer-dependent wave manipulation in 3D structures. An experimental study results in the attainment of complete wave fields that illustrate 2D topological waveguides and multi-polarized wave control in a physical testbed. The outcomes from this work provide insight that will aid future research on 3D topological mechanical metamaterials and reveal the applicability of the proposed metamaterial for wave control applications.

Synthetically non-Hermitian nonlinear wave-like behavior in a topological mechanical metamaterial

Topological mechanical metamaterials have enabled new ways to control stress and deformation propagation. Exemplified by Maxwell lattices, they have been studied extensively using a linearized formalism. Herein, we study a two-dimensional topological Maxwell lattice by exploring its large deformation quasi-static response using geometric numerical simulations and experiments. We observe spatial nonlinear wave-like phenomena such as harmonic generation, localized domain switching, amplification-enhanced frequency conversion, and solitary waves. We further map our linearized, homogenized system to a non-Hermitian, nonreciprocal, one-dimensional wave equation, revealing an equivalence between the deformation fields of two-dimensional topological Maxwell lattices and nonlinear dynamical phenomena in one-dimensional active systems. Our study opens a regime for topological mechanical metamaterials and expands their application potential in areas including adaptive and smart materials and mechanical logic, wherein concepts from nonlinear dynamics may be used to create intricate, tailored spatial deformation and stress fields greatly transcending conventional elasticity.

Numerical and experimental investigation of second-order mechanical topological insulators

Recently, higher-order topological insulators (HOTIs) as a novel frontier of topological phases of matter have been induced in mechanical systems, opening new routes to manipulate the propagation of elastic waves. Here, second-order mechanical topological insulators (SMTIs) implemented by mechanical metamaterials are systematically investigated in the rectangular lattice, the kagome lattice, the square lattice and the hexagonal lattice. The mechanical metamaterials are constructed from the generalized 2D Su–Schrieffer–Heeger (SSH) models. The topological mechanical metamaterials are characterized by the theories of topological indices and Wannier centers. With simulations and experiments, the corner states and edge states are observed in the topological mechanical metamaterials. Interestingly, the numbers of corner, edge and bulk states are respectively equal to the number of sites located at the corners, edges and bulk. This work offers an inspiring and unified model to study the higher-order topology in mechanical systems, and provides a new way for designing functional and integrated topological devices.

Topological transformability and reprogrammability of multistable mechanical metamaterials

Concepts from quantum topological states of matter have been extensively utilized in the past decade to create mechanical metamaterials with topologically protected features, such as one-way edge states and topologically polarized elasticity. Maxwell lattices represent a class of topological mechanical metamaterials that exhibit distinct robust mechanical properties at edges/interfaces when they are topologically polarized. Realizing topological phase transitions in these materials would enable on-and-off switching of these edge states, opening opportunities to program mechanical response and wave propagation. However, such transitions are extremely challenging to experimentally control in Maxwell topological metamaterials due to mechanical and geometric constraints. Here we create a Maxwell lattice with bistable units to implement synchronized transitions between topological states and demonstrate dramatically different stiffnesses as the lattice transforms between topological phases both theoretically and experimentally. By combining multistability with topological phase transitions, this metamaterial not only exhibits topologically protected mechanical properties that swiftly and reversibly change, but also offers a rich design space for innovating mechanical computing architectures and reprogrammable neuromorphic metamaterials. Moreover, we design and fabricate a topological Maxwell lattice using multimaterial 3D printing and demonstrate the potential for miniaturization via additive manufacturing. These design principles are applicable to transformable topological metamaterials for a variety of tasks such as switchable energy absorption, impact mitigation, wave tailoring, neuromorphic metamaterials, and controlled morphing systems.

Engineering nonreciprocal wave dispersion in a nonlocal micropolar metabeam

Active metamaterials with electronic control schemes can exhibit nonreciprocal and/or complex elastic coefficients that result in non-Hermitian wave phenomena. Here, we investigate theoretically and experimentally a non-Hermitian micropolar metabeam with piezoelectric elements and electronic nonlocal feed-forward control. Since the nonlocal feed-forward control breaks spatial reciprocity, the proposed metabeam supports nonreciprocal flexural wave propagation, featuring unidirectional amplification/attenuation and non-Hermitian skin effect. Theoretical homogenization modeling is developed to consider the nonlocal effect into an effective complex bending stiffness. The unidirectional wave amplification/attenuation is attributed to the energy conversion between electrical power and mechanical work. The non-Hermitian skin effect, characterized by a winding number, is the manifestation of the flexural nonreciprocity and admits an extensive number of localized bulk eigenmodes on open boundaries. The nonlocal metabeam is also employed to engineer the anomalous wave dispersion such as tunable roton-like dispersion and band tilting. The nonlocal micropolar metabeam could pave the ways for designing non-Hermitian topological mechanical metamaterials featuring programmable nonreciprocal wave transmission and engineering roton-like wave dispersion relations under ambient environments.

Scalable 3D printing for topological mechanical metamaterials

Mechanical metamaterials are structures designed to exhibit an exotic response, such as topological soft modes at a surface. Here we explore single-material 3D prints of these topological structures by translating a ball-and-spring model into a physical prototype. By uniaxially compressing the 3D-printed solid having marginal rigidity, we observe that the surfaces are consistently softer than the bulk. However, we also find that either of two opposite surfaces can be the softest, in contrast to the topologically robust predictions of the linear model. Finite-element simulations allow us to bridge this gap. We explore how the printing geometry and deformation amplitude could affect surface softness. For small strains, we find qualitative agreement with the ball-and-spring model but, surprisingly, nonlinear deformations can select which side is softest. Our work contextualizes the predictions of topological mechanics for real 3D materials and their potential for cushioning applications.

Topological state transfer in Kresling origami

Topological mechanical metamaterials have been widely explored for their boundary states, which can be robustly isolated or transported in a controlled manner. However, such systems often require pre-configured design or complex active actuation for wave manipulation. Here, we present the possibility of in-situ transfer of topological boundary modes by leveraging the reconfigurability intrinsic in twisted origami lattices. In particular, we employ a dimer Kresling origami system consisting of unit cells with opposite chirality, which couples longitudinal and rotational degrees of freedom in elastic waves. The quasi-static twist imposed on the lattice alters the strain landscape of the lattice, thus significantly affecting the wave dispersion relations and the topology of the underlying bands. This in turn facilitates an efficient topological state transfer from one edge to the other. This simple and practical approach to energy transfer in origami-inspired lattices can thus inspire a new class of efficient energy manipulation devices.

Transformable topological mechanical metamaterials based on Maxwell lattices

Maxwell lattices are mechanical networks on the verge of instability and feature convenient mechanisms of transformation. They exhibit topologically protected floppy modes and states of self-stress, offering an excellent platform for topologically robust and yet transformable mechanical and acoustic properties. In this talk, we will discuss recent progress in developing topological mechanical metamaterials based on Maxwell lattices, from dramatic changes of surface stiffness upon a small stimuli, to programmable stress distribution for fracturing protection, and nonreciprocal propagation for nonlinear waves. These results reveal great potential for Maxwell lattices as a new class of topological mechanical metamaterials with emerging applications.

Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control.

We introduce a method to design topological mechanical metamaterials that are not constrained by Newtonian dynamics. The unit cells in a mechanical lattice are subjected to active feedback forces that are processed through autonomous controllers preprogrammed to generate the desired local response in real time. As an example, we focus on the quantum Haldane model, which is a two-band system with nonreciprocal coupling terms, the implementation of which in mechanical systems requires violating Newton's third law. We demonstrate that the required topological phase characterized by chiral edge modes can be achieved in an analogous mechanical system only with closed-loop control. We then show that our approach enables us to realize, a modified version of the Haldane model in a mechanical metamaterial. Here, the complex-valued couplings are polarized in a way that modes on opposite edges of a lattice propagate in the same direction, and are balanced by counterpropagating bulk modes. The proposed method is general and flexible, and could be used to realize arbitrary lattice parameters, such as nonlocal or nonlinear couplings, time-dependent potentials, non-Hermitian dynamics, and more, on a single platform.

Observation of Flat Frequency Bands at Open Edges and Antiphase Boundary Seams in Topological Mechanical Metamaterials

Motivated by the recent theoretical studies on a two-dimensional (2D) chiral Hamiltonian based on the Su-Schrieffer-Heeger chains [L. Zhu, E. Prodan, and K. H. Ahn, Phys. Rev. B 99, 041117(R) (2019)PRBMDO2469-995010.1103/PhysRevB.99.041117], we experimentally and computationally demonstrate that topological flat frequency bands can occur at open edges of 2D planar metamaterials and at antiphase boundary seams of ring-shaped or tubular metamaterials. Specifically, using mechanical systems made of magnetically coupled spinners, we reveal that the presence of the edge or seam bands that are flat in the entire projected reciprocal space follows the predictions based on topological winding numbers. The edge-to-edge distance sensitively controls the flatness of the edge bands and the localization of excitations, consistent with the theoretical analysis. The analog of the fractional charge state is observed. Possible realizations of flat bands in a large class of metamaterials, including photonic crystals and electronic metamaterials, are discussed.

Soft Topological Metamaterials with Pronounced Polar Elasticity in Mechanical and Dynamic Behaviors

We realize soft topological mechanical metamaterials with pronounced polar elastic responses (i.e., softer on one edge than the other) in both the quasistatic and dynamic regimes. Numerical simulations and experimental results confirm the presence of directional dependence in metamaterial response at low and high strain rates, despite the use of lossy elastomer as bulk media. The metamaterials exhibit means to tailor the location of topologically protected uniaxial mechanical stiffnesses by virtue of both loading orientation and geometric changes to the lattice architecture. High-speed video recordings show strong topologically protected asymmetric wave propagation for the soft metamaterials subjected to impact. The results indicate a class of metamaterial architectures possessing polar elastic behavior and confirm the persistence of the response in lossy media.

Topological mechanical metamaterials: A brief review

Topological mechanical metamaterials have emerged with the development of topological phases and topological phase transitions in modern condensed matter physics. Their attractive topological properties provide promising applications that are hard to achieve with traditional mechanical metamaterials, such as waveguiding without backscattering loss, vibration isolation, and free motion of structures. In this review, we briefly retrospectively examine the most flourishing works on topological mechanical metamaterials and identify the mechanisms underlying these topological mechanical phases, such as analogs to quantum Hall effects and Weyl semimetals. Topological mechanical phases are classified into two categories of t depending on their behavior when working in different frequency domains, as finite frequency properties (ω ≠ 0) are related to elastic wave propagation and zero frequency properties (ω = 0) are related to quasi-static free motion. We conclude by outlining future challenges and opportunities for the topological mechanism, and the design/fabrication and application of topological mechanical metamaterials.

One-way transmission in topological mechanical metamaterials based on self-locking

Directional response is of great use both in daily life and in technological areas, for example, in a semiconductor diode or the directional propagation of waves. We realize a mechanical directional response, i.e., one-way displacement transmission, using a novel topological mechanical metamaterial. The one-way transmission is predicted by theoretical analysis and verified by simulations and experiments. The difference in the directional response when the structure is loaded at opposite sides can reach many dozen-fold. A design guide for the displacement reduction factor is proposed to achieve a more significant one-way transmission property. The proposed topological mechanical metamaterial provides a new concept in achieving a directional response and could be applied as signal transport and isolation, mechanical diodes, mechanical logic gates and so on.

Topological Boundary Floppy Modes in Quasicrystals

We study topological mechanics in two-dimensional quasicrystalline parallelogram tilings. Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices. In this paper we extend this concept to quasicrystalline parallelogram tillings and we use the Penrose tiling as our example to demonstrate how these topological boundary floppy modes arise with a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We prove the existence of these topological boundary floppy modes using a duality theorem which relates floppy modes and states of self stress in parallelogram tilings and fiber networks, which are Maxwell reciprocal diagrams to one another. We find that, due to the unusual rotational symmetry of quasicrystals, the resulting topological polarization can exhibit orientations not allowed in periodic lattices. Our result reveals new physics about the interplay between topological states and quasicrystalline order, and leads to novel designs of quasicrystalline topological mechanical metamaterials.

Periodic topological lattice with different indentation hardness on opposite surfaces

Different surface properties are needed simultaneously in many applications, especially under an indentation load or impact load. This study proposes one class of novel periodic topological mechanical metamaterials, 2D topological honeycomb structure and 3D topological lattice, whose opposite surfaces have significantly different indentation hardness. The difference of hardness is predicted by theoretical analysis and validated by simulations and experiments, which can be up to 7 times. In comparison with the traditional honeycomb structure with the same parameters, the topological honeycomb structure exhibits higher resistance to indentation loads and it can reduce the influence range and degree of indentation loads at the same time. A design guide of parameters is proposed to achieve a more significant difference of hardness between the opposite surfaces. General design rules at the level of both basic unit piece and lattice structure are proposed, which renders the topological lattice to have outstanding designability to meet different demands in applications. The topological lattice concept will open new avenues to design asymmetric structures and expand the existing design space of mechanical metamaterials.

Experimental realization of on-chip topological nanoelectromechanical metamaterials.

Guiding waves through a stable physical channel is essential for reliable information transport. However, energy transport in high-frequency mechanical systems, such as in signal-processing applications1, is particularly sensitive to defects and sharp turns because of back-scattering and losses2. Topological phenomena in condensed matter systems have shown immunity to defects and unidirectional energy propagation3. Topological mechanical metamaterials translate these properties into classical systems for efficient phononic energy transport. Acoustic and mechanical topological metamaterials have so far been realized only in large-scale systems, such as arrays of pendulums4, gyroscopic lattices5,6, structured plates7,8 and arrays of rods, cans and other structures acting as acoustic scatterers9-12. To fulfil their potential in device applications, mechanical topological systems need to be scaled to the on-chip level for high-frequency transport13-15. Here we report the experimental realization of topological nanoelectromechanical metamaterials, consisting of two-dimensional arrays of free-standing silicon nitride nanomembranes that operate at high frequencies (10-20 megahertz). We experimentally demonstrate the presence of edge states, and characterize their localization and Dirac-cone-like frequency dispersion. Our topological waveguides are also robust to waveguide distortions and pseudospin-dependent transport. The on-chip integrated acoustic components realized here could be used in unidirectional waveguides and compact delay lines for high-frequency signal-processing applications.

Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies.

Although topological mechanical metamaterials have been extensively studied from a theoretical perspective, their experimental characterization has been lagging. To address this shortcoming, we present a systematic, laser-assisted experimental characterization of topological kagome lattices, aimed at elucidating their in-plane phononic and topological characteristics. We specifically explore the continuum elasticity limit, which is established when the ideal hinges that appear in the theoretical models are replaced by ligaments capable of supporting bending deformation, as observed for instance in realistic physical lattices. We reveal how the zero-energy floppy edge modes predicted for ideal configurations morph into finite-frequency phonon modes that localize at the edges. By probing the lattices with carefully designed excitation signals, we are able to extract and characterize all the features of a complex, low-frequency acoustic regime in which bulk modes and topological edge modes overlap and entangle in response. The experiments provide unequivocal evidence of the existence of strong asymmetric wave transport regimes at finite frequencies.

Topological node lines in mechanical metacrystals

Topological acoustic and elastic waves have recently emerged as an exciting interdisciplinary field which is still mainly focused on low-dimensional structures and model systems. Here we demonstrate numerically an elastic-wave analogue of topological node-lines in three-dimensional mechanical metacrystals with ribbon- or drumhead-like surface states. These two-dimensional topological surface states offer unprecedented, robust subwavelength confinement of elastic waves. Design principles for topological mechanical metamaterials, from both material and symmetry aspects, are unveiled and connected to fundamental conservation laws and nonsymmorphic space group. Our study paves the way toward the synergy between three-dimensional mechanical metamaterials and topological wave dynamics.

Topological mechanics of gyroscopic metamaterials

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--composed of coupled gyroscopes on a lattice--that breaks time-reversal symmetry. The vibrational spectrum displays a sonic gap populated by topologically protected edge modes that propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We demonstrate this functionality in experiment and envision applications of these edge modes to the design of one-way acoustic waveguides.