Thin-walled tubular structures are extensively used for energy absorption. However, conventional structures often suffer from an inherent performance trade-off between enhancing energy absorption capacity and maintaining crushing stability. To address this long-standing performance conflict, this study introduces a new chiral re-entrant hybrid circular tube (CRHT). Then, quasi-static axial compression tests and validated finite element models are used to investigate their energy absorption performance. Results show that the chiral node rotation and re-entrant wall contraction are synergistic, which results in a unique topological “self-locking” mechanism. It has a clear secondary geometric hardening. Quantitatively, CRHT has a specific energy absorption of 7.05 J/g, which is 141% higher than the re-entrant circular tube (RCT) and 56% higher than the chiral circular tube (CCT), while maintaining a competitive crushing force efficiency of 58.24%. A parametric study shows that chiral rib thickness, wall thickness, and re-entrant angle have an influence on key energy absorption indicators. Compared to existing metamaterial tubes, the proposed CRHT has a better high-performance region. Its dependable mechanical performance and adaptable design make it a viable structural solution for cutting-edge multi-scale impact protection systems in both automotive and aerospace sectors.

The bandgap of structures can be actively adjusted through external excitations such as stress, electric, or magnetic fields, among which mechanical loading is the simplest and most direct approach. However, traditional trampoline metamaterials are typically loaded only in one- or two-dimensional directions, whereas the potential of three-dimensional loading for bandgap tuning has scarcely been explored. This study proposes a trampoline metamaterial with a negative Poisson's ratio (NP-TM), enabling low-frequency bandgap tuning through subtle deformation under three-dimensional loading. By comparison with its positive Poisson's ratio counterpart (PPTM), NP-TM exhibits lower bandgap frequencies, broader bandwidths, and improved tunability. The tunability of NP-TM under prestrain is further investigated, and numerical results show that its bandgap shifts to lower frequencies under prestrain. In particular, the reduction in the starting frequency increases from 7.42 Hz under twodimensional loading to 74.46 Hz under three-dimensional loading (a tenfold increase). Numerical simulations and experimental results show the NP-TM's bandgap to effectively attenuate elastic waves. Notably, the proposed NP-TM achieves significant frequency reduction and bandwidth expansion without increasing structural mass. This work overcomes the limitations of traditional loading strategies and provides a new perspective for real-time and flexible bandgap adjustment in metamaterial systems.

Metamaterials refer to a series of man-made materials exhibiting unnatural physical properties. Since its inception, this concept has continuously developed, expanding from electromagnetics to fields such as optics, acoustics, and mechanics, demonstrating various unique innovative advantages. In recent years, the research on metamaterials has gradually entered a novel stage of interdisciplinary intersection. Among them, the combination of metamaterials and electromechanical coupling materials (EMCMs) has shown great potential in intelligent systems by integrating the physical properties of both. On this basis, this review comprehensively summarizes the combination of metamaterials and EMCMs, aiming to point out a novel direction for future development of metamaterials, providing advanced solutions in fields such as energy harvesting, sensing, intelligent structures, and vibration suppression. Through reviewing the development process of metamaterials and EMCMs, the problems faced by traditional EMCMs are pointed out, and the necessity of introducing metamaterials to the development of EMCMs is highlighted. Detailed comparative analysis is conducted on the combination cases of metamaterials and EMCMs, extracting their collaborative working mechanism, and exploring development path of their combination. Finally, several research topics worthy of attention are pointed out from the perspectives of theoretical research, material design, manufacturing technology, functions, and applications.

To enhance the mechanical properties of auxetic structures, numerous designs have been developed and analyzed. However, existing structural configurations predominantly focus on regular geometries or their combinations, which limit the scope of design. Inspired by starfish, this study employs Bezier curves to expand the design space of auxetic metamaterials. The bio-inspired starfish perforated plate structure exhibits auxetic behavior, whose compressive stress-strain curve demonstrates a unique triple-plateau phenomenon. This response indicates that the structure can deform in a phased and controllable manner over a large strain range, achieving extremely smooth and efficient energy absorption. The bio-inspired starfish perforated plate structure exhibits a 27.36-fold increase in specific energy absorption over the elliptical perforated plate structure. Simultaneously, load fluctuations are reduced, and deformation stability is enhanced. Parametric studies reveal that the specific energy absorption can be tuned within the range of 11.69 to 22.47 J/g. The multi-stage energy absorption characteristics of this structure endow it with significant potential for application in fields such as civil engineering shock absorption, aerospace buffering, and traffic collision protection systems. By introducing Bezier curves, this study expands the design space for auxetic structures and provides valuable insights for the further development of their design methodologies.

This study proposes a novel dual mechanical tuning framework based on rigid and pillared phononic crystals to address the inherent spectral rigidity of conventional passive elastic metamaterials. The bifurcated strategy integrates geometric reconfiguration with controllable mechanical prestress. Firstly, inspired by the rotating-lifting mechanism of a lipstick tube, a screw-driven system continuously adjusts the vertical elevation of a central inertial lead core. This actively alters the unit cell's effective mass distribution and moment of inertia, providing a robust 'coarse-tuning' mechanism to shift the absolute bandgap across a broad frequency range whilst preserving structural load-bearing integrity. Secondly, a dedicated tensioning mechanism applies controlled horizontal mechanical prestress to the supporting substrate. By exploiting stress-stiffening effects, this mechanism allows for the highly precise 'fine-tuning' of local resonance frequencies without necessitating alterations to the structural geometry. The underlying mechanisms of the mid-to-high frequency absolute bandgap are rigorously elucidated via Bloch-Floquet analysis, complex effective medium theory, and three-dimensional finite element (FE) simulations. Experimental validation thoroughly confirms the theoretical predictions, representing the first successful realization of controllable prestress tuning in a rigid PnC system. Ultimately, this compact and purely mechanical paradigm offers a practical pathway for next-generation adaptive vibration isolation applications.

Auxetic metamaterials have attracted significant attention in protective engineering due to their unusual deformation behavior and remarkable mechanical properties. However, re-entrant auxetic structures, typically designed with straight ligaments, often exhibit limitations in compressive stability and energy absorption (EA). To address these challenges, this paper presents a novel curved re-entrant configuration through the design of cubic function-shaped ligaments. First, a theoretical model based on Castigliano's second theorem is established to analytically predict the effective elastic modulus and Poisson's ratio, providing a foundational framework for performance-guided design. Quasi-static compression experiments and finite element analyses are then conducted to further investigate the deformation modes and EA characteristics. It is found that the cubic ligament-architected structure, particularly the one with self-contact enhancement effect, exhibits superior compressive stability over the traditional straight ligament design, thereby improving EA. Furthermore, a detailed parametric study is performed to examine the effects of ligament shape parameters and unit cell sizes on the mechanical properties of the new structure. To bridge the gap from material properties to engineering application, the study is further extended to impact analysis. After validating material-level impact performance via small-scale unit cell simulations, we propose a novel self-locking modular strategy for large-scale protective assemblies. Large-scale impact simulations demonstrate that the assembly maintains its integrity under extreme loads and exhibits superior cushioning performance. These findings confirm the proposed structure's exceptional potential, not only as a novel material but also as a viable and superior solution for advanced protective engineering applications.

The low energy density and conversion efficiency of environmental vibrations hinder piezoelectric energy harvesting and its application in self-powered wireless sensor networks. To address this issue, this work innovatively integrates defect-mode phononic crystals and auxetic structures to create three types of auxetic defect-mode phononic crystal meta-plates, including elliptical perforated (EPCM), missing-rib chiral (MPCM), and double-arrowed re-entrant (DPCM). These are compared with a solid defect-mode phononic crystal meta-plate (SPCM) and a plain plate. The results indicate that the DPCM exhibits superior energy harvesting performance, with an output power 26.2 times and 68 times greater than that of the SPCM and the plain plate, respectively. Mechanism analysis reveals that the defect-mode phononic crystal localizes vibration energy to increase input mechanical energy density. The auxetic substrate provides the samesign average stress that avoids charge cancellation and induces stress concentration, and the double-arrowed re-entrant angle further enhances this concentration, thereby improving electromechanical conversion efficiency. Based on these findings, a parametric study has been conducted using an experimentally validated model to investigate the effects of various parameters on the DPCM's energy-harvesting efficiency. The results reveal that the beam thickness in the double-arrowed structure significantly affects the DPCM's resonant frequency. Furthermore, modifying the short beam side length can substantially enhance the energy harvesting performance of the DPCM. These findings provide theoretical support for the application of defect-mode superlattice structures in self-powered systems.

In recent years, twisting metamaterials have attracted significant attention due to their unique deformation and mechanical properties. However, maintaining a balance between their high stability and strong torsion remains a challenge, which limits their energy absorption capabilities and application scenarios. In this study, we combine helical rods with annular nesting to propose a novel bilayer chiral metamaterial (BCM) with helical rods, aimed at enhancing energy absorption and twisting behavior. The axial and lateral compressive behaviors of the BCM and monolayer anti-chiral metamaterials (MAM) are investigated through experiments and finite element simulations. The results indicate that the BCM can achieve a balance between compression-torsion coupling and energy absorption, while exhibiting a tunable twist angle. Compared to MAM, the specific energy absorption of the proposed BCM with negative and positive Poisson's ratios is significantly improved by 120.82% and 56.85%, respectively. Additionally, the designed structure enables the control of the twist angle by adjusting the rotation direction of the helical ribs and the ratio of the inner pitch to the outer one, offering greater flexibility and applicability. Furthermore, the advantages of the BCM in impact cushioning and protection are verified through fragile object drop tests, demonstrating its potential applications in fields such as sensors, robotics, and shock protection.

External mechanical loadings can change the bandgap of phononic metamaterials by altering their structure or material properties. However, traditional trampoline metamaterials are typically loaded in one or two dimensions. The potential to adjust the bandgap by loading in three dimensions is still in the early stages. This study proposes a trampoline metamaterial with a negative Poisson's ratio (TM-N), which adjusts the bandgap through small deformations under three-dimensional loading. The dispersion curves of TM-N and TM-P are compared using mass-spring models and finite element (FE) simulations. Compared to TM-N, TM-P shows an opposite trend in the bandgap when the substrate is compressed. The adjustable performance of the TM-N bandgap under prestress is also discussed. Numerical results show that increasing the strain ratio chi expands the bandgap and increases its bandwidth. The effects of cylinder perforated ellipticity and substrate thickness T on the bandgap are analyzed. With chi = -2, = 4, and T = 5.5 mm, the minimum starting frequency of the bandgap is 134.5 Hz, and the relative bandwidth is 86%. The proposed TM-N effectively reduces the bandgap frequency and widens the bandgap range under three-dimensional loading, offering new possibilities for real-time bandgap adjustment.

To address the issues of buckling and low energy absorption efficiency in traditional straight-walled acoustic cavities under axial compression, as well as the narrow sound absorption bandwidth and limited coefficients resulting from the typically inefficient enumeration methods used to optimize embedded tube parameters, this paper proposes a novel origami-based integrated acoustic-mechanical design strategy. By constructing a MiuraWaterbomb origami structure (MWOS) that replaces conventional straight-walled cavities with programmable folded cavities, the mechanical response of the structure is fundamentally improved. During compression, it exhibits low initial stress, stable plateau stress, and controllable deformation modes, thereby avoiding the instability issues associated with straight-walled cavities. Its specific energy absorption (SEA) can be increased from 6.5 J/g to 15.2 J/g, representing an improvement of 134%. In terms of acoustic performance, the MWOS achieves absorption coefficients of no less than 0.9 within the 312-481 Hz frequency range, and through genetic algorithm optimization, the absorption bandwidth is further expanded by 14.6%. This design effectively integrates the load-bearing capacity of the structure with its low-frequency broadband sound absorption performance, offering a new design approach for the multifunctional application of acoustic metamaterials.

Auxetic sandwich structures (ASS) are widely investigated for their lightweight and high energy absorption characteristics. Their bending performance is a key research focus, as superior flexural properties are often cited as a distinctive advantage. However, most existing studies on the bending of ASS are limited to three-point bending tests. A detailed analysis and comparison under four-point bending, which better represents realistic loading conditions, is notably lacking. In this study, four-point bending tests were conducted to evaluate the bending resistance and energy absorption properties of ASS. Nine performance indicators, including a method for determining rigid deflection based on the second derivative of the load-deflection curve, were employed. A combined experimental and numerical analysis was performed on three typical auxetics (re-entrant (Re), star-shaped (St), and chiral (Ch)) as well as two non-auxetic counterparts (honeycomb (Ho) and semi-re-entrant (Se) structure). The results show that Re exhibits optimal bending resistance and energy absorption capacity. Parametric studies were also conducted to consider the variability in practical bending scenarios. This work provides useful insights for applying ASS in energy-absorbing and protective applications.

Conventional materials exhibit uniformly positive coefficients of thermal expansion (CTE). While anomalous CTE values have been documented, including negative or zero coefficients, the achievable deformation modes remain constrained to the orthogonal direction. Realizing thermally driven rotational or torsional deformation continues to present fundamental challenges. Here, we introduce a design strategy integrating thermostat metal strips into 3D chiral metamaterials. The critical geometrical parameters are analyzed numerically, including tessellating cellular numbers and strips' relative lengths. An oil bath heating test is conducted to examine the thermal rotating effect of the assembled specimen. Results indicate that the increase in cellular number diminishes the rotating behavior. Enhancing the relevant length of metal strips will enhance intrinsic bending-driven rotating mechanisms, thereby amplifying the angle. A maximum rotating angle of 13.8 degrees is achieved over a temperature range of 25 degrees C to 300 degrees C. These findings expand the scope of thermally responsive metamaterials and show the potential application for temperature-sensitive devices in structural engineering.

In recent years, bio-inspired design has provided new strategies for metamaterials due to its advantages in lightweight characteristics, high stability, and multifunctional integration. However, existing metamaterials still suffer from insufficient low-frequency broadband sound absorption, large stress plateau fluctuations, and limited energy absorption capability, making it difficult to satisfy the multifunctional performance requirements in complex engineering environments. Therefore, a bio-inspired multifunctional Voronoi metastructure (BMVM) is proposed by integrating a bio-inspired Voronoi acoustic cavity (BVAC) with a bio-inspired Voronoi lattice (BVL). In mechanical behavior, the BMVM exhibits a dual-plateau deformation mode and graded energy absorption. It maintains a relatively low initial peak load while achieving high mean stress and a specific energy absorption of 19.33 J/g. Besides, two low-frequency absorbers based on the upper cavities are designed, with average absorption coefficients exceeding 0.9 in 384-644 Hz and 0.8 in 340-708 Hz. A genetic algorithm is employed to optimize embedded-tube parameters, increasing the corresponding bandwidths by 97.0% and 37.3%. The effects of key dimensional parameters on both mechanical and acoustic performance are further analyzed. Finally, several potential applications in highway guardrails and aircraft cabins are proposed, which integrate sound absorption and energy dissipation capabilities.

Recently, the combination of sandwich structures and auxetic structures has been extensively researched, because of its excellent mechanical properties. However, there has been limited research on sandwich structures designed as cylindrical sandwich tubes. Therefore, this paper proposes a cylindrical sandwich tube filled with elliptical perforated auxetic structure (CSTE), and uses a cylindrical sandwich filled with double-arrowed auxetic structure (CSTD) as a comparison. The results indicate that CSTE exhibits superior energy absorption capacity and higher load-bearing capacity. Additionally, the elliptical perforated auxetic core layer alters the distribution of the original energy absorption contribution rate in CSTD. Moreover, parametric analysis is conducted using the experimentally validated model to investigate the influence of various parameters on the mechanical properties of CSTE. The results show that an increase in the hollow section ratio is most effective in increasing the stiffness of CSTE, and the radius thickness ratio plays a dominant role in the energy absorption capacity. Furthermore, when the ratio of the major and minor axis of an ellipse is 1.88, the energy absorption capacity of the CSTE is significantly enhanced. These findings can facilitate the application of cylindrical sandwich tubes in protective engineering.

Auxetic materials exhibit exceptional mechanical properties and distinctive deformation characteristics. A novel compression-torsion coupled auxetic tube is introduced in this study, which integrates an auxetic structure with a compression-torsion coupling mechanism. By modifying the inner tube and ribs of the structure, the compression-torsion coupling effect is enhanced, improving both the mechanical properties and deformation characteristics. Three compression-torsion coupled auxetic tubes (CATs) were fabricated using 3D printing technology. They were compared with conventional auxetic tubes (AT) to examine the influence of compression- torsion coupling on structural behavior. Experimental results were compared with simulation, confirming the validity of the finite element model. Numerical analysis was conducted to investigate the influence of the direction of compression-torsion coupling and outer wall thickness on CAT structures. The results demonstrate that the compression-torsion coupling effect changes the wall thickness under compression, enhancing energy absorption and structural stability. The structure has a densification delay of 28.5 % compared to other perforated tubes, and the SEA has increased by 105 %. Additionally, the application of compression-torsion coupled auxetic tubes in auxetic springs was explored, revealing that the compression-torsion coupling effect significantly prolongs the working displacement of the structure while improving its capacity for elastic energy storage. CAT has broad application prospects in the fields of soft robots and protective engineering.

This paper investigates a piezoelectric micro-cantilevered wide-plate resonator for liquid sensing. The higher-order flexural mode featuring two-dimensional vibrations of the resonator is exploited to enable precise measurements under viscous liquid conditions. The analytical model based on fluid-structure interaction successfully explains this non-conventional flexural mode and resonance characteristics, which provides an optimization design method for the resonator. For on-chip fully electrical interfaces, the piezoelectric aluminum nitride (AlN) film is employed in combination with tailored electrode design to allow self-actuation and self-sensing capabilities when submerged in liquid media. The experiments demonstrated that the density and dynamic viscosity of various liquids can be individually determined from their high-linear relationships with the resonant frequency and quality factor of the resonator. The proposed piezoelectric resonator exhibited excellent sensing characteristics, resulting in accuracies of 0.48% for density with a sensitivity of 27.94 kHz/(g·cm-3), and 3.37% for viscosity. In addition, the minimum detectable changes were evaluated to be 1.79×10-4 g·cm-3 and 9.29 μPa·s for the liquid density and viscosity, respectively. The results presented here show the outstanding potential of two-dimensional vibrational modes using micro-plate resonators for achieving high accuracy and compact design in liquid monitoring applications.

The construction industry is rapidly evolving towards intelligence. The emergence of multifunctional metamaterials aligns with this trend. This paper introduced a novel 3D re-entrant sandwich box structure (Re-box). A mesh sandwich box structure (Me-box) was designed as a control group to analyze the differences between positive and negative Poisson's ratio sandwich cores. The structure's energy absorption (EA), durability, and acoustic characteristics were studied. Experimental and FEA results demonstrate the Re-box's superior EA capabilities. Notably, the Re-box maintained excellent stiffness under cyclic loading. Furthermore, the Re-box proposed in this study achieved nearly perfect sound absorption in the mid-to-low frequency range. Therefore, the structure provides protective functions while simultaneously reducing ambient noise levels. Compared with traditional concrete structures, the proposed Re-box in this paper serves mechanical-acoustic functions. It achieves both lightweight design and effective control of sound waves. The Re-box structure can be used as a protective device for the internal structures of aircraft and automobiles through an assembly and combination approach.

Low-frequency broadband sound absorption is a hot topic in the field of acoustics. For the Helmholtz resonator, the low-frequency sound wave can be controlled by adjusting the size of the structure. However, the frequency bandwidth of the sound absorption is narrow. The micro-perforated panel (MPP) absorber predominantly targets mid-to-high frequency noise. To achieve broadband sound absorption, an auxetic star-shaped metastructure (ASM) based on the Helmholtz resonator and MPP absorber is proposed. The ASM employs an auxetic star-shaped structure as a unit cell, wherein triangular cavities formed at the junction of the unit cells are strategically designed to function as MPP resonators. Firstly, the theoretical formula of the ASM is derived by electro-acoustic analogy, and the numerical simulation results are compared with the theoretical results. Besides, the sound absorption mechanism of the ASM is studied by the acoustic pressure distribution, particle vibration velocity distribution, and power dissipation density distribution. Secondly, the sound absorption performance of the ASM is studied by adjusting the structural parameters. Finally, it is proved that when the thickness of the ASM structure is only 40 mm, the average sound absorption coefficient of 0.9 at 580-1150 Hz. In this paper, a novel method is presented for designing a broadband sound-absorbing metastructure.

Auxetic metamaterials refer to materials and structures with extraordinary deformation, i.e., transverse expansion (contraction) under uniaxial tension (compression). In recent decades, a very wide range of innovative and functional performance has been discovered stemming from this extraordinary behavior. This desirable exhibition of adaptivity, programmability, and functionality provides great potential in soft intelligent systems. However, thus far, the mainstream research on auxetic metamaterials has focused on subjective design, monotonic mechanical properties, and passive tunability. This review provides a thorough overview of auxetic metamaterials from classical mechanical properties to intelligent applications, with the primary objective of proposing a new roadmap of auxetics for intelligent advances in this interdisciplinary field. The fundamental works are categorized in different configurations and mechanisms. In particular, the intelligent functional integration of shape morphing, actuation, sensing, multiphysical response, and inverse design is reviewed in detail. To accelerate the development of auxetics in smart materials and structural systems, the potential intelligent applications of auxetic metamaterials are generalized into soft robotics (outside the body), human–machine interaction (surrounding the body), and healthcare devices (inside the body). Finally, several significant research topics for intelligent auxetics are emphasized in theory, design, material choice, manufacturing technique, properties, and applications.

As an exemplary energy absorption structure, thin-walled metallic tubes have been extensively studied. Introducing dimple defects into the tube wall can induce the desired deformation in thin-walled metallic tubes to enhance their energy absorption performance. Existing research has only discussed dimpled tubes with relatively thin wall thicknesses and shallow dimples, which is insufficient to meet the demands of widespread applications. This study introduces two novel tubular structures by incorporating predefined dimples into the walls of smooth tubes. Through finite element simulation and experiment, the influence of wall thickness, dimple aspect ratio, and the orientation of the dimples on the energy absorption capacity of the structures is parametrically analyzed. A comparison with traditional smooth tubes is also conducted. The results indicate that the wall thickness, dimple aspect ratio, and orientation of the dimples have significant effects on reducing the initial peak force, enhancing specific energy absorption, and improving structural stability. By appropriately selecting geometric parameters, energy absorption tubular structures adaptable to various application scenarios can be designed. The two novel tubular structures proposed provide new design insights for the study of energy absorption in thin-walled metallic tubes.