Locally resonant sonic materials

Tuning stiffness of mechanical metamaterial unit cells via transitions to second-order rigid and pre-stressed states

Mechanical metamaterials have been widely studied for their broad range of exotic mechanical properties, and there is particular interest in imparting these materials with tunability to rationally alter their mechanical response on demand. Here, the concept of second-order rigidity is leveraged to design metamaterials that possess a floppy deformation mode, but that can be rigidified by altering the length of the constituent beams, such that a self-stress emerges and the floppy mode vanishes. This simple change in beam length can also give rise to controllable prestress in the material, allowing for further tuning of the elastic properties. Using a design validated with macroscopic 2D unit cells, a microfabricated 3D lattice material is demonstrated. Due to the generality of the rigidity transition, the design can be expanded to any combination of beam lengths for a given topology. Finally, a temperature-responsive hydrogel is incorporated to access the rigidity transition in situ. This design represents a simple and scalable method to assemble mechanical metamaterials with tunable rigidity.

Topology optimization of multi-material underwater broadband sound absorption metamaterial based on genetic algorithm

Combining multiple sound energy dissipation mechanisms is essential for improving the sound absorption performance of underwater acoustic metamaterials. The calculation of absorption coefficients of the acoustic structures uses the finite element method, and the hexagonal unit is approximated to a two-dimensional axial symmetry unit. Genetic algorithms and topology optimization methods are combined to design the microstructure of acoustic metamaterials. The rubber, air, and scatterer are taken as optimized materials for microstructure to find the optimal material distribution within the metamaterial. A data filtering method is proposed to eliminate the checkerboard phenomenon. The sound absorption mechanism of the topology structure is analyzed. The advantages of the three-phase material topology structure are revealed by comparing it with two-phase material topology structures. The influences of material parameters, structural parameters, and incident angles on sound absorption performance are studied. The results showed that the average sound absorption coefficient of the optimal topology structure is 0.9574 in the frequency range of 500-10 000 Hz. The material parameters of rubber have no obvious effect on sound absorption performance, which is convenient for selecting matrix materials. The research method provides some ideas for designing low-frequency broadband underwater acoustic metamaterials with multiphase materials.

Compact acoustic bilayer metasurfaces for high-efficiency flexible beamsplittinga)

Tunable beamsplitting is important for the flexible control of sound wave radiation in acoustics, which has garnered an increasing amount of attention recently. Twisted bilayer metasurfaces, capable of dynamically manipulating acoustic waves by altering the interlayer angle, offer the significant advantage of facile adjustability. Here, we introduce a compact acoustic bilayer metasurface (ABM) with near-zero interlayer distance that enables high-efficiency flexible beamsplitting. The ABM integrates two metasurfaces with identical phase distribution, allowing for four distinct phase configurations by rotating one metasurface in 90° increments, thereby achieving beamsplitting function with four types of far-field radiation patterns. The periodic design permits the ABM to be infinitely large, while its compact structure assures stability. Both numerical simulations and experimental validations confirm the effectiveness of the ABM. Our work offers a compact and versatile solution for advanced acoustic beamsplitting and multifunctional applications.

Achieving High-Performance Transcranial Ultrasound Transmission Through Mie and Fano Resonance in Flexible Metamaterials

Transcranial ultrasound holds great potential in medical applications. However, the effective transmission of ultrasound through the skull remains challenging due to the acoustic impedance mismatch, as well as the non-uniform thickness, and the curved surface. To overcome these challenges, this work introduces an innovative Mie-resonance flexible metamaterial (MRFM), which consists of periodically arranged low-speed micropillars embedded within a high-speed flexible substrate. The MRFM generates Mie-resonance, which couples with the skull to form Fano resonance, thereby enhancing ultrasound transmittance through the skull. Simulation results demonstrate that the proposed resonance solution significantly increases transcranial ultrasound transmittance from 33.7% to 75.2% at 0.309 MHz. For the fabrication of the MRFM, porous nickel foam is used as the Mie micropillars, and agarose hydrogel serves as the flexible substrate. Experimental results demonstrate enhanced ultrasound transmittance from 20.6% to 73.3% at 0.33 MHz with the MRFM, which shows good agreement with the simulation results, further validating the effectiveness of the design. The simplicity, tunability, and flexibility of the MRFM represent a significant breakthrough, addressing the limitations of conventional rigid metamaterials. This work lays a solid theoretical and experimental foundation for advancing the clinical application of transcranial ultrasound stimulation and neuromodulation.

Deep-Subwavelength Composite Metamaterial Unit for Concurrent Ventilation and Broadband Acoustic Insulation

Balancing ventilation and broadband sound insulation remains a significant challenge in noise control engineering, particularly when simultaneous airflow and broadband noise reduction are required. Conventional porous absorbers and membrane-type metamaterials remain fundamentally constrained by ventilation-blocking configurations or narrow operational bandwidths. This study presents a ventilated composite metamaterial unit (VCMU) co-integrating optimized labyrinth channels and the Helmholtz resonators within a single-plane architecture. This design achieves exceptional ventilation efficiency through a central flow channel while maintaining sub-λ/30 thickness (λ/31 at 860 Hz). Coupled transfer matrix modeling and finite-element simulations reveal that Fano-Helmholtz resonance mechanisms synergistically generate broadband transmission loss (STL) spanning 860-1634 Hz, with six STL peaks in the 860 and 1634 Hz bands (mean 18.4 dB). Experimental validation via impedance tube testing confirmed excellent agreement with theoretical and simulation results. The geometric scalability allows customizable acoustic bandgaps through parametric control. This work provides a promising solution for integrated ventilation and noise reduction, with potential applications in building ventilation systems, industrial pipelines, and other noise-sensitive environments.

Singular topological edge states in locally resonant metamaterials

Band topology has emerged as a novel tool for material design across various domains, including photonic and phononic systems, and metamaterials. A prominent model for band topology is the Su-Schrieffer-Heeger (SSH) chain, which reveals topological in-gap states within Bragg-type gaps (BG) formed by periodic modification. Apart from classical BGs, another mechanism for bandgap formation in metamaterials involves strong coupling between local resonances and propagating waves, resulting in a local resonance-induced bandgap (LRG). Previous studies have shown the challenge of topological edge state emergence within the LRG. Here, we reveal that topological edge states can emerge within an LRG by achieving both topological phase and bandgap transitions simultaneously. We describe this using a model of inversion-symmetric extended SSH chains for locally resonant metamaterials. Notably, this topological state can lead to highly localized modes, comparable to a subwavelength unit cell, when it emerges within the LRG. We experimentally demonstrate distinct differences in topologically protected modes-highlighted by wave localization-between the BG and the LRG using locally resonant granule-based metamaterials. Our findings suggest the scope of topological metamaterials may be extended via their bandgap nature.

Enhanced Deformability Through Distributed Buckling in Stiff Quasicrystalline Architected Materials

Architected materials achieve unique mechanical properties through precisely engineered microstructures that minimize material usage. However, a key challenge of low-density materials is balancing high stiffness with stable deformability up to large strains. Current microstructures, which employ slender elements such as thin beams and plates arranged in periodic patterns to optimize stiffness, are largely prone to instabilities, including buckling and brittle collapse at low strains. This challenge is here addressed by introducing a new class of aperiodic architected materials inspired by quasicrystalline lattices. Beam networks derived from canonical quasicrystalline patterns, such as the Penrose tiling in two dimensions and icosahedral quasicrystals (IQCs) in three dimensions, are shown to create stiff, stretching-dominated topologies with non-uniform force chain distributions, effectively mitigating the global instabilities observed in periodic designs through distributed localized buckling instabilities. Numerical and experimental results confirm the effectiveness of these designs in combining stiffness and stable deformability at large strains, representing a significant advancement in the development of low-density metamaterials for applications requiring high impact resistance and energy absorption. These results demonstrate the potential of deterministic quasi-periodic topologies to bridge the gap between periodic and random structures, while branching toward uncharted territory in the property space of architected materials.

Interband targeted energy transfer, wave arrest, and redirection in phononic lattices with strongly nonlinear local resonators

Intentionally introducing nonlinearity into phononic metamaterials has facilitated the development of novel passive elastoacoustic devices (e.g., diodes and nonlinear waveguides). The performance of these devices is primarily governed by the capability of the metamaterial to achieve intermodal targeted energy transfer. In this study, we explore phononic metamaterials with strongly nonlinear local resonators that are capable of significant interband targeted energy transfer (IBTET), that is, of nonlinear energy scattering from a primary, high-energetic pass band containing the energy of external excitation to higher- or lower-frequency secondary bands. The nonlinearity arises from pronounced geometric effects, specifically from the inclusion of local (internal) resonators with inclined linear stiffnesses. This geometric arrangement can exhibit characteristics such as softening-hardening nonlinearity and bistability, contingent upon the initial angle of inclination where the local resonator is at equilibrium. We conducted numerical simulations on a one-dimensional (1D) semi-infinite phononic lattice (modeled as a 1D lattice composed of a large number of coupled oscillators, possessing free boundaries) with varied distributions of nonlinearity and different initial angles of inclination of the internal resonators. The results demonstrate that the system exhibits robust IBTET at specific wave amplitudes. Furthermore, we show that strong nonlinearity can profoundly influence the bandgap topology under specific parameters. This band alteration can induce wave arrest and localization within the nonlinear phononic lattice and give rise to phenomena such as negative group velocity and break of acoustic reciprocity. To provide quantitative measures for the efficacy of the nonlinear phononic lattice for IBTET and wave manipulation, we quantify the induced nonlinear energy scattering across different bands using a wavelet-based technique, which on broader context, is valid for decomposition of multiscale acoustics in general classes of acoustic waveguide. Potential applications are discussed.

Negative-Viscosity Materials: Exploiting the Effect of Negative Mass

The research is motivated by the search for materials with negative viscosity to exploit the effect of negative mass. We introduce media (gaseous and liquid) that demonstrate negative viscosity. Consider the vibrated plate, which is vertically pulled through the ideal gas and built from the core-shell "meta-molecules". Vibrating the vertical plate supplies an excess vertical momentum to the core-shell meta-molecules. If the frequency of vibrations is larger than the resonant frequency, the excess moment is oriented against the direction of the vertical motion; thus, the effect of negative viscosity becomes possible. The effective viscosity becomes negative when the frequency of the plate vibrations approaches the resonant frequency from above. Thus, a novel physical mechanism resulting in negative viscosity is introduced. No violation of energy conservation is observed; the energy is supplied to the system by the external source vibrating the plate. The effect of the negative viscosity is also possible in liquids. Frequency dependence of the viscosity is addressed. Asymptotic expressions are derived for the frequency-dependent viscosity. Introduced meta-materials may be exploited for the development of media with prescribed rheological properties. Possible realizations of the negative-viscosity media are discussed.

Hybrid mechanical metamaterials: Advances of multi-functional mechanical metamaterials with simultaneous static and dynamic properties

Mechanical metamaterials are architected structures with unique functionalities, such as negative Poisson's ratio and negative stiffness, which are widely employed for absorbing energy of quasi-static and impact loads, giving improved mechanical response. Acoustic/elastic metamaterials, their dynamic counterparts, rely on frequency-dependent properties of their microstructure elements, including mass density and bulk modulus, to control the propagation of waves. Although such metamaterials introduced significant contribution for solving independently static and dynamic problems, they were facing certain resistance to their use in real-world engineering problems, mainly because of a lack of integrated systems possessing both mechanical and vibration attenuation performance. Advances in manufacturing processes and material and computational science now enable the creation of hybrid mechanical metamaterials, offering multifunctionality in terms of simultaneous static and dynamic properties, giving them the ability of controlling waves while withstanding the applied loading conditions. Exploring towards this direction, this review paper introduces the hybrid mechanical metamaterials in terms of their design process and multifunctional properties. We emphasize the still remaining challenges and how they can be potentially implemented as engineering solutions.

Mathematically inspired structure design in nanoscale thermal transport

Mathematically inspired structure design has emerged as a powerful approach for tailoring material properties, especially in nanoscale thermal transport, with promising applications both within this field and beyond. By employing mathematical principles, based on number theory, such as periodicity and quasi-periodic organizations, researchers have developed advanced structures with unique thermal behaviours. Although periodic phononic crystals have been extensively explored, various structural design methods based on alternative mathematical sequences have gained attention in recent years. This review provides an in-depth overview of these mathematical frameworks, focusing on nanoscale thermal transport. We examine key mathematical sequences, their foundational principles, and analyze the influence of thermal behavior, highlighting recent advancements in this field. Looking ahead, further exploration of mathematical sequences offers significant potential for the development of next-generation materials with tailored, multi-functional properties suited to diverse technological applications.

Inertial effects on single-perforation plates resistivity at high flow rates: Computational fluid dynamics and experimental studies

This article is focused on the viscous and inertial effects on airflow resistivity of periodic arrays of single-perforation plates spaced by thin air cavities. Analyzing this effect would provide better insight into losses within the material, including additional losses due to increasing sound excitation levels. In this way, the material pressure drop is predicted by computational fluid dynamics function (CFD) of the flow rate for corresponding pore Reynolds numbers between 0.3 and 1500. The static airflow resistivity coefficient is determined by the linear part of the pressure drop (viscous effect) and the Forchheimer coefficient from the nonlinear part of the pressure drop (inertial effect). Both coefficients are determined on the entirety of the material (globally) and at the plate levels (locally). Good agreement is observed between CFD predictions and experimental measurements on the whole range of studied Reynolds numbers. By locally investigating the pressure drops, the observations show that the viscous effects are constant through the material. With increasing pore Reynolds number, inertial effects of the first plate dominate over those of the other plates. The consideration of the local inertial effect will be a key component in the acoustic modeling of this type of material under high sound excitation levels.

Blind-label subwavelength ultrasound imaging

There is a long-existing trade-off between the imaging resolution and penetration depth in acoustic imaging caused by the diffraction limit. Most existing approaches addressing this trade-off require controlled "labels," i.e., metamaterials or contrast agents, to be deposited close to the objects and to either remain static or be tracked precisely during imaging. We propose a "blind-label" approach for acoustic subwavelength imaging. The blind labels are randomly distributed acoustic scatterers with deep-subwavelength sizes whose exact locations and trajectories are not necessary information in image reconstruction. The proposed method achieves the resolution of 0.24 wavelengths in ultrasound imaging experiments and 0.2 wavelengths in simulations, providing over 10 times improvement compared to the diffraction limit. We also elucidate the influence of scatterer size and concentration on imaging performance. The proposed "blind-label" approach relaxes the restrictions of existing acoustic subwavelength imaging technologies relying on controlled labels, therefore substantially improving the practicality of acoustic subwavelength imaging in biomedical ultrasound imaging, sonar, and nondestructive testing.

Damping Optimization and Energy Absorption of Mechanical Metamaterials for Enhanced Vibration Control Applications: A Critical Review

Metamaterials are pushing the limits of traditional materials and are fascinating frontiers in scientific innovation. Mechanical metamaterials (MMs) are a category of metamaterials that display properties and performances that cannot be realized in conventional materials. Exploring the mechanical properties and various aspects of vibration and damping control is becoming a crucial research area. Their geometries have intricate features inspired by nature, which make them challenging to model and fabricate. The fabrication of MMs has become possible because of the emergence of additive manufacturing (AM) technology. Mechanical vibrations in engineering applications are common and depend on inertia, stiffness, damping, and external excitation. Vibration and damping control are important aspects of MM in vibrational environments and need to be enhanced and explored. This comprehensive review covers different vibration and damping control aspects of MMs fabricated using polymers and other engineering materials. Different morphological configurations of MMs are critically reviewed, covering crucial vibration aspects, including bandgap formation, energy absorption, and damping control to suppress, attenuate, isolate, and absorb vibrations. Bandgap formation using different MM configurations is presented and reviewed. Furthermore, studies on the energy dissipation and absorption of MMs are briefly discussed. In addition, the vibration damping of various lattice structures is reviewed along with their analytical modeling and experimental measurements. Finally, possible research gaps are highlighted, and a general systematic procedure to address these areas is suggested for future research. This review paper may lay a foundation for young researchers intending to start and pursue research on additive-manufactured MM lattice structures for vibration control applications.

Coupling between topological edge state and defect mode-based biosensor using phononic crystal

A wealth of details regarding an individual's state of health, like a person's respiratory and metabolic functioning, can be studied by analyzing the volatile molecules and atoms in human exhaled breath. Besides, the salinity of seawater is a crucial factor in understanding its characteristics because any variation in the salinity of seawater represents the variations in the hydrological, biological, and chemical distributions. In this paper, a symmetrical one-dimensional phononic structure is theoretically designed using two symmetrical crystals separated with a defective cavity. This structure has been designed to excite a topological edge state coupled with defect mode. The coupled mode achieves high sensitivity to NaCl concentration in an aqueous solution, seven times higher than the defective one. By ranging the NaCl concentration from 0 to 21%, the average sensitivity is 467 and 3160 Hz/% for defect mode and coupled modes, respectively. The bandwidth of the coupled mode of 170 Hz is much narrower than that of the defect mode of 671 Hz for detecting salinity. For detecting the increase in [Formula: see text] concentration in dry exhaled breath by ranging the [Formula: see text] concentration from 0 ppm to 100 ppm, the average sensitivity is [Formula: see text] Hz/ppm for coupled mode. As a result of these enhancements in the sensitivity and bandwidth of the coupled mode, the coupled mode is recommended to be used in different biosensing applications.

Topology Design of Soft Phononic Crystals for Tunable Band Gaps: A Deep Learning Approach

The phononic crystals composed of soft materials have received extensive attention owing to the extraordinary behavior when undergoing large deformations, making it possible to provide tunable band gaps actively. However, the inverse designs of them mainly rely on the gradient-driven or gradient-free optimization schemes, which require sensitivity analysis or cause time-consuming, lacking intelligence and flexibility. To this end, a deep learning-based framework composed of a conditional variational autoencoder and multilayer perceptron is proposed to discover the mapping relation from the band gaps to the topology layout applied with prestress. The nonlinear superelastic neo-Hookean model is employed to describe the constitutive characteristics, based on which the band structures are obtained via the transfer matrix method accompanied with Bloch theory. The results show that the proposed data-driven approach can efficiently and rapidly generate multiple candidates applied with predicted prestress. The band gaps are in accord with each other and also consistent with the prescribed targets, verifying the accuracy and flexibility simultaneously. Furthermore, based on the generalization performance, the design space is deeply exploited to obtain desired soft structures whose stop bands are characterized by wider bandwidth, lower location, and enhanced wave attenuation performance.

Temperature-responsive metamaterials made of highly sensitive thermostat metal strips

Temperature-responsive metamaterials have remarkable shape-morphing ability during thermal energy conversion. However, integrating the thermal shape programmability, wide-working temperature range, fast temperature response, and actuation into metamaterials remains challenging. Here, we introduce using thermostat metal strips to assemble metamaterials with desirable and balanced temperature-responsive properties, and we systematically investigate the thermal deformation performance. Achieving 70 to 80% of the designed strain requires only 5 seconds of heating. A thermal strain of around 30% is achieved for the assembled metamaterials, surpassing other bimetallic metamaterials by a magnitude of 100 to 200. The actuation capacity of thermostat metal strips exceeds 26 times their weight. Further, by leveraging the highly programmable thermal deformation, the tuneable bandgap range is 3847 to 40,000 hertz. These fully integrated mechanical performances in the multiphysics have great application potential, for example, as soft actuators and soft robots in intelligent structure systems, vibration isolation and noise reduction in hypersonic vehicles, and unique thermal deformation in precision instruments.

Surface wave isolation by variable depth infilled trenches

Excessive environmental vibrations generated by urban traffic pose adverse effects on nearby structures and residents. These vibrations are predominantly carried by surface waves, which are localized within the surface layer of soil. The isolation of surface waves through the embedding of periodic wave barriers in soils between the source and the receiver has gained significant attention in recent years. In this paper, a novel approach is proposed for isolating surface waves induced by urban traffic through the use of variable depth infilled trenches. This innovative design not only achieves efficient surface wave isolation but also minimizes the consumption of structural materials. Based on the measured dominant frequency range of rail transit and the available soil parameters, variable depth infilled trenches are designed with suitable dimensions. The eigenvalue equation is solved using the finite element method to derive the dispersion relations and bandgap of identical regularly spaced trenches. To study the efficacy of the proposed structure, a finite element model of the soil-infilled trench system is developed using COMSOL. The mechanism underlying the isolation of surface wave is elucidated, and the effect of variable angle α on the isolation efficiency within 40-50 Hz η40-50Hz of surface waves is studied. The results of this study reveal that for variable angle α of 15°, the surface wave isolation efficiency within 40-50 Hz η40-50Hz is 90.9 % and 92.5 % for uniformly increasing depth infilled trenches and uniformly decreasing depth infilled trenches, respectively. Although the surface wave isolation efficiencies predicted for the variable depth infilled trench arrangements are only 93.8 % and 95.5 % of those predicted for the regularly spaced identical infilled trenches, the variable depth arrangements result in a remarkable 34 % reduction in material usage. These findings highlight the potential of the proposed variable depth infilled trenches as a cost-effective and efficient solution for surface wave isolation.

Inherent Temporal Metamaterials with Unique Time-Varying Stiffness and Damping

Time-varying metamaterials offer new degrees of freedom for wave manipulation and enable applications unattainable with conventional materials. In these metamaterials, the pattern of temporal inhomogeneity is crucial for effective wave control. However, existing studies have only demonstrated abrupt changes in properties within a limited range or time modulation following simple patterns. This study presents the design, construction, and characterization of a novel temporal elastic metamaterial with complex time-varying constitutive parameters induced by self-reconfigurable virtual resonators (VRs). These VRs, achieved by simulating the resonating behavior of mechanical resonators in digital space, function as virtualized meta-atoms. The autonomously time-varying VRs cause significant temporal variations in both the stiffness and loss factor of the metamaterial. By programming the time-domain behavior of the VRs, the metamaterial's constitutive parameters can be modulated according to desired periodic or aperiodic patterns. The proposed time-varying metamaterial has demonstrated capabilities in shaping the amplitudes and frequency spectra of waves in the time domain. This work not only facilitates the development of materials with sophisticated time-varying properties but also opens new avenues for low-frequency signal processing in future communication systems.

Automated discovery of reprogrammable nonlinear dynamic metamaterials

Harnessing the rich nonlinear dynamics of highly deformable materials has the potential to unlock the next generation of functional smart materials and devices. However, unlocking such potential requires effective strategies to spatially engineer material architectures within the nonlinear dynamic regime. Here we introduce an inverse-design framework to discover flexible mechanical metamaterials with a target nonlinear dynamic response. The desired dynamic task is encoded via optimal tuning of the full-scale metamaterial geometry through an inverse-design approach powered by a fully differentiable simulation environment. By deploying such a strategy, mechanical metamaterials are tailored for energy focusing, energy splitting, dynamic protection and nonlinear motion conversion. Furthermore, our design framework can be expanded to automatically discover reprogrammable architectures capable of switching between different dynamic tasks. For instance, we encode two strongly competing tasks-energy focusing and dynamic protection-within a single architecture, using static precompression to switch between these behaviours. The discovered designs are physically realized and experimentally tested, demonstrating the robustness of the engineered tasks. Our approach opens an untapped avenue towards designer materials with tailored robotic-like reprogrammable functionalities.

Multi-functional programmable active acoustic meta-device: acoustic switch, lens, and barrier

Active acoustic metamaterials (AAMM) have garnered special attention because of their potential as multi-function devices. In this direction, the present article demonstrates a novel AAMM that can be programmed as a multi-functional Active Acoustic Meta-device (AAMD) that can switch functionalities between Acoustic Switch (AS), Acoustic Lens (AL), and Acoustic Barrier (AB). Functionality: AL corresponds to the wave vector space, and AS and AB correspond to the frequency space of the proposed AAMM. Additional functionality, such as acoustic logic gates in phase space, is also envisaged. The proposed design is found to change the dispersion diagram by acquiring different configurations while keeping the basic design parameters constant. These design parameters include constituent elements, lattice constants, and filling fractions. Further, for the said functionalities, the proposed AAMM does not rely on the deformation characteristics of the constituents. It rather capitalises on the possible relative displacements of the scatterers. As an AL, AAMM demonstrates zero angle refraction, i.e., collimation, and negative refraction of the transmitted beam at a given angle of incidence over a frequency range of 200 kHz (22.22% of the applied frequency sweep, a.f.s.). AB is shown to attenuate acoustic energy over a frequency range of 700 kHz (77.78% of a.f.s.) compared to its reference and foundation design, a statically designed Phononic Crystal (PnC). Furthermore, as AS, it operates over the entire range of applied frequency sweep (100 kHz to 1000 kHz), i.e., over the frequency range of 900 kHz (100% of a.f.s.).

Toward mechanical proprioception in autonomously reconfigurable kirigami-inspired mechanical systems

Mechanical metamaterials have recently been exploited as an interesting platform for information storing, retrieval and processing, analogous to electronic devices. In this work, we describe the design and fabrication a two-dimensional (2D) multistable metamaterial consisting of building blocks that can be switched between two distinct stable phases, and which are capable of storing binary information analogous to digital bits. By changing the spatial distribution of the phases, we can achieve a variety of different configurations and tunable mechanical properties (both static and dynamic). Moreover, we demonstrate the ability to determine the phase distribution via simple probing of the dynamic properties, to which we refer as mechanical proprioception. Finally, as a simple demonstration of feasibility, we illustrate a strategy for building autonomous kirigami systems that can receive inputs from their environment. This work could bring new insights for the design of mechanical metamaterials with information processing and computing functionalities. This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Composite metastructure with tunable ultra-wide low-frequency three-dimensional band gaps for vibration and noise control

Low-frequency vibration and noise control present enduring engineering challenges that garner extensive research attention. Despite numerous active and passive control solutions, achieving multiple ultra-wide attenuation regions remains elusive. Addressing vibration and noise control across a multidirectional broad low-frequency spectrum, three-dimensional metastructures have emerged as innovative solutions. This study introduces a novel three-dimensional composite metastructure featuring multiple ultra-wide three-dimensional complete band gaps. The research emphasizes the design strategy of elastic ligaments to achieve multiple ultra-wide attenuation regions spanning from 0.7 to 40 kHz. The band structures are elucidated through modal analysis and further substantiated by an analytical model based on a spring-mass chain with an additional resonator. The underlying physical mechanism for the formation of multiple ultra-wide band gaps is revealed through novel vibration modes from finite element analyses. Furthermore, we demonstrate that the distribution and the relative width of the ultra-wide band gaps can be tuned by modifying the geometric parameters of the metastructure. Utilizing additive manufacturing, prototypes are fabricated, and low-amplitude vibration tests are conducted to evaluate real-time vibration attenuation properties. Consistency is observed among theoretical, numerical, and experimental results. The proposed structure shows significant potential for high-performance meta-devices aimed at controlling noise and vibration across an extremely wide low-frequency spectrum.

An efficient multiscale method for subwavelength transient analysis of acoustic metamaterials

A reduced-order homogenization framework is proposed, providing a macro-scale-enriched continuum model for locally resonant acoustic metamaterials operating in the subwavelength regime, for both time and frequency domain analyses. The homogenized continuum has a non-standard constitutive model, capturing a metamaterial behaviour such as negative effective bulk modulus, negative effective density and Willis coupling. A suitable reduced space is constructed based on the unit cell response in a steady-state regime and the local resonance regime. A frequency domain numerical example demonstrates the efficiency and suitability of the proposed framework.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Water-tank metabarrier for seismic Rayleigh wave attenuation

An innovative concept of metabarrier is presented for seismic Rayleigh wave attenuation, which consists of a periodic array of cylindrical water tanks acting as resonant units above the soil surface. A pertinent theoretical framework is developed and implemented in COMSOL Multiphysics. The framework treats the dynamics of the water tank by a well-established three-dimensional linear, pressure-based model for fluid-structure interaction under earthquake excitation, accounting for the flexibility of the tank wall; furthermore, the soil is idealized as a homogeneous and isotropic medium. Floquet-Bloch dispersion analysis of the unit cell demonstrates the presence of relevant band gaps in the low-frequency range below 20 Hz and in the higher frequency range as well. The dispersion analysis is validated by comparison with the frequency-domain analysis of a soil domain with a finite array of water tanks. The band gaps are of interest to attenuate seismic Rayleigh waves and, more generally, Rayleigh waves caused by other ground vibration sources such as road or railway traffic. The water-tank resonant units are readily tunable by varying the water level, which allows changing opening frequencies/widths of the wave attenuation zones. This is a remarkable advantage over alternative seismic metamaterials that, in general, are not designed to be tunable.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Selective dynamic band gap tuning in metamaterials using graded photoresponsive resonator arrays

The introduction of metamaterials has provided new possibilities to manipulate the propagation of waves in different fields of physics, ranging from electromagnetism to acoustics. However, despite the variety of configurations proposed so far, most solutions lack dynamic tunability, i.e. their functionality cannot be altered post-fabrication. Our work overcomes this limitation by employing a photo-responsive polymer to fabricate a simple metamaterial structure and enable tuning of its elastic properties using visible light. The structure of the metamaterial consists of graded resonators in the form of an array of pillars, each giving rise to different resonances and transmission band gaps. Selective laser illumination can then tune the resonances and their frequencies individually or collectively, thus yielding many degrees of freedom in the tunability of the filtered or transmitted wave frequencies, similar to playing a keyboard, where illuminating each pillar corresponds to playing a different note. This concept can be used to realize low-power active devices for elastic wave control, including beam splitters, switches and filters.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Ultra-broadband illusion acoustics for space and time camouflages

Invisibility cloaks that can suppress wave scattering by objects have attracted a tremendous amount of interest in the past two decades. In comparison to prior methods that were severely limited by narrow bandwidths, here we present a practical strategy to suppress sound scattering across an ultra-broad spectrum by leveraging illusion metamaterials. Consisting of a collection of subwavelength tunnels with precisely crafted internal structures, this illusion metamaterial has the ability to guide acoustic waves around the obstacles and accurately recreate the incoming wavefront on the exit surface. Remarkably, two ultra-broadband illusionary effects are produced, disappearing space and time shift. Sound scatterings are removed at all frequencies below a limit determined by the tunnel width, as confirmed by full-wave simulations and acoustic experiments. Our strategy represents a universal approach to solve the key bottleneck of bandwidth limitation in the field of cloaking in transmission, and establishes a metamaterial platform that enables the long-desired ultra-broadband sound manipulation such as acoustic camouflage and reverberation control, opening up exciting new possibilities in practical applications.

Low-Frequency Sound-Insulation Performance of Labyrinth-Type Helmholtz and Thin-Film Compound Acoustic Metamaterial

This paper presents a type of acoustic metamaterial that combines a labyrinth channel with a Helmholtz cavity and a thin film. The labyrinth-opening design and thin-film combination contribute to the metamaterial's exceptional sound-insulation performance. After comprehensive research, it is observed that in the frequency range of 20-1200 Hz, this acoustic metamaterial exhibits multiple sound-insulation peaks, showing a high overall sound-insulation quality. Specifically, the first sound-insulation peak is 26.3 Hz, with a bandwidth of 13 Hz and giving a transmission loss of 56.5 dB, showing excellent low-frequency sound-insulation performance. To further understand the low-frequency sound-insulation mechanism, this paper uses the equivalent model method to conduct an acoustic-electrical analogy, construct an equivalent model of the acoustic metamaterial, and delve into the sound-insulation mechanism at the first sound-insulation peak. To confirm the validity of the theoretical calculations, physical experiments are carried out by 3D printing experimental samples. The analysis of the experimental data has yielded results that are consistent with the simulation data, providing empirical evidence for the accuracy of the theoretical model. The material has significant practical application value. Finally, various factors are studied in depth based on the established equivalent model, which can provide valuable insights for the design and practical engineering application of acoustic metamaterials.

Current developments in elastic and acoustic metamaterials science

The concept of metamaterial recently emerged as a new frontier of scientific research, encompassing physics, materials science and engineering. In a broad sense, a metamaterial indicates an engineered material with exotic properties not found in nature, obtained by appropriate architecture either at macro-scale or at micro-/nano-scales. The architecture of metamaterials can be tailored to open unforeseen opportunities for mechanical and acoustic applications, as demonstrated by an impressive and increasing number of studies. Building on this knowledge, this theme issue aims to gather cutting-edge theoretical, computational and experimental studies on elastic and acoustic metamaterials, with the purpose of offering a wide perspective on recent achievements and future challenges. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Methods of Manipulation of Acoustic Radiation Using Metamaterials with a Focus on Polymers: Design and Mechanism Insights

The manipulation of acoustic waves is becoming increasingly crucial in research and practical applications. The coordinate transformation methods and acoustic metamaterials represent two significant areas of study that offer innovative strategies for precise acoustic wave control. This review highlights the applications of these methods in acoustic wave manipulation and examines their synergistic effects. We present the fundamental concepts of the coordinate transformation methods and their primary techniques for modulating electromagnetic and acoustic waves. Following this, we deeply study the principle of acoustic metamaterials, with particular emphasis on the superior acoustic properties of polymers. Moreover, the polymers have the characteristics of design flexibility and a light weight, which shows significant advantages in the preparation of acoustic metamaterials. The current research on the manipulation of various acoustic characteristics is reviewed. Furthermore, the paper discusses the combined use of the coordinate transformation methods and polymer acoustic metamaterials, emphasizing their complementary nature. Finally, this article envisions future research directions and challenges in acoustic wave manipulation, considering further technological progress and polymers' application potential. These efforts aim to unlock new possibilities and foster innovative ideas in the field.

Broadband acoustic illusion coating based on thin conformal metasurface

Acoustic metasurface with rationally distributed phase manipulating characteristic provides a promising platform to reshape the wavefront of scattering wave. Such acoustic illusion carpet suffers from limitation of narrow bandwidth and relatively large volume to contain the object to be hidden. Here, we propose and experimentally demonstrate broadband conformal acoustic illusion coatings composed of subwavelength-thick metacells that are designed by two types of modified Helmholtz resonators with 2π reflection phase. By deliberate design of reflection phase distributions of illusion coating, the reflected wavefront can be reshaped between trapezoid and triangles and vice versa. Furthermore, an enlarged illusion is obtained by this methodology. More importantly, the illusion behaviors are verified both numerically and experimentally from 3000 Hz to 4500 Hz, resulting in relatively broad bandwidth up to 40.5%, which is definitely of extreme importance for potential applications.

Ocean wave energy harvesting with high energy density and self-powered monitoring system

Constructing a ocean Internet of Things requires an essential ocean environment monitoring system. However, the widely distributed existing ocean monitoring sensors make it impractical to provide power and transmit monitored information through cables. Therefore, ocean environment monitoring systems particularly need a continuous power supply and wireless transmission capability for monitoring information. Consequently, a high-strength, environmentally multi-compatible, floatable metamaterial energy harvesting device has been designed through integrated dynamic matching optimization of materials, structures, and signal transmission. The self-powered monitoring system breaks through the limitations of cables and batteries in the ultra-low-frequency wave environment (1 to 2 Hz), enabling real-time monitoring of various ocean parameters and wirelessly transmitting the data to the cloud for post-processing. Compared with solar and wind energy in the ocean environment, the energy harvesting device based on the defective state characteristics of metamaterials achieves a high-energy density (99 W/m3). For the first time, a stable power supply for the monitoring system has been realized in various weather conditions (24 h).

Design of Locally Resonant Acoustic Metamaterials with Specified Band Gaps Using Multi-Material Topology Optimization

Locally Resonant Acoustic Metamaterials (LRAMs) have significant application potential because they can form subwavelength band gaps. However, most current research does not involve obtaining LRAMs with specified band gaps, even though such LRAMs are significant for practical applications. To address this, we propose a parameterized level-set-based topology optimization method that can use multiple materials to design LRAMs that meet specified frequency constraints. In this method, a simplified band-gap calculation approach based on the homogenization framework is introduced, establishing a restricted subsystem and an unrestricted subsystem to determine band gaps without relying on the Brillouin zone. These subsystems are specifically tailored to model the phenomena involved in band gaps in LRAMs, facilitating the opening of band gaps during optimization. In the multi-material representation model used in this method, each material, except for the matrix material, is depicted using a similar combinatorial formulation of level-set functions. This model reduces direct conversion between materials other than the matrix material, thereby enhancing the band-gap optimization of LRAMs. Two problems are investigated to test the method's ability to use multiple materials to solve band-gap optimization problems with specified frequency constraints. The first involves maximizing the band-gap width while ensuring it encompasses a specified frequency range, and the second focuses on obtaining light LRAMs with a specified band gap. LRAMs with specified band gaps obtained in three-material or four-material numerical examples demonstrate the effectiveness of the proposed method. The method shows great promise for designing metamaterials to attenuate specified frequency spectra as required, such as mechanical vibrations or environmental noise.

Tailoring Phonon Dispersion of a Genetically Designed Nanophononic Metasurface

Phonon engineering at the nanoscale holds immense promise for a myriad of applications. However, the design of phononic devices continues to rely on regular shapes chosen according to long-established simple rules. Here, we demonstrate an inverse design approach to create a two-dimensional phononic metasurface exhibiting a highly anisotropic phonon dispersion along the main axes of the Brillouin zone. A partial hypersonic bandgap of approximately 3.5 GHz is present along one axis, with gap closure along the orthogonal axis. Such a level of control is achieved through genetically optimized unit cells, with shapes exceeding conventional intuition. We experimentally validated our theoretical predictions using Brillouin light scattering, confirming the effectiveness of the inverse design method. Our approach unlocks the potential for automated engineering of phononic metasurfaces with on-demand functionalities, thus leading toward innovative phononic devices beyond the limitations of traditional design paradigms.

Light People: Professor Che Ting Chan, curiosity drives to create the impossibilities

EDITORIAL: "When something is said to be impossible, there are two points for researchers to initially clarify: whether it really is forbidden by the laws of nature; or whether it is simply that no material that currently exists in nature can do that." Metamaterials are such magical beings, which have physical properties like invisibility, negative refraction, super-resolution, and perfect absorption that are absent from natural materials. It has been rated by Science as one of the top ten scientific and technological breakthroughs affecting human beings in the 21st century.In this issue of Light People, we spoke with a "magic" creator, Professor Che Ting Chan, the Associate Vice-President (Research & Development) of the Hong Kong University of Science and Technology (HKUST), Member of the Hong Kong Academy of Sciences and Fellow of the American Physical Society. He has researched a number of theoretical problems in material physics, investigated the theory behind what they seek to achieve, and modulated light (electromagnetism) and acoustic waves through metamaterials. In the following, let's take a closer look at Professor Che Ting Chan's research life, and appreciate his style and the background of his accomplishment.

Propagation of elastic waves in correlated dispersions of resonant scatterers

The propagation of coherent longitudinal and transverse waves in random distributions of spherical scatterers embedded in an elastic matrix is studied. The investigated frequency range is the vicinity of the resonance frequencies of the translational and rotational motion of the spheres forced by the waves, where strong dispersion and attenuation are predicted. A technique for making samples made of layers of carbide tungsten beads embedded in epoxy resin is presented, which allows control of the scatterers distribution, induce short-range positional correlations, and minimize the anisotropy of samples. Comparison between phase velocity and attenuation measurements and a model based on multiple scattering theory (MST) shows that bulk effective properties accurately described by MST are obtained from three beads layers. Besides, short-range correlations amplify the effect of mechanical resonances on the propagation of longitudinal and transverse coherent waves. As a practical consequence, the use of short-range positional correlations may be used to enhance the attenuation of elastic waves by disordered, locally resonant, elastic metamaterials, and MST globally correctly predicts the effect of short-range positional order on their effective properties.

Nonreciprocal field transformation with active acoustic metasurfaces

Field transformation, as an extension of the transformation optics, provides a unique means for nonreciprocal wave manipulation, while the experimental realization remains a substantial challenge as it requires stringent material parameters of the metamaterials, e.g., purely nonreciprocal bianisotropic parameters. Here, we develop and demonstrate a nonreciprocal field transformation in a two-dimensional acoustic system, using an active metasurface that can independently control all constitutive parameters and achieve purely nonreciprocal Willis coupling. The field-transforming metasurface enables tailor-made field distribution manipulation, achieving localized field amplification by a predetermined ratio. The metasurface demonstrates the self-adaptive capability to various excitation conditions and can be extended to other geometric shapes. The metasurface also achieves nonreciprocal wave propagation for internal and external excitations, demonstrating a one-way acoustic device. The nonreciprocal field transformation not only extends the framework of the transformation theory for nonreciprocal wave manipulation but also holds great potential in applications such as ultrasensitive sensors and nonreciprocal communication.

Elastoacoustic wave propagation in a biphasic mechanical metamateriala)

Humans are sensitive to air-borne sound as well as to mechanical vibrations propagating in solids in the frequency range below 20 kHz. Therefore, the development of multifunctional filters for both vibration reduction and sound insulation within the frequency range of human sensitivity is a research topic of primary interest. In this paper, a high-contrast biphasic mechanical metamaterial, composed of periodic elastic solid cells with air-filled voids, is presented. By opening intercellular air-communicating channels and introducing channel-bridging solid-solid couplings, the frequency dispersion spectrum of the metamaterial can be modified to achieve complete and large bandgaps for acoustic and elastic waves. From a methodological viewpoint, the eigenproblem governing the free wave propagation is solved using a hybrid analytical-computational technique, while the waveform classification is based on polarization factors expressing the fraction of kinetic and elastic energies stored in the solid and fluid phases. Based on these theoretical results, a mechanical metafilter consisting of an array of a finite number of metamaterial cells is conceived to provide a technical solution for engineering applications. The forced response of the metafilter is virtually tested in a computational framework to assess its performance in passively controlling the propagation of broadband sound and vibration signals within solid and fluid environments. Quantitative results synthesized by transmission coefficients demonstrate that the metafilter can remarkably reduce the transmitted response in the frequency band of human sensitivity.

Machine Learning Aided Design and Optimization of Thermal Metamaterials

Artificial Intelligence (AI) has advanced material research that were previously intractable, for example, the machine learning (ML) has been able to predict some unprecedented thermal properties. In this review, we first elucidate the methodologies underpinning discriminative and generative models, as well as the paradigm of optimization approaches. Then, we present a series of case studies showcasing the application of machine learning in thermal metamaterial design. Finally, we give a brief discussion on the challenges and opportunities in this fast developing field. In particular, this review provides: (1) Optimization of thermal metamaterials using optimization algorithms to achieve specific target properties. (2) Integration of discriminative models with optimization algorithms to enhance computational efficiency. (3) Generative models for the structural design and optimization of thermal metamaterials.

Meta-structure enhanced second harmonic S0 waves for material microstructural changes monitoring

Cumulative second harmonic Lamb waves in nonlinear media feature increasing amplitudes with propagation distance, conducive to the monitoring of material microstructural changes in structures. The phenomenon can be readily generated by zero-order symmetric (S0) mode waves in the low-frequency range. However, in a practical piezoelectric-transducer-activated system, both S0 and A0 (zero-order antisymmetric) mode Lamb waves are inevitably excited, while only the former is responsible for cumulative effects. The generation efficiency of the cumulative second harmonics is then affected by the presence of the A0 waves. To tackle the problem, this study develops a metamaterial structure, referred to as a meta-structure, to tactically enhance the cumulative second harmonic S0 Lamb waves by converting the A0 mode components into S0 mode waves. Topology optimization is conducted to design the meta-structure, which is surface-mounted onto the structure under inspection, to achieve high-efficiency A0-to-S0 wave mode conversion. Through tuning the parameters and constraints of the optimization, the designed single-sided meta-structure breaks the structural symmetry in the thickness direction, while facilitating its practical implementation. Typical scenarios with different meta-structure materials are discussed. Numerical simulations demonstrate that the strain amplitudes of the fundamental S0 mode waves can be increased by 60% with the deployment of the meta-structure, alongside an enhancement of the second harmonic S0 mode waves at different sensing distances. Finally, the designed meta-structure is fabricated via 3D printing technique and tested experimentally on an aluminum plate subjected to thermal aging treatment for monitoring the heating-induced microstructural changes inside the structure. Experimental results confirm an increase in the wave amplitudes of the linear S0 mode waves with the assistance of the meta-structure. The developed system improves the sensitivity of nonlinear Lamb wave-based monitoring methods in characterizing material microstructural changes, which shows great promise for detecting incipient damage in practical structural health monitoring applications.

Auxetics and FEA: Modern Materials Driven by Modern Simulation Methods

Auxetics are materials, metamaterials or structures which expand laterally in at least one cross-sectional plane when uniaxially stretched, that is, have a negative Poisson's ratio. Over these last decades, these systems have been studied through various methods, including simulations through finite elements analysis (FEA). This simulation tool is playing an increasingly significant role in the study of materials and structures as a result of the availability of more advanced and user-friendly commercially available software and higher computational power at more reachable costs. This review shows how, in the last three decades, FEA proved to be an essential key tool for studying auxetics, their properties, potential uses and applications. It focuses on the use of FEA in recent years for the design and optimisation of auxetic systems, for the simulation of how they behave when subjected to uniaxial stretching or compression, typically with a focus on identifying the deformation mechanism which leads to auxetic behaviour, and/or, for the simulation of their characteristics and behaviour under different circumstances such as impacts.

Band gap characteristics of new composite multiple locally resonant phononic crystal metamaterial

Locally resonant phononic crystal (LRPC) exhibit elastic wave band gap characteristics within a specific low-frequency range, but their band gap width is relatively narrow, which has certain limitations in practical engineering applications. In order to open a lower frequency band gap and broaden the band gap range, this paper proposes a new composite multiple locally resonant phononic crystal (CMLRPC). Firstly, the band structure of the CMLRPC is calculated by using the finite element method, and then the formation mechanism of the band gap of the CMLRPC is studied by analyzing its vibration mode, and the band gap width is expanded by adjusting the size of the single primitive cell in the supercell model of the CMLRPC. Secondly, an equivalent mass-spring system model for CMLRPC is established to calculate the starting frequency and cut-off frequency of the band gap, and the calculated results are in good agreement with the finite element calculation. Finally, the frequency response function of the CMLRPC is calculated and its attenuation characteristics are analyzed. Within the band gap frequency range, the attenuation values of the CMLRPC are mostly above 20 dB, indicating a good attenuation effect. Compared with traditional LRPC, this new CMLRPC opens multiple band gaps in the frequency range of 200 Hz, with a wider band gap width and better attenuation effect. In addition, considering both the contact between single primitive cell and the adjustment of their spacing in the supercell model of the CMLRPC, lower and wider band gap can be obtained. The research results of this paper provide a new design idea and method for obtaining low-frequency band gap in LRPC, and can provide reference for the design of vibration reduction and isolation structures in the field of low-frequency vibration control.

Band gap of shear horizontal waves for one-dimensional phononic crystals with chiral materials

Extensive applications of chiral lattice structures in the field of acoustic wave manipulation and vibration modulation show the effectiveness of chirality route to the design of phononic crystals. However, how and to what extent the material chirality affects the band gap properties of phononic crystals remains unclear. In this study, one-dimensional phononic crystals made of chiral materials is proposed, and a theoretical model of shear horizontal (SH) wave propagation in the chiral phononic crystals is developed based on the noncentrosymmetric micropolar elasticity theory. Through the transfer matrix method, the dispersion relationship of SH wave propagation is obtained and the effects of material chirality on the band-gap properties are investigated. Our work demonstrates that the change of material chirality can significantly affect the dispersion relationship of phononic crystals, leading to the wide band gap and low frequency. In a unit cell, when the chiral coefficients of the two parts have opposite signs but the same magnitude and the chiral directions are consistent with the vibrational direction, it is the most favorable for the phononic crystals to achieve the lowest frequency and widest band gap. This study suggests that the material chirality can be harnessed to effectively tune the band-gap properties of phononic crystals. The present study provides insight for the chirality route to the design of phononic crystals.

Dynamical characteristics of honeycomb two-dimensional gyroscopic metamaterials

Suppression of noise and vibration suppression is important in various fields, such as the living environment, industrial development, and national defense and security. The bandgap properties of phononic crystal metamaterials provide an approach for controlling and eliminating harmful vibrations in equipment and noise in the environment. In this study, we used two types of two-dimensional honeycomb gyroscopic metamaterials: free and constrained. The dynamic equations of the two systems were established using angular momentum and Lagrange theorems. The dispersion relations of the two systems were obtained based on the Bloch theorem, and the influence of the gyroscope angular momentum or gyroscope speed on the dispersion relations was analyzed. Numerical simulations were conducted to analyze the wave propagation characteristics and polarization under different excitation conditions in a limited space for both types of metamaterial structures. The constrained-type and free-type metamaterials were compared, and the regularities of the dispersion relations and wave propagation characteristics by the gyroscope effect were summarized. This study provided a comprehensive and in-depth understanding of the bandgap and wave propagation properties of gyroscopic metamaterials and provided ideas for the design of bandgap modulation in metamaterials.

Simultaneous pseudospin and valley topological edge states of elastic waves in phononic crystals made of distorted Kekulé lattices

Topological metamaterials protected by the spatial inversion symmetry mainly support single type edge state, interpreted by either the quantum valley Hall effect or the quantum spin Hall effect. However, owing to the existence of the complicated couplings and waveform conversions during elastic wave propagation, realizing topologically protected edge states that support both pseudospin and valley degrees of freedom in elastic system remains a great challenge. Here, we propose a two-dimensional Kekulé phononic crystal (PC) that can simultaneously possess pseudospin- and valley-Hall edge states in different frequency bands. By inhomogeneously changing the elliptical direction in a Kekulé lattice of elliptical cylinders, three complete phononic bandgaps exhibiting distinct topological phase transitions can be obtained, one of which supports a pair of pseudospin-Hall edge states and the other hosts valley-Hall edge states in the low and high frequency regime. Furthermore, a sandwiched PC heterostructure and a four-channel cross-waveguide splitter are constructed to achieve selective excitation and topological robust propagation of pseudospin- and valley-momentum locking edge states in a single configuration. These results provide new possibilities for manipulating in-plane bulk elastic waves with both pseudospin and valley degrees of freedom in a single configuration, which has potential applications for multiband and multifunctional waveguiding.

Polydimethylsiloxane Polymerized Emulsions for Acoustic Materials Prepared Using Reactive Triblock Copolymer Surfactants

Porous polymers have interesting acoustic properties including wave dampening and acoustic impedance matching and may be used in numerous acoustic applications, e.g., waveguiding or acoustic cloaking. These materials can be prepared by the inclusion of gas-filled voids, or pores, within an elastic polymer network; therefore, porous polymers that have controlled porosity values and a wide range of possible mechanical properties are needed, as these are key factors that impact the sound-dampening properties. Here, the synthesis of acoustic materials with varying porosities and mechanical properties that could be controlled independent of the pore morphology using emulsion-templated polymerizations is described. Polydimethylsiloxane-based ABA triblock copolymer surfactants were prepared using reversible addition-fragmentation chain transfer polymerizations to control the emulsion template and act as an additional cross-linker in the polymerization. Acoustic materials prepared with reactive surfactants possessed a storage modulus of ∼300 kPa at a total porosity of 71% compared to materials prepared using analogous nonreactive surfactants that possessed storage modulus values of ∼150 kPa at similar porosities. These materials display very low longitudinal sound speeds of ∼35 m/s at ultrasonic frequencies, making them excellent candidates in the preparation of acoustic devices such as metasurfaces or lenses.

Local-Nonlinearity-Enabled Deep Subdiffraction Control of Acoustic Waves

Diffraction sets a natural limit for the spatial resolution of acoustic wave fields, hindering the generation and recording of object details and manipulation of sound at subwavelength scales. We propose to overcome this physical limit by utilizing nonlinear acoustics. Our findings indicate that, contrary to the commonly utilized cumulative nonlinear effect, it is in fact the local nonlinear effect that is crucial in achieving subdiffraction control of acoustic waves. We theoretically and experimentally demonstrate a deep subwavelength spatial resolution up to λ/38 in the far field at a distance 4.4 times the Rayleigh distance. This Letter represents a new avenue towards deep subdiffraction control of sound, and may have far-reaching impacts on various applications such as acoustic holograms, imaging, communication, and sound zone control.

Nonlocal effective medium theory for phononic temporal metamaterials

We have developed a nonlocal effective medium theory (EMT) for phononic temporal metamaterials using the multiscale technique. Our EMT yields closed-form expressions for effective constitutive parameters and reveals these materials as reciprocal media with symmetric band dispersion. Even without spatial symmetry breaking, nonzero Willis coupling coefficients emerge with time modulation and broken time-reversal symmetry, when the nonlocal effect is taken into account. Compared to the local EMT, our nonlocal version is more accurate for calculating the bulk band at high wavenumbers and essential for understanding nonlocal effects at temporal boundaries. This nonlocal EMT can be a valuable tool for studying and designing phononic temporal metamaterials beyond the long-wavelength limit.

Architecture Controls Phonon Propagation in All-Solid Brush Colloid Metamaterials

Brillouin light scattering and elastodynamic theory are concurrently used to determine and interpret the hypersonic phonon dispersion relations in brush particle solids as a function of the grafting density with perspectives in optomechanics, heat management, and materials metrology. In the limit of sparse grafting density, the phonon dispersion relations bear similarity to polymer-embedded colloidal assembly structures in which phonon dispersion can be rationalized on the basis of perfect boundary conditions, i.e., isotropic stiffness transitions across the particle interface. In contrast, for dense brush assemblies, more complex dispersion characteristics are observed that imply anisotropic stiffness transition across the particle/polymer interface. This provides direct experimental validation of phonon propagation changes associated with chain conformational transitions in dense particle brush materials. A scaling relation between interface tangential stiffness and crowding of polymer tethers is derived that provides a guideline for chemists to design brush particle materials with tailored phononic dispersion characteristics. The results emphasize the role of interfaces in composite materials systems. Given the fundamental relevance of phonon dispersion to material properties such as thermal transport or mechanical properties, it is also envisioned that the results will spur the development of novel functional hybrid materials.