Developing materials that combine both softness and stiffness is crucial for meeting the demands of complex and versatile applications. The realization of multistability through elaborate units has been demonstrated, but the trade-off between performance and light weight across different states remains underdeveloped. In this work, we pioneer the application of the soft-stiff responsive strategy to lightweight cellular materials through architecturally nesting two materials with contrasting properties. The proposed cellular materials can be reconfigured and switched between soft and stiff states, as demonstrated experimentally, theoretically and numerically. The soft state represents high perturbation sensitivity and prominent vibration isolation properties. The stiff state exhibits a strong load-carrying capability due to multi-synergistic mechanisms, with a crushing modulus and strength 668.78 and 1037.55 times as high, respectively, as the soft state in the cases of soft materials embedded in metal materials. The manipulable mechanical properties can be tuned across a broad design space while maintaining robust switchability. These advantages of the proposed bistate cellular materials offer promising application prospects from adaptive protection to shock absorption and beyond.

Nonreciprocal circulators have enabled robust topological edge transport in acoustic systems, yet creating their passive nonreciprocal counterparts in mechanics is a challenge: existing mechanical topological systems based on the Maxwell framework are largely limited to quasi-static responses and are generally incapable of supporting mechanical signal transport along complex pathways. Here, we propose and experimentally validate a passive, highly nonlinear, and nonreciprocal mechanical circulator based on angular bias, achieving giant nonreciprocal transmission of mechanical displacement signals with strong isolation. Building on this design, we further develop a mechanical reflection mechanism and realize a mechanical topological-like insulator assembled from multiple circulators, in which mechanical signals propagate as transition waves rather than conventional harmonic waves. Although the intrinsic nonlinearity of the system prevents a rigorous definition of topological invariants, experiments demonstrate stable topological-like transport featuring edge localization, robustness against sharp corners and defects, and pronounced nonreciprocity. Our work extends nonreciprocal circulators to nonlinear mechanics and advances topological-like mechanical behavior from static response to dynamic transport.

Understanding and controlling the dynamic interactions between fluid flows and solid materials and structures-a field known as fluid-structure interaction-is central not only to established disciplines such as aerospace and naval engineering, but also to emerging technologies such as energy harvesting, soft robotics, and biomedical devices. In recent years, the advent of metamaterials has provided exciting opportunities to rethink and redesign fluid-structure interactions. The idea of engineering the internal structure of materials that interface with fluid flows opens a new horizon for the precise and effective manipulation and control of coupled fluidic, acoustic, and elastodynamic responses. This review focuses on this relatively unexplored interdisciplinary theme with broad technological significance. Salient potential applications, such as reduction of fuel consumption in transport systems, efficiency of renewable energy extraction, noise mitigation, and resilience against structural fatigue, depend on controlling interactions among flow, acoustic, and vibration mechanisms. Flow control, for example, which spans a wealth of regimes such as laminar, transitional, turbulent, and unsteady separated flows, is strongly influenced by fluid-structure interaction. This review surveys and discusses conceptual frameworks that describe the interplay between fluids and elastic solids, with a focus on contemporary and emerging concepts. The paper is organised into three main sections: fluid-structure and flow-phonon interactions, flow-induced acoustic interactions with metamaterials, and exotic metamaterial concepts with potential impact on fluid-structure interaction. It concludes with perspectives on current challenges and future directions in this rapidly expanding area of research.

Although lattice mechanical metamaterials offer low weight and tailorable properties, they face a fundamental barrier to adoption at low relative densities: optimising elastic-plastic performance usually results in reduced buckling resistance (nonlinear stability). Here, we present a novel shell-lattice metamaterial design methodology that eliminates the need to compromise between high yield strength and nonlinear stability at low relative densities. This methodology also provides high specific stiffness and high energy absorption. Our design features seamlessly integrated elliptical hollow struts and hollow spherical nodes. Leveraging a stretching-dominated mechanism augmented by contact-enhanced stabilisation, the architecture provides compensatory reinforcement under large deformations. We numerically investigate and experimentally validate the influence of key geometrical ratios on the mechanical properties. Crucially, elastic isotropy can be achieved through parameter optimisation, and broad tenability enables customised anisotropic elastic responses for diverse applications. Across relative densities ranging from 0.01 to 0.5, our proposed shell lattices demonstrate consistent superiority over conventional truss and shell lattices of equal density. At a relative density of 0.1, the designs deliver a 5% rise in Young's modulus, a 38% increase in yield strength, and almost double the energy absorption capacity, significantly outperforming conventional TPMS-like shell lattices. These enhancements arise from internal contact mechanisms that stabilise post-buckling behaviour, yielding consistent or enhanced stress-strain responses. This methodology overcomes the limitations of low-density stretching-dominated lattices, paving the way for advanced, lightweight, load-bearing structures, energy absorbers, and multifunctional metamaterials.

Leveraging membrane-dominated deformation modes, plate lattice metamaterials exhibit superior stiffness, strength, and toughness amongst all lattice metamaterials. Beyond mechanical performances, plate lattices are also emerging as versatile platforms for harnessing a broad spectrum of physical properties, including acoustical, thermal, and vibrational functionalities. This review presents a comprehensive overview of the design principles, classification schemes, underlying mechanisms, and multiphysical properties of plate lattice metamaterials. Architecturally, we propose a classification into three categories: (i) pure plates, (ii) perforated plates, and (iii) hybrid plates. In terms of functions, pure plate lattices maximize mechanical efficiency through in-plane stress transfer; perforated plates enable manufacturability and offer acoustic and thermal active geometries via engineered porosity; hybrid plates integrate truss or other elements to enhance vibration attenuation. The key property-governing mechanisms, such as membrane stress, resonance behaviors, Bragg scattering, forced convection, are deeply explained. We further highlight the intrinsic interplay between different physical responses, illustrating how a single geometric design can concurrently harness multiple functionalities. The review concludes with a forward-looking perspective on emerging applications and the integration of advanced physics-informed methods to accelerate the optimization and implementation of multifunctional plate lattices.

Nonlinear mechanical metamaterials can exhibit emergent transport phenomena that mimic topological protection without relying on linear band topology. Here, we realize a bifurcation-induced nonreciprocal lattice that supports robust propagation of elastic kink waves. Each unit is a prestrained, hinged-beam circulator that develops angular momentum bias during snap-through transitions between buckling states, producing an effective breaking of time reversal symmetry. Coupling such units into a hexagonal array yields a mechanically chiral network where localized soliton-like excitations propagate unidirectionally along interfaces and edges, immune to sharp bends. We demonstrate non-dispersive kink transport governed by a SineGordon type field whose effective bias encodes mechanical chirality. This framework bridges bifurcation dynamics and nonreciprocal transport, establishing a nonlinear route toward topological like mechanical functionality without magnetic or gyroscopic bias.

Lattice materials offer highly customizable mechanical properties, but their practical application is often limited by pronounced anisotropy, which makes them unsuitable for non-deterministic, multi-axial loading environments. While significant progress has been made in achieving elastic isotropy, controlling yield anisotropy, critical for nonlinear large deformations, remains a challenge. To address this, we introduce a novel design strategy that offsets the central node of a cubic unit cell along its spatial diagonal, creating a tunable hybrid architecture that interpolates between Simple Cubic and Body-Centered Cubic configurations. We systematically map the design space defined by this offset ratio and relative density to tailor elastic isotropic properties. Crucially, numerical and experimental results reveal that this ratio also provides precise control over yield anisotropy. We demonstrate a high degree of yield isotropy, achieving a near-ideal anisotropy ratio of 1.05 at a relative density of 0.25. This performance represents a notable advancement in the development of isotropic lattice architectures within the nonlinear regime. This exceptional isotropy remains stable across increasing densities, confirming the design's robustness. Combined with high inherent stiffness and strength, these near-isotropic lattices are prime candidates for advanced load-bearing applications under uncertain loading conditions. Our strategy provides a powerful method for controlling anisotropy across linear and nonlinear regimes, with promising applications in aerospace, biomedical engineering, and beyond.

Recently, we revealed anomalous static response in metamaterials with strong beyond-nearest-neighbor interactions or nonlocal interactions. Therein, the displacement field of a metamaterial beam when stretched is not simply linear in space like for ordinary materials, but rather exhibits pronounced spatial oscillations. The unusual behavior originates from evanescent Bloch modes at zero frequency, or frozen evanescent modes, with large decaying length. Here, we start from a discrete nonlocal mass-and-spring model and adopt an effective-medium approach based on higher-order differential equation to describe the anomalous behaviors. We demonstrate that the theory well captures the frozen evanescent modes and predicates the exact spatial oscillations of the displacement field. The strong dependence of the displacement field on the beam length is also revealed. The feasibility of the effective-medium approach is validated by comparison with the uniaxial tensile test results of metamaterials designed to support the anomalous frozen evanescent phonons. This theory can potentially be used for exploring other intriguing phenomena in nonlocal materials.

Tubular lattice metamaterials are prized for their lightweight nature and exceptional mechanical properties, particularly resistance to bending and buckling. However, their performance is inherently limited by hollow nodal connections, which act as stress-concentrating geometric imperfections that compromise stiffness, strength, and stability. Inspired by the reinforced skeletal architecture of the seahorse tail, we introduce a novel alternating collinear plate-reinforced tubular (ACPT) lattice metamaterial. Through integrated simulation and experimental analysis, we demonstrate that our bioinspired design eliminates these detrimental hollow nodes. The ACPT lattice achieves remarkable enhancements over conventional simple cubic tubular (SCT) lattices, including a 219% increase in Young’s modulus and a 120% increase in yield strength. The hybrid plate reinforcement simultaneously boosts buckling resistance, resulting in a 59% improvement in specific energy absorption and superior compressive stability. Furthermore, we show that the elastoplastic properties and large deformation behavior can be effectively tuned via the plate-to-tube thickness ratio. These demonstrable advantages underscore the ACPT lattice’s high potential for advanced lightweight applications requiring exceptional load-bearing capacity and energy absorption, showcasing a successful bioinspired strategy to overcome the inherent limitations of conventional lattice metamaterials.

Topological insulators enable robust, unidirectional edge modes resistant to defects. Inspired by this, we present a topologically protected mechanical metamaterial exhibiting spin-like bifurcation-driven nonreciprocity for one-way elastic siliton-wave propagation. By leveraging angular momentum bias in a resonator lattice—analogous to magnetic bias in photonics—we break time-reversal symmetry, creating a mechanical analogue of magnetically biased graphene. Additionally, we explore topology-nonlinearity interplay using bistable networks with asymmetric energy landscapes, inducing nonlinear transition waves that act as mechanical diodes. Numerical simulations and experiments confirm the robustness and tunability of these states, enabling precise soliton-wave control. Our work advances phononic metamaterials for vibration isolation, energy harvesting, and nonreciprocal waveguiding. In addition, we will discuss how active solicitation can drastically change the landscape of mechanical metamaterials.

Mechanical metamaterials have recently driven significant advancements, and this field has currently been extended to break the reciprocity principle in static mechanics and wave propagation. Here, we demonstrate a type of three-dimensional mechanical metamaterials that possess nonreciprocal static elastic behaviors and tunable dynamic wave properties. The metamaterial is designed with suitably tailored microstructure asymmetry, which exhibits vastly different deformation configurations upon loading from different sides. Such contrast in deformation induces distinct force-displacement responses, which gives nonlinear elastic moduli that are dependent on both the magnitude and direction of applied loads. We fabricate such metamaterials with 3D printing technique at the microscale. The non-reciprocal mechanical behavior is validated by analytical means, simulations, and experiments. Besides, tunable band structure characteristics are obtained when the metamaterial is loaded in opposite directions or by different magnitudes. The band structure deforms in asymmetrical ways, which indicates flexible control on transmit-prohibit switching of elastic waves propagation (in certain frequency ranges), and this is realized by only switching the external mechanical loading direction. These peculiar behaviors show great prospects in enabling unidirectional elasticity and wave transmission within a solid material, paving avenues to new one-way functional devices.

High-performance and reusable energy-absorbing materials have tremendous potential in industrial applications. Achieving both high performance and reusability has long been a challenge due to their apparent incompatibility. To address this, we proposed a solid-liquid dual-state mechanical metamaterial. This meta-material exhibits robust mechanical properties when the liquid metal is solid and achieves high energy absorption through its plastic deformation. Upon heating-induced solid-liquid state transition, its deformed state fully recovers its initial state, ensuring reusability. The metamaterials can be fabricated by injecting liquid metal into an hollow elastic lattice structure manufactured through additive manufacturing processes. The mechanical properties of solid-liquid dual-state mechanical metamaterials prepared from different liquid metal, such as gallium, Field's metal, and Wood's metal, are analyzed in this paper through a combined approach of experiments, theoretical analysis, and numerical simulations. The results reveal that the proposed metamaterial significantly outperforms all previously reported reusable energy-absorbing materials in specific energy absorption (SEA). This breakthrough driven by the solid-liquid state transition redefines the limits of reusable energy absorption and opens the path to develop a complete family of robust, reusable materials.

The miniaturization of mechanical mechanisms is crucial to enable the development of compact, high-performance micromachines. However, the downscaling actuation of conventional gears and micromotors has remained limited by the inherent challenges of implementing mechanical/electrical powering. Here, we present the design, fabrication, and characterization of an optomechanical, gear-driven micromachine realized through two-photon polymerization 3D printing. The actuation is achieved using optical tweezers. The device integrates a microgear transmission system with an optically actuated part, enabling light-controlled micromachines. When illuminated by a highly focused laser source, the first gear generates rotational torque within the gear assembly, converting optical energy into directional mechanical work that can be transmitted to the coupled gear. We demonstrate the fabrication of micromachines using two-photon polymerization (2PP) laser writing, enabling the fabrication of spur gear trains and bevel gears that can produce out-of-plane rotations, which is not achievable with traditional micromachining fabrication techniques. The micromachines are composed of a single gear or a train of two or three gears without any unwanted adhesion between the components, leading to functioning systems. Experimentally, the fabricated micromachines were actuated using optical tweezers, demonstrating continuous gear rotation, effective motion transmission in gear trains, out-of-plane rotations, and the ability to amplify velocity or torque. Optical-tweezer actuation broadens the potential applications of these micromachines, particularly in biomedical and lab-on-a-chip systems, where precise, minimally invasive control at the microscale is essential.

Designing acoustic metamaterials with high sound absorption coefficients under low-frequency and broad-bandwidth conditions remains a highly challenging task. This paper proposes a tunable acoustic metamaterial based on a multistable structure to achieve low-frequency broadband sound absorption. The metamaterial integrates multistable thin-walled tube (MTWT) units with embedded neck structures to form Helmholtz-type resonators. The introduction of multistability enables a synergistic combination of multiple dissipation mechanisms: beyond classical Helmholtz resonance, the structure incorporates acoustic soft boundaries induced by thin-wall vibrations of the multistable units, as well as enhanced thermoviscous dissipation within the confined narrow regions. This multi-mechanism coupling not only enriches acoustic energy dissipation pathways but also provides a structural basis for tunable sound absorption. Furthermore, the multistable characteristic offers discrete and self-sustained geometric configurations, allowing the absorber to switch between well-defined acoustic states without continuous external actuation, thereby ensuring robust and energy-efficient tunability. Experimental and simulation results demonstrate that, considering low frequency, bandwidth, and structural compactness, the metamaterial achieves near-perfect sound absorption within the frequency range of 436-1141 Hz, demonstrating significant potential for broad applications in low-frequency broadband noise control. Notably, within this range, the absorption coefficient can be continuously tuned from 0 to 1, representing a highly flexible and nontrivial capability enabled by the multistable design. This work provides a new strategy for the design of acoustic metamaterials with multi-dimensional tunability.

We create wave-matter stimuli-responsive metamaterials using optical trapping forces to manipulate mass-spring chains and create zero-frequency and zero-wave-number band gaps: the bosonic nature of phonons, and hence this elastodynamic setting, traditionally prohibits either zero-frequency or zero-wave-number band gaps. Here we generate zero-frequency band gaps using optomechanical interactions within a three-dimensional mass-spring chain by applying an optical trapping force to hold or manipulate a mass in a contactless manner independent of its elastodynamic excitations. Through careful modification of the geometrical parameters in the trapped monoatomic mass-spring chain, we demonstrate the existence of a zero-frequency band gap generated by the optical forces on the masses. The precise control we have over the system allows us to drive another set of masses and springs out of phase with its traveling wave, thereby creating a zero-wave-number band gap. This paper is a contribution to the Physical Review Applied collection titled Phononics and Metamaterials.

In this work, we examine the application of phononic metamaterials for elastic impact noise insulation in tiled flooring, through the development of an innovative ceramic metatile that incorporates phononic crystals with optimized joint configurations. First, we optimize the geometrical and material parameters of the proposed metatile, which is composed of small ceramic subtiles connected by silicon joints, in order to reduce longitudinal and flexural wave propagation on tiled floors, which are responsible for noise vibrations in tiled environments. A bandgap is achieved that effectively suppresses the transmission of impact noise through the periodic structural configuration. For flexural waves, the ceramic metatile exhibits a pronounced attenuation of wave transmission in the range of 500-1900 Hz along the [100] direction, and 500-1400 Hz along the [110] direction. For longitudinal waves, a broad bandgap is observed, spanning from 400 Hz to 1950 Hz in both the [100] and [110] directions. Additionally, the bandgaps shift toward lower frequencies with increasing width of the subtiles and silicon joints, or with a decrease in the Young's modulus of the silicon. In both experimental and numerical tests, it is demonstrated that the integration of silicon joints inside the ceramic metatile improves the acoustic insulation performance, as measured by the reduction of impact noise levels across a wide range of low frequencies. The findings highlight the potential of metamaterials in architectural acoustics, offering innovative solutions for elastic wave control in tiled environments.

We investigate a composite elastic meta-slab with exceptional transmission properties, particularly the presence of a W-shaped bandgap. A comprehensive study, utilizing experimental measurements, the finite element method, and an analytical approach, identifies this specific bandgap. The meta-slab design involves cutting an array of composite materials arranged in parallel with strategically placed incisions. This configuration ensures that the materials between the slits act as plate-like waveguides within the surrounding medium. The incorporation of steel into ABS-based Fabry-Perot cavities induces a notable coupling effect between longitudinal waves and localized modes traversing the structure, leading to the formation of two distinct Fabry-Perot resonators. These coupling effects generate a series of resonances and antiresonances, ultimately producing the W-band gap through the interaction of two symmetric Fano resonances.

Thermal metamaterials represent a transformative paradigm in modern physics, synergizing thermodynamic principles with metamaterial engineering to master heat flow at will. As next-generation technologies demand multi-scale thermal control, this field urgently requires systematic frameworks to unify its multidisciplinary advances. Curated through a global collaboration involving over 50 specialists across 25 subdisciplines, this review primarily summarizes two decades of advancements, ranging from theoretical breakthroughs to functional implementations. The review reveals groundbreaking innovations in heat manipulation through the exploration of both classical and non-classical transport regimes, topological thermal control mechanisms, and quantum-informed phonon engineering strategies. By bridging physical insights like non-Hermitian thermal dynamics and valleytronic phonon transport with cutting-edge applications, we demonstrate paradigm-shifting capabilities: environment-adaptive thermal cloaks, AI-optimized metamaterials, and nonlinear thermal circuits enabling heat-based computation. Experimental milestones include 3D thermal null media with reconfigurable invisibility and thermal designs breaking classical conductivity limits. This collaborative effort establishes an indispensable roadmap for physicists, highlighting pathways to quantum thermal management, entropy-controlled energy systems, and topological devices. As thermal metamaterials transition from laboratory marvels to technological cornerstones, this work provides the foundational lexicon and design principles for the coming era of intelligent thermal matter.

Tubular lattice materials have garnered significant attention for their exceptional bending and compressive properties. However, conventional simple cubic tubular lattice materials often exhibit premature failure due to the presence of hollow nodes within discontinuous tubes. To overcome this limitation, we propose a novel three-directional alternating collinear tubular lattice material featuring continuous tubes that eliminate hollow nodes. The mechanical performance of this design is investigated through theoretical analysis, numerical simulations, and experimental validation. At low relative densities, the deformation behavior is predominantly governed by the vertical continuous tubes, which contribute approximately 95% and 91% to the overall stiffness and strength of the lattice, respectively—representing enhancements of 2.3-fold and 1.6-fold compared to the conventional design. As the relative density increases, material overlap and tube coupling effects become significant, with horizontal tubes providing displacement restraint and buckling control for vertical tubes, thereby further enhancing structural performance. At high relative densities, the synergistic action of vertical and horizontal tubes results in stable plastic bending deformation within the ACT lattice. The proposed lattice achieves a normalized yield strength 29% higher than that of the stiffest smooth shell-like lattice structure at a relative density of 0.5, while also demonstrating superior specific energy absorption at a relative density of 0.3. These results underscore its potential for applications in load-bearing and energy absorption.