Mechanical Metamaterials Research Articles

Metamaterials with modulated coefficient of thermal expansion and ultra-low thermal stress

Mechanical Metamaterials, which integrate multi-material systems, possess the exclusive capability to modulate the coefficient of thermal expansion (CTE). However, the thermal stress induced by the uncoordinated deformation of multi-material seriously restricts their engineering applications under cyclic and extreme temperature variations. Here, an innovative Zigzag Connection (ZC) metamaterial is originally developed to integrate the modulated CTE and ultra-low thermal stress, in contrast to the End-to-end Connection (EC) and Side-to-side Connection (SC) metamaterials reported in the literature. The mechanism and theoretical analysis of the CTE and thermal stress are established and validated through numerical simulations. It is revealed that the EC and SC metamaterials consistently generate the high thermal stress far beyond the yield strength, while the newly designed ZC metamaterial simultaneously exhibits the modulated CTE and ultra-low thermal stress. Moreover, an Ashby plot of CTE versus thermal stress is illustrated, and the concept of temperature variation tolerance is defined to guide the comprehensive design of these metamaterials. The ZC metamaterial shows a higher temperature variation tolerance within compared with the EC and SC metamaterials. Overall, the ZC metamaterial emerges as a solution for the inherent conflict between the modulate CTE and thermal stress, highlighting its obvious superiority of applications under high-temperature environments.

Metamaterial-based vibration control for offshore wind turbines operating under multiple hazard excitation forces

Wind energy holds growing investment perspectives due to its renewable and sustainable energy production potential. The harvesting capability of wind turbines is directly related to their size. Therefore, those wind energy generators still encounter challenges related to excessive vibrations aggravated by environmental factors, compromising energy generation and resulting in fatigue damage and downtime. Various vibration control strategies have been explored to address these issues, with passive control emerging as a preferred choice due to its ease of manufacture, cost-effectiveness, and simple installation. Nevertheless, the limitations of these controls lie in their substantial size and weight associated with optimal installation positions for achieving a good performance. Recently, mechanical metamaterials have demonstrated tremendous advancements in efficiency regarding band isolation and vibration mitigation, coupled with enhanced manufacturing possibilities. Hence, this paper proposes a novel approach to control the vibration of wind turbines employing mechanical metamaterials in their design. A spectral approach is used to model the metamaterial turbine and its interaction with external excitations, such as wind, waves, and blade rotation. The numerical results show the efficiency of the metamaterial turbine by its tunable stopband features and vibration amplitude reduction under multiple hazard excitations, emphasising its superior suppressing vibrations compared to conventional tuned mass damper. Thus, the proposed wind turbine metastructures offer a compelling combination of effective vibration attenuation while reducing dynamic resonators’ overall stiffness, mass, and size. The outcome advances wind turbine design and energy technology for reliable wind energy production.

Lightweight recoverable mechanical metamaterials for efficient buffering of continuous multi extreme impacts

When projectiles penetrate multistory buildings, their internal fuze microsystem needs to withstand continuous and multiple strong mechanical impacts. Similar mechanical conditions also exist in automobile collisions and in other industrial scenarios. Therefore, buffer materials with high energy absorption and recoverability are essential to protect the core devices of projectiles from failures in such scenarios. In this study, an ingeniously designed lightweight mechanical metamaterial with a bistable symmetric curved beam structure (BCBS) is proposed for high elastic energy absorption performance and recoverability using a bistable mechanical design. Given its significantly lower structural density than that of the traditional configuration, BCBS can maintain the weight of the buffer using a high-strength TC4 material, which aids practical applications such as fuzes. The optimal parameter design of a BCBS was derived using the bending beam theory. Finite element calculations were used to analyze the performance advantages and mechanism origins of the energy absorption and recoverability of the BCBS compared with those of classical buffer materials and negative- stiffness sandwich bistable structures (NSMSs). Further, the experimental performance under two typical mechanical conditions of a projectile fuze was tested using a project-specialized mechanical impact experimental system. After three consecutive ultra-high energy impacts (energy up to 3800 J per impact), the maximum energy absorption ratio and recoverability of the BCBS were found to be 213.2% and 12.1% higher than those of the NSMSs, respectively. The BCBS maintained energy absorption stability under five consecutive ultra-high acceleration impacts (peak acceleration amplitude = 2500 g), effectively protecting the electromechanical system.

Assessment of 3D printed mechanical metamaterials for prosthetic liners.

This study focuses on novel design and evaluation of Elastic 50A (EL50) mechanical metamaterials with open-cell patterns for its potential application to lower limb residuum/socket interfaces, specifically that of a transtibial (TT) amputee. Mechanical characteristics, that is, effective Young's modulus (E), was tuned by altering metamaterial porosity, which was experimentally verified. Specifically, pore radius of the unit cell was varied to achieve a range of E-values (0.05-1.71 MPa) for these 3D printed metamaterials. Finite Element Analysis (FEA) was conducted to evaluate pressure distribution across key load-bearing anatomical sites of a TT residuum. Using designed metamaterials for homogeneous liners, pressure profiles were studied and compared with a silicone liner case. Additionally, a custom metamaterial liner was designed by assigning appropriate metamaterials to four load-sensitive and tolerant anatomical sites of the TT residuum. The results suggest that lowest pressure variation (PV), as a measure of pressure distribution levels and potential comfort for amputees, was achieved by the custom metamaterial liner compared to any of the homogeneous liners included in this study. It is envisaged that this work may aid future design and development of custom liners using now commonly available 3D printing technologies and available elastomer materials to maximise comfort, tissue safety and overall rehabilitation outcomes for lower limb amputees.

Three-Dimensional Optical Imaging of Internal Deformations in Polymeric Microscale Mechanical Metamaterials.

Recent advances in two-photon polymerization fabrication processes are paving the way to creating macroscopic metamaterials with microscale architectures, which exhibit mechanical properties superior to their bulk material counterparts. These metamaterials typically feature lightweight, complex patterns such as lattice or minimal surface structures. Conventional tools for investigating these microscale structures, such as scanning electron microscopy, cannot easily probe the internal features of these structures, which are critical for a comprehensive assessment of their mechanical behavior. In turn, we demonstrate an optical confocal microscopy-based approach that allows for high-resolution optical imaging of internal deformations and fracture processes in microscale metamaterials under mechanical load. We validate this technique by investigating an exemplary metamaterial lattice structure of 80 × 80 × 80 μm3 in size. This technique can be extended to other metamaterial systems and holds significant promise to enhance our understanding of their real-world performance under loading conditions.

De Novo Atomistic Discovery of Disordered Mechanical Metamaterials by Machine Learning.

Architected materials design across orders of magnitude length scale intrigues exceptional mechanical responses nonexistent in their natural bulk state. However, the so-termed mechanical metamaterials, when scaling bottom down to the atomistic or microparticle level, remain largely unexplored and conventionally fall out of their coarse-resolution, ordered-pattern design space. Here, combining high-throughput molecular dynamics (MD) simulations and machine learning (ML) strategies, some intriguing atomistic families of disordered mechanical metamaterials are discovered, as fabricated by melt quenching and exemplified herein by lightweight-yet-stiff cellular materials featuring a theoretical limit of linear stiffness-density scaling, whose structural disorder-rather than order-is key to reduce the scaling exponent and is simply controlled by the bonding interactions and their directionality that enable flexible tunability experimentally. Importantly, a systematic navigation in the forcefield landscape reveals that, in-between directional and non-directional bonding such as covalent and ionic bonds, modest bond directionality is most likely to promotes disordered packing of polyhedral, stretching-dominated structures responsible for the formation of metamaterials. This work pioneers a bottom-down atomistic scheme to design mechanical metamaterials formatted disorderly, unlocking a largely untapped field in leveraging structural disorder in devising metamaterials atomistically and, potentially, generic to conventional upscaled designs.

A self-recoverable negative stiffness metamaterial with enhanced bearing and energy dissipation capacity

Because of their desirable properties, mechanical metamaterials have drawn increasing attention. Negative stiffness (NS) metamaterials can be used as reusable energy dissipation devices, but they usually have low bearing capacity. In this study, a self-recoverable NS structure with enhanced bearing and energy dissipation capacity was proposed. It breaks free from the size limitations of curved beams or thin rods, and can have high bearing and energy dissipation capacity through the mutual extrusion and friction between the snap plug and the layered snap groove. The mechanical properties of the proposed NS structure were studied by finite element analysis and experiments. The reusability of the structure was verified by cyclic loading experiments. The results show that compared with the traditional curved beam NS structure and the previously self-recoverable NS structure, the bearing and energy dissipation capacity of the proposed structure have been greatly improved.

Flexible sensors with zero Poisson's ratio.

Flexible sensors have been developed for the perception of various stimuli. However, complex deformation, usually resulting from forces or strains from multi-axes, can be challenging to measure due to the lack of independent perception of multiaxial stimuli. Herein, flexible sensors based on the metamaterial membrane with zero Poisson's ratio (ZPR) are proposed to achieve independent detection of biaxial stimuli. By deliberately designing the geometric dimensions and arrangement parameters of elements, the Poisson's ratio of an elastomer membrane can be modulated from negative to positive, and the ZPR membrane can maintain a constant transverse dimension under longitudinal stimuli. Due to the accurate monitoring of grasping force by ZPR sensors that are insensitive to curvatures of contact surfaces, rigid robotic manipulators can be guided to safely grasp deformable objects. Meanwhile, the ZPR sensor can also precisely distinguish different states of manipulators. When ZPR sensors are attached to a thermal-actuation soft robot, they can accurately detect the moving distance and direction. This work presents a new strategy for independent biaxial stimuli perception through the design of mechanical metamaterials, and may inspire the future development of advanced flexible sensors for healthcare, human-machine interfaces and robotic tactile sensing.

Mechanical properties of homogeneous and functionally graded spinodal structures

This paper investigates the compressive mechanical behavior of spinodoid metamaterials in a quasi-static state through experimental and numerical analysis at the macroscopic level. This homogeneous structure exhibits weak strain hardening, resulting in a lower initial peak compression force and higher specific absorption energy compared to other mechanical metamaterials. The homogeneous model has multiple low-density regions uniformly distributed within the three-dimensional space due to the random nature of the Gaussian field. Thus, the transition from low-density to high-density regions is described as a gradual process, implying that the deformation of metamaterial shifts to region-by-region compaction. Besides, the functionally graded spinodoid structure shows strong strain hardening, whose deformation mainly tends to collapse layer by layer along a positive graded direction. The graded structures with low densities have a lower energy absorption capacity than the corresponding homogeneous structure, while higher-density structures show a reverse trend. This phenomenon originates from the superimposed effect of two kinds of strain hardening.

4D printed zero Poisson’s ratio metamaterials with vibration isolation properties for magnetic response

Although mechanical metamaterials possess high specific energy absorption, they suffer from drawbacks such as irreversible deformations and non-adjustable mechanical properties. Magnetic excitation is considered to be one of the most promising methods for special working environments; for which uniform incorporation of UV-cured four-dimensional (4D) printed resin is considered to be an effective approach to achieving fine structural features. Our study investigated the impact of soft magnetic particle content on the mechanical and dynamic mechanical properties of a shape memory polymer matrix material. This paper presents a 4D printed metamaterial with a zero Poisson’s ratio that can sense magnetic field intensity and alter its mechanical properties. Its rapid shape recovery, achieved through magnetic excitation, enables multiple energy absorption within a short timeframe. By increasing the curvature radius, the stress concentration in the hexagonal honeycomb structure is reduced, ensuring the metamaterial maintains its zero Poisson’s ratio even under in-plane loading. The study investigates the energy absorption performance and force–displacement curve of metamaterials with different layers and cell sizes, focusing on a four-layer metamaterial for the analysis. Furthermore, the paper explores the tunable energy absorption characteristics of the four-layer metamaterial under time-varying electromagnetic fields, aiming to enhance the stability of a lander’s center of gravity while landing on uneven terrain.

Ultralight, strong, and self-reprogrammable mechanical metamaterials.

Versatile programmable materials have long been envisioned that can reconfigure themselves to adapt to changing use cases in adaptive infrastructure, space exploration, disaster response, and more. We introduce a robotic structural system as an implementation of programmable matter, with mechanical performance and scale on par with conventional high-performance materials and truss systems. Fiber-reinforced composite truss-like building blocks form strong, stiff, and lightweight lattice structures as mechanical metamaterials. Two types of mobile robots operate over the exterior surface and through the interior of the system, performing transport, placement, and reversible fastening using the intrinsic lattice periodicity for indexing and metrology. Leveraging programmable matter algorithms to achieve scalability in size and complexity, this system design enables robust collective automated assembly and reconfiguration of large structures with simple robots. We describe the system design and experimental results from a 256-unit cell assembly demonstration and lattice mechanical testing, as well as a demonstration of disassembly and reconfiguration. The assembled structural lattice material exhibits ultralight mass density (0.0103 grams per cubic centimeter) with high strength and stiffness for its weight ( 11.38 kilopascals and 1.1129 megapascals, respectively), a material performance realm appropriate for applications like space structures. With simple robots and structure, high mass-specific structural performance, and competitive throughput, this system demonstrates the potential for self-reconfiguring autonomous metamaterials for diverse applications.

Transforming Auxetic Metamaterials into Superhydrophobic Surfaces

Superhydrophobic materials are often inspired by nature, whereas metamaterials are engineered to have properties not usually occurring naturally. In both, the key to their unique properties is structure. Here, it is shown that a negative Poisson's ratio (auxetic) mechanical metamaterial can transform into a unique superhydrophobic material. When stretched, its surface has the counterintuitive property that it also expands in the orthogonal lateral direction. The change in the solid surface fraction as strain is applied is modeled, and it is shown that it decreases as the space between solid elements of the auxetic lattice expands. This results in a unique dependence of the superhydrophobicity on strain. Experimental models are constructed to illustrate the relationship between different states of strain and superhydrophobicity as the lattice transitions from an auxetic to a conventional structure. The findings offer a new approach to designing superhydrophobic materials for self‐cleaning surfaces, droplet transportation, droplet encapsulation, and oil–water separation.

Study on the mechanical properties of cylindrical mechanical metamaterials with biomimetic honeycomb units of the diabolical ironclad beetle

In the long process of evolution in nature, the elytra of the diabolical ironclad beetle are connected in a jigsaw way, so that the overall structure of the beetle has strong pressure resistance. The study of the geometric features and interlocking effect of elytra junctions provides new ideas for the development of new bionic applications. The honeycomb structure is a new type of material structure with excellent mechanical properties, and has broad application prospects in building structure, aerospace and other aspects. Through the reasonable design and modification of the honeycomb structure, the honeycomb structure has different characteristics. Based on the concave hexagonal honeycomb structure, combined with the geometric characteristics of the diabolical ironclad beetle jigsaw connection, the concave hexagonal honeycomb structure is redesigned, and a new type of bionic honeycomb structure is proposed. Through the combination of experiments and simulations, the mechanical response of the bionic honeycomb structure of diabolical ironclad beetles was studied. Research has shown that as the connection angle increases, the curvature on both sides of the unit also increases, making the units more compact. The overall structure exhibits two types of mechanical responses under compression: "U" and "Γ". The structure with connection angle of 25° can rely on the support and buckling on both sides of the unit, thus having the best energy absorption characteristics. As the axial ratio of the ellipse (a:b) increases, the degree of concavity in the structural unit continues to deepen, resulting in three forms of deformation of the structural unit. The structural unit changes from being supported on both sides to being bent on both sides, resulting in a stacking phenomenon in structures with ratios of 2.2:1 and 2.4:1, and the overall structure has better deformation resistance.

A series of auxetic metamaterials with negative thermal expansion based on L-shaped microstructures

Mechanical metamaterials are facing various multi-functional requirements. In this study, a series of auxetic metamaterials with enhanced negative thermal expansion and improved stiffness are proposed. These metamaterials consist of four novel L-shaped microstructures connected in various clockwise or counterclockwise directions. Two length ratios and four angle parameters are utilized to define the geometry of these metamaterials. Both analytical analysis and validated numerical homogenization methods are employed to determine their effective thermoelastic properties, including effective Young's modulus, Poisson's ratio, and coefficient of thermal expansion. It is demonstrated that tailoring these microstructural geometries can modulate the effective thermoelastic properties of these metamaterials accordingly. By appropriately tailoring the geometric parameters, these metamaterials exhibit increased effective stiffness as well as more pronounced auxeticity and negative thermal expansion compared to traditional triangle and trapezoid microstructures. Notably, the in-plane effective anisotropic or isotropic Poisson's ratio and coefficient of thermal expansion can be adjustable over a broader range from negative to positive values. High stiffness, High strength, and near-zero thermal expansion can be achieved concurrently in these metamaterials, which is very conducive for structural designing in thermal environments. These metamaterials with a coupled design of stiffness, thermal expansion, and Poisson's ratio hold significant potential for advancing applications in satellite platforms, space structures, composite sandwiches, and precision equipment.

Nonlinear interaction of head-on solitary waves in integrable and nonintegrable systems

This study numerically investigates the nonlinear interaction of head-on solitary waves in a granular chain (a nonintegrable system) and compares the simulation results with the theoretical results in fluid (an integrable system). Three stages (the pre-in-phase traveling stage, the central-collision stage, and the post-in-phase traveling stage) are identified to describe the nonlinear interaction processes in the granular chain. The nonlinear scattering effect occurs in the central-collision stage, which decreases the amplitude of the incident solitary waves. Compared with the leading-time phase in the incident and separation collision processes, the lagging-time phase in the separation collision process is smaller. This asymmetrical nonlinear collision results in an occurrence of leading phase shifts of time and space in the post-in-phase traveling stage. We next find that the solitary wave amplitude does not influence the immediate space-phase shift in the granular chain. The space-phase shift of the post-in-phase traveling stage is only determined by the measurement position rather than the wave amplitude. The results are reversed in the fluid. An increase in solitary wave amplitude leads to decreased attachment, detachment, and residence times for granular chains and fluid. For the immediate time-phase shift, leading and lagging phenomena appear in the granular chain and the fluid, respectively. These results offer new knowledge for designing mechanical metamaterials and energy-mitigating systems.

A comparative study of enriched computational homogenization schemes applied to two-dimensional pattern-transforming elastomeric mechanical metamaterials

A comparative study of enriched computational homogenization schemes applied to two-dimensional pattern-transforming elastomeric mechanical metamaterials

3D Tiled Auxetic Metamaterial: A New Family of Mechanical Metamaterial with High Resilience and Mechanical Hysteresis.

For artificial materials, desired properties often conflict. For example, engineering materials often achieve high energy dissipation by sacrificing resilience and vice versa, or desired auxeticity by losing their isotropy, which limits their performance and applications. To solve these conflicts, a strategy is proposed to create novel mechanical metamaterial via 3D space filling tiles with engaging key-channel pairs, exemplified via auxetic 3D keyed-octahedron-cuboctahedron metamaterials. This metamaterial shows high resilience while achieving large mechanical hysteresis synergistically under large compressive strain. Especially, this metamaterial exhibits ideal isotropy approaching the theoretical limit of isotropic Poisson's ratio, -1, as rarely seen in existing 3D mechanical metamaterials. In addition, the new class of metamaterials provides wide tunability on mechanical properties and behaviors, including an unusual coupled auxeticity and twisting behavior under normal compression. The designing methodology is illustrated by the integral of numerical modeling, theoretical analysis, and experimental characterization. The new mechanical metamaterials have broad applications in actuators and dampers, soft robotics, biomedical materials, and engineering materials/systems for energy dissipation.

Mechanical metamaterial design with the customized low-frequency bandgap and negative Poisson's ratio via topology optimization

The precise control of both the mechanical deformation and wave propagation characteristics of metamaterial through design holds significant importance and presents a challenging task. This paper proposes a novel two-stage topological optimization design method for customizing both negative Poisson's ratio and locally resonant bandgap in the mechanical metamaterial. In the optimized model, the negative Poisson’s ratio structure is firstly obtained by optimizing the material distribution within the matrix region, then the metamaterial with the customized negative Poisson’s ratio and bandgap range is obtained through the second stage optimization. In the analysis of the metamaterial unit cell, the topology-dependent Poisson’s ratio is calculated based on the equivalent elastic matrix obtained through the homogenization method. The range of bandgap is estimated using the effective mass analytical model of the spring-mass system. Thus, the range of bandgap is determined by only a few geometric parameters instead of topological structure under given assumptions. The customized bandgap ranges can be extended by introducing more resonators into the unit cell and combining different unit cells into an assembled structure. Numerical examples are provided to demonstrate the efficacy of the proposed method.

Achieving synchronous compression-shear loading on SHPB by utilizing mechanical metamaterial

Materials in service often experience complex stress states, such as a combination of shear and compression or tension. Therefore, it is crucial to experimentally measure the mechanical responses of materials under complex stress states before designing structures, as these responses differ from those under uniaxial loading. However, conducting combined loading experiments, especially under dynamic impact, is challenging and usually requires complex and costly equipment. In the present work, by employing compression-torsion coupling metamaterials, an easy method is proposed for the first time to achieve synchronous dynamic compression-shear loading on 1D Split Hopkinson Pression Bar (SHPB), which is also feasible for quasi-static experiments on universal material testing machine. The compression-torsion coupling metamaterial can convert a compression wave into combined waves of compression and torsion, and ensures the two waves naturally synchronously act on the thin-walled cylinder specimen. Since the compression-shear dynamic loading experiment can be performed on a traditional 1-D SHPB, it is a cost-effective, convenient, and easily implementable method. Both the dynamic and quasi-static mechanical properties of 1060 Al were measured under various shear-compression ratios, and a well von-Mises yield surface was obtained with strain rate insensitivity, confirming the validity of the proposed experimental methods.

Anisotropic thermal expansion based on a novel metamaterial

Metamaterials exhibiting exceptional thermoelastic properties are emerging as promising candidates for scientific and engineering applications. Previous studies on mechanical metamaterials with negative thermal expansion (NTE) have primarily focused on enhancing isotropic NTE, often resulting in a high coefficient of thermal expansion (CTE) but low stiffness that characterizes bending-dominated NTE metamaterials. In this study, we proposed a novel mechanical metamaterial with significant anisotropic thermal expansion behavior and substantial stiffness based on the cross structure, re-entrant structure, and triangular structure with NTE. The programmable CTE and effective elastic modulus were analytically derived using the unit load method and stiffness matrix method, respectively, which were validated by numerical results obtained from finite element analysis (FEA). Drawing inspiration from the body-centered cubic and face-centered cubic strategies, two types of extended three-dimensional metamaterials can be obtained. The results demonstrate that a larger length ratio λ and angle θ3 can enhance the NTE effect, while reducing the Young's modulus. The maximum magnitudes of NTE and positive thermal expansion (PTE) are achieved at approximately θ2 = 90°, resulting in a decreased stiffness and slight negative Poisson's ratio (NPR). By adjusting the angles θ2 of re-entrant structures, six distinct anisotropic thermal expansion behaviors can be obtained in this planar metamaterial. Furthermore, a wider range of isotropic CTE as well as an extended range of anisotropic CTE can be achieved in the present metamaterial compared to its original metamaterials. The proposed metamaterial can be combined with traditional triangle metamaterials to enhance thermoelastic properties. The analysis also provides valuable insights into designing metamaterials with large CTE, optimal stiffness, and lightweight properties simultaneously for engineering applications.