Reprogrammable Phononic Metasurfaces

Locally Resonant Metagrating by Elastic Impedance Modulation

Optical and acoustic metagratings have addressed the challenges of low-efficiency wave manipulation and high-complexity fabrication associated with metamaterials and metasurfaces. In this research, the concept of locally resonant elastic metagrating (LREM) is both theoretically and experimentally demonstrated, which is underpinned by the unique elastic impedance modulation and the hybridization of intrinsic evanescent waves. Remarkably, the LREM overcomes the size limitations of conventional metagratings and offers a distinctive design paradigm for highly efficient, compact, and lightweight structures for wave manipulation in elastic wave systems. Importantly, the LREM tackles a key challenge inherent to all elastic wave-manipulation metastructures, which consists in the unavoidable vibration modes in finite structures hindering their real-world applications.

Tailored ultrasound propagation in microscale metamaterials via inertia design

The quasi-static properties of micro-architected (meta)materials have been extensively studied over the past decade, but their dynamic responses, especially in acoustic metamaterials with engineered wave propagation behavior, represent a new frontier. However, challenges in miniaturizing and characterizing acoustic metamaterials in high-frequency (megahertz) regimes have hindered progress toward experimentally implementing ultrasonic-wave control. Here, we present an inertia design framework based on positioning microspheres to tune responses of 3D microscale metamaterials. We demonstrate tunable quasi-static stiffness by up to 75% and dynamic longitudinal-wave velocities by up to 25% while maintaining identical material density. Using noncontact laser-based dynamic experiments of tunable elastodynamic properties and numerical demonstrations of spatio-temporal ultrasound wave propagation, we explore the tunable static and elastodynamic property relation. This design framework expands the quasi-static and dynamic metamaterial property space through simple geometric changes, enabling facile design and fabrication of metamaterials for applications in medical ultrasound and analog computing.

Validating an algebraic approach to characterizing resonator networks

Resonator networks are ubiquitous in natural and engineered systems, such as solid-state materials, electrical circuits, quantum processors, and even neural tissue. To understand and manipulate these networks it is essential to characterize their building blocks, which include the mechanical analogs of mass, elasticity, damping, and coupling of each resonator element. While these mechanical parameters are typically obtained from response spectra using least-squares fitting, this approach requires a priori knowledge of all parameters and is susceptible to large error due to convergence to local minima. Here we validate an alternative algebraic means to characterize resonator networks with no or minimal a priori knowledge. Our approach recasts the equations of motion of the network into a linear homogeneous algebraic equation and solves the equation with a set of discrete measured network response vectors. For validation, we employ our approach on noisy simulated data from a single resonator and a coupled resonator pair, and we characterize the accuracy of the recovered parameters using high-dimension factorial simulations. Generally, we find that the error is inversely proportional to the signal-to-noise ratio, that measurements at two frequencies are sufficient to recover all parameters, and that sampling near the resonant peaks is optimal. Our simple, powerful tool will enable future efforts to ascertain network properties and control resonator networks in diverse physical domains.

Emerging topics in nanophononics and elastic, acoustic, and mechanical metamaterials: an overview

This broad review summarizes recent advances and "hot" research topics in nanophononics and elastic, acoustic, and mechanical metamaterials based on results presented by the authors at the EUROMECH 610 Colloquium held on April 25-27, 2022 in Benicássim, Spain. The key goal of the colloquium was to highlight important developments in these areas, particularly new results that emerged during the last two years. This work thus presents a "snapshot" of the state-of-the-art of different nanophononics- and metamaterial-related topics rather than a historical view on these subjects, in contrast to a conventional review article. The introduction of basic definitions for each topic is followed by an outline of design strategies for the media under consideration, recently developed analysis and implementation techniques, and discussions of current challenges and promising applications. This review, while not comprehensive, will be helpful especially for early-career researchers, among others, as it offers a broad view of the current state-of-the-art and highlights some unique and flourishing research in the mentioned fields, providing insight into multiple exciting research directions.

Temperature-Responsive Multistable Metamaterials

The ability for materials to adapt their shape and mechanical properties to the local environment is useful in a variety of applications, from soft robots to deployable structures. In this work, we integrate liquid crystal elastomers (LCEs) with multistable structures to allow autonomous reconfiguration in response to local changes in temperature. LCEs are incorporated in a kirigami-inspired system in which squares are connected at their vertices by small hinges composed of LCE-silicone bilayers. These bend and soften as the temperature increases above room temperature. By choosing geometric parameters for the hinges such that bifurcation points in the stability exist, a transition from mono- or tristability to bistability can be triggered by a sufficient increase in temperature, forcing rearrangements of the structure as minima in the energy landscape are removed. We demonstrate temperature-induced propagation of transition waves, enabling local structural changes to autonomously propagate and affect other parts of the structure. These effects could be harnessed in applications in interface control, reconfigurable structures, and soft robotics.

A reprogrammable mechanical metamaterial with stable memory

Metamaterials are designed to realize exotic physical properties through the geometric arrangement of their underlying structural layout1,2. Traditional mechanical metamaterials achieve functionalities such as a target Poisson's ratio3 or shape transformation4-6 through unit-cell optimization7-9, often with spatial heterogeneity10-12. These functionalities are programmed into the layout of the metamaterial in a way that cannot be altered. Although recent efforts have produced means of tuning such properties post-fabrication13-19, they have not demonstrated mechanical reprogrammability analogous to that of digital devices, such as hard disk drives, in which each unit can be written to or read from in real time as required. Here we overcome this challenge by using a design framework for a tileable mechanical metamaterial with stable memory at the unit-cell level. Our design comprises an array of physical binary elements (m-bits), analogous to digital bits, with clearly delineated writing and reading phases. Each m-bit can be independently and reversibly switched between two stable states (acting as memory) using magnetic actuation to move between the equilibria of a bistable shell20-25. Under deformation, each state is associated with a distinctly different mechanical response that is fully elastic and can be reversibly cycled until the system is reprogrammed. Encoding a set of binary instructions onto the tiled array yields markedly different mechanical properties; specifically, the stiffness and strength can be made to range over an order of magnitude. We expect that the stable memory and on-demand reprogrammability of mechanical properties in this design paradigm will facilitate the development of advanced forms of mechanical metamaterials.

Randomized resonant metamaterials for single-sensor identification of elastic vibrations

Vibrations carry a wealth of useful physical information in various fields. Identifying the multi-source vibration information generally requires a large number of sensors and complex hardware. Compressive sensing has been shown to be able to bypass the traditional sensing requirements by encoding spatial physical fields, but how to encode vibration information remains unexplored. Here we propose a randomized resonant metamaterial with randomly coupled local resonators for single-sensor compressed identification of elastic vibrations. The disordered effective masses of local resonators lead to highly uncorrelated vibration transmissions, and the spatial vibration information can thus be physically encoded. We demonstrate that the spatial vibration information can be reconstructed via a compressive sensing framework, and this metamaterial can be reconfigured while maintaining desirable performance. This randomized resonant metamaterial presents a new perspective for single-sensor vibration sensing via vibration transmission encoding, and potentially offers an approach to simpler sensing devices for many other physical information.

Designing efficient and flexible metamaterial with uncorrelated transmissions for spatial vibration encoding and identification remains a challenge. Here, the authors propose a randomized resonant metamaterial with randomly coupled local resonators for single-sensor identification of elastic vibrations.

Frequency-doubling effect in acoustic reflection by a nonlinear, architected rotating-square metasurface

Nonlinear acoustic metamaterials offer the potential to enhance wave control opportunities beyond those already demonstrated via dispersion engineering in linear metamaterials. Managing the nonlinearities of a dynamic elastic system, however, remains a challenge, and the need now exists for new strategies to model and design these wave nonlinearities. Inspired by recent research on soft architected rotating-square structures, we propose herein a design for a nonlinear elastic metasurface with the capability to achieve nonlinear acoustic wave reflection control. The designed metasurface is composed of a single layer of rotating squares connected to thin and highly deformable ligaments placed between a rigid plate and a wall. It is shown that during the process of reflection at normal incidence, most of the incoming fundamental wave energy can be converted into the second harmonic wave. A conversion coefficient of approximately 0.8 towards the second harmonic is derived with a reflection coefficient of <0.05 at the incoming fundamental frequency. The theoretical results obtained using the harmonic balance method for a monochromatic pump source are confirmed by time-domain simulations for wave packets. The reported design of a nonlinear acoustic metasurface can be extended to a large family of architected structures, thus opening new avenues for realistic metasurface designs that provide for nonlinear or amplitude-dependent wave tailoring.

Origami-based impact mitigation via rarefaction solitary wave creation

The principles underlying the art of origami paper folding can be applied to design sophisticated metamaterials with unique mechanical properties. By exploiting the flat crease patterns that determine the dynamic folding and unfolding motion of origami, we are able to design an origami-based metamaterial that can form rarefaction solitary waves. Our analytical, numerical, and experimental results demonstrate that this rarefaction solitary wave overtakes initial compressive strain waves, thereby causing the latter part of the origami structure to feel tension first instead of compression under impact. This counterintuitive dynamic mechanism can be used to create a highly efficient-yet reusable-impact mitigating system without relying on material damping, plasticity, or fracture.

Programmable Acoustic Metasurfaces

Metasurfaces open up unprecedented potential for wave engineering using subwavelength sheets. However, a severe limitation of current acoustic metasurfaces is their poor reconfigurability to achieve distinct functions on demand. Here a programmable acoustic metasurface that contains an array of tunable subwavelength unit cells to break the limitation and realize versatile two-dimensional wave manipulation functions is reported. Each unit cell of the metasurface is composed of a straight channel and five shunted Helmholtz resonators, whose effective mass can be tuned by a robust fluidic system. The phase and amplitude of acoustic waves transmitting through each unit cell can be modulated dynamically and continuously. Based on such mechanism, the metasurface is able to achieve versatile wave manipulation functions, by engineering the phase and amplitude of transmission waves in the subwavelength scale. Through acoustic field scanning experiments, multiple wave manipulation functions, including steering acoustic waves, engineering acoustic beams, and switching on/off acoustic energy flow by using one design of metasurface are visually demonstrated. This work extends the metasurface research and holds great potential for a wide range of applications including acoustic imaging, communication, levitation, and tweezers.

Hydrogel-matrix encapsulated Nitinol actuation with self-cooling mechanism

We encapsulate Nitinol shape-memory-alloy wire in a hydrogel-matrix to fabricate a lightweight (≈1 g), self-cooling actuator (HENA) for soft robots.

Observation of Nonreciprocal Wave Propagation in a Dynamic Phononic Lattice

Acoustic waves in a linear time-invariant medium are generally reciprocal; however, reciprocity can break down in a time-variant system. In this Letter, we report on an experimental demonstration of nonreciprocity in a dynamic one-dimensional phononic crystal, where the local elastic properties are dependent on time. The system consists of an array of repelling magnets, and the on-site elastic potentials of the constitutive elements are modulated by an array of electromagnets. The modulation in time breaks time-reversal symmetry and opens a directional band gap in the dispersion relation. As shown by experimental and numerical results, nonreciprocal mechanical systems like the one presented here offer opportunities to create phononic diodes that can serve for rectification applications.

Electrical tuning of elastic wave propagation in nanomechanical lattices at MHz frequencies

Nanoelectromechanical systems (NEMS) that operate in the megahertz (MHz) regime allow energy transducibility between different physical domains. For example, they convert optical or electrical signals into mechanical motions and vice versa¹. This coupling of different physical quantities leads to frequency-tunable NEMS resonators via electromechanical non-linearities^2-4. NEMS platforms with single- or low-degrees of freedom have been employed to demonstrate quantum-like effects, such as mode cooling⁵, mechanically induced transparency⁵, Rabi oscillation^6,7, two-mode squeezing⁸ and phonon lasing⁹. Periodic arrays of NEMS resonators with architected unit cells enable fundamental studies of lattice-based solid-state phenomena, such as bandgaps^10,11, energy transport^10-12, non-linear dynamics and localization^13,14, and topological properties¹⁵, directly transferrable to on-chip devices. Here we describe one-dimensional, non-linear, nanoelectromechanical lattices (NEML) with active control of the frequency band dispersion in the radio-frequency domain (10-30 MHz). The design of our systems is inspired by NEMS-based phonon waveguides^10,11 and includes the voltage-induced frequency tuning of the individual resonators^2-4. Our NEMLs consist of a periodic arrangement of mechanically coupled, free-standing nanomembranes with circular clamped boundaries. This design forms a flexural phononic crystal with a well-defined bandgap, 1.8 MHz wide. The application of a d.c. gate voltage creates voltage-dependent on-site potentials, which can significantly shift the frequency bands of the device. Additionally, a dynamic modulation of the voltage triggers non-linear effects, which induce the formation of a phononic bandgap in the acoustic branch, analogous to Peierls transition in condensed matter¹⁶. The gating approach employed here makes the devices more compact than recently proposed systems, whose tunability mostly relies on materials' compliance^17,18 and mechanical non-linearities^19-22.

Tunable Acoustic Metasurface with High-Q Spectrum Splitting

We propose a tunable acoustic metasurface using a nested structure as the microunit, which is constituted by two distinct resonators. Thanks to the coupling resonance for the microunit and by simply adjusting the rotation angle of the inner split cavity, this nested structure provides nearly 2π phase shift. The full-wave simulations demonstrate that the constructed metasurface can be tuned to reflect incident sound waves to different directions in the operation frequency region with a very narrow bandwidth, which is a key functionality for many applications such as filtering and imaging. Meanwhile, the reflected sound waves out of the operation frequency region always remain unchanged. As a result, a high Q-factor spectrum splitting can be realised. The presented metasurface is of importance to develop many metamaterial-based devices, such as tunable acoustic cloaks and acoustic switching devices.

Spiral-Based Phononic Plates: From Wave Beaming to Topological Insulators

Phononic crystals and metamaterials can sculpt elastic waves, controlling their dispersion using different mechanisms. These mechanisms are mostly Bragg scattering, local resonances, and inertial amplification, derived from ad hoc, often problem-specific geometries of the materials' building blocks. Here, we present a platform that ultilizes a lattice of spiraling unit cells to create phononic materials encompassing Bragg scattering, local resonances, and inertial amplification. We present two examples of phononic materials that can control waves with wavelengths much larger than the lattice's periodicity. (1) A wave beaming plate, which can beam waves at arbitrary angles, independent of the lattice vectors. We show that the beaming trajectory can be continuously tuned, by varying the driving frequency or the spirals' orientation. (2) A topological insulator plate, which derives its properties from a resonance-based Dirac cone below the Bragg limit of the structured lattice of spirals.

Harnessing bistability for directional propulsion of soft, untethered robots

In most macroscale robotic systems, propulsion and controls are enabled through a physical tether or complex onboard electronics and batteries. A tether simplifies the design process but limits the range of motion of the robot, while onboard controls and power supplies are heavy and complicate the design process. Here, we present a simple design principle for an untethered, soft swimming robot with preprogrammed, directional propulsion without a battery or onboard electronics. Locomotion is achieved by using actuators that harness the large displacements of bistable elements triggered by surrounding temperature changes. Powered by shape memory polymer (SMP) muscles, the bistable elements in turn actuate the robot's fins. Our robots are fabricated using a commercially available 3D printer in a single print. As a proof of concept, we show the ability to program a vessel, which can autonomously deliver a cargo and navigate back to the deployment point.

Vibration of Mechanically-Assembled 3D Microstructures Formed by Compressive Buckling

Micro-electromechanical systems (MEMS) that rely on structural vibrations have many important applications, ranging from oscillators and actuators, to energy harvesters and vehicles for measurement of mechanical properties. Conventional MEMS, however, mostly utilize two-dimensional (2D) vibrational modes, thereby imposing certain limitations that are not present in 3D designs (e.g., multi-directional energy harvesting). 3D vibrational microplatforms assembled through the techniques of controlled compressive buckling are promising because of their complex 3D architectures and the ability to tune their vibrational behaviour (e.g., natural frequencies and modes) by reversibly changing their dimensions by deforming their soft, elastomeric substrates. A clear understanding of such strain-dependent vibration behaviour is essential for their practical applications. Here, we present a study on the linear and nonlinear vibration of such 3D mesostructures through analytical modeling, finite element analysis (FEA) and experiment. An analytical solution is obtained for the vibration mode and linear natural frequency of a buckled ribbon, indicating a mode change as the static deflection amplitude increases. The model also yields a scaling law for linear natural frequency that can be extended to general, complex 3D geometries, as validated by FEA and experiment. In the regime of nonlinear vibration, FEA suggests that an increase of amplitude of external loading represents an effective means to enhance the bandwidth. The results also uncover a reduced nonlinearity of vibration as the static deflection amplitude of the 3D structures increases. The developed analytical model can be used in the development of new 3D vibrational microplatforms, for example, to enable simultaneous measurement of diverse mechanical properties (density, modulus, viscosity etc.) of thin films and biomaterials.

3D auxetic single material periodic structure with ultra-wide tunable bandgap

The design and the combination of innovative metamaterials are attracting increasing interest in the scientific community because of their unique properties that go beyond the ones of natural materials. In particular, auxetic materials and phononic crystals are widely studied for their negative Poisson's ratio and their bandgap opening properties, respectively. In this work, auxeticity and phononic crystals bandgap properties are properly combined to obtain a single phase periodic structure with a tridimensional wide tunable bandgap. When an external tensile load is applied to the structure, the auxetic unit cells change their configurations by exploiting the negative Poisson's ratio and this results in the tuning, either hardening or softening, of the frequencies of the modes limiting the 3D bandgap. Moreover, the expansion of the unit cell in all the directions, due to the auxeticity property, guarantees a fully 3D bandgap tunability of the proposed structure. Numerical simulations and analytical models are proposed to prove the claimed properties. The first experimental evidence of the tunability of a wide 3D bandgap is then shown thanks to the fabrication of a prototype by means of additive manufacturing.