Three-dimensional Metamaterials Research Articles

MEMS-actuated terahertz metamaterials driven by phase-transition materials

The non-ionizing and penetrative characteristics of terahertz (THz) radiation have recently led to its adoption across a variety of applications. To effectively utilize THz radiation, modulators with precise control are imperative. While most recent THz modulators manipulate the amplitude, frequency, or phase of incident THz radiation, considerably less progress has been made toward THz polarization modulation. Conventional methods for polarization control suffer from high driving voltages, restricted modulation depth, and narrow band capabilities, which hinder device performance and broader applications. Consequently, an ideal THz modulator that offers high modulation depth along with ease of processing and operation is required. In this paper, we propose and realize a THz metamaterial comprised of microelectromechanical systems (MEMS) actuated by the phase-transition material vanadium dioxide (VO2). Simulation and experimental results of the three-dimensional metamaterials show that by leveraging the unique phase-transition attributes of VO2, our THz polarization modulator offers notable advancements over existing designs, including broad operation spectrum, high modulation depth, ease of fabrication, ease of operation condition, and continuous modulation capabilities. These enhanced features make the system a viable candidate for a range of THz applications, including telecommunications, imaging, and radar systems.Graphical

Angle-Resolved Polarimetry with Quasi-Bound States in the Continuum Plasmonic Metamaterials via 3D Aerosol Nanoprinting.

Three-dimensional (3D) plasmonic metamaterials, featuring well-arranged subwavelength nanostructures, facilitate effective coupling between electrical dipoles and incident electromagnetic waves. This coupling allows for unique optical responses including localized surface plasmon resonance (LSPR) and quasi-bound states in the continuum (q-BIC). While 3D plasmonic metamaterials with LSPR and q-BIC have been independently explored for sensors, achieving simultaneous optical responses in the near-infrared region remains challenging. Here, we present 3D plasmonic metamaterials that integrate LSPR and q-BIC within a single π-shaped plasmonic structure, fabricated using a 3D aerosol nanoprinting technique. This printing technique controls the local electrostatic field to precisely position charged metallic nanoaerosols, enabling parallel printing of π-shaped plasmonic structures under ambient conditions. The printed π-shaped plasmonic structures exhibit two distinct optical modes: x-polarization-sensitive LSPR and transverse magnetic mode-sensitive q-BIC within the near-infrared region. Exploiting these dual optical responses, we demonstrate simultaneous polarization detection and incident angle analysis by integrating the π-shaped plasmonic structures into commercial Fourier-transform infrared spectroscopy, termed "numerical aperture-detective polarimetry". This approach holds promise for evaluating alignment in optical and imaging systems with light distribution analysis. Furthermore, the 3D aerosol nanoprinting technique provides an avenue for fabricating 3D plasmonic metamaterials with intricate geometries and optical properties, expanding their potential applications in nano-optics.

Accessing quasi-static impact process by 3D-NPR corrugated metamaterials

The conventional impact process is a quintessential impulse process that causes substantial damage due to the high initial impact force. However, the impact effect can be significantly diminished by making the impulse process quasi-statically by using a three-dimensional negative Poisson's ratio corrugated metamaterial (3D-NPRCM) structure. This paper proposes a novel 3D-NPRCM obtained by folding the 2D-NPRCM. This study examines the crashworthiness properties and impact force of 3D-NPRCM subjected to impact using the finite element method (FEM). The results reveal that the sequential matrix structure has the ability to make impact impulse processes quasi-statically. The effects of various folding angles, arrangements, and geometrical parameters on the properties are also explored. Finally, the 3D-NPRCM is employed in an automobile crash box design. Through axial quasi-static compression simulation, the peak crushing force of the 3D-NPRCM crash box is reduced by 25.374 % from 211.652 kN to 157.946 kN, and the energy absorbed is increased by 23.830 % from 11.259 kJ to 13.942 kJ, compared to the conventional crash box. Through cart lateral impact simulation, the peak crushing force of the 3D-NPRCM crash box is reduced by 18.076 % from 206.9 kN to 169.5 kN, and the compressive displacement is decreased by 9.457 % from 235.8 mm to 213.5 mm. This work presents a novel design proposition for a crash box in vehicle engineering and demonstrates a fresh approach to expand the design of three-dimensional mechanical metamaterials.

Three-dimensional acoustic metamaterials with topological states of different orders and multidirectional waveguiding

Three-dimensional acoustic metamaterials with topological states of different orders and multidirectional waveguiding

3D compression-twist lattice metamaterials for surface reconfigurability of future architecture

Metamaterials refer to a class of materials with special properties, whose characteristics mainly come from the microstructures designed artificially. Among them, those metamaterials with tunable shape and mechanical properties under external stimuli provide a new inspiration for the design of the multifunctional structures. This work deals with the three-dimensional (3D) compression-twist lattice metamaterials, studies the surface reconfigurability under external forces, and reveals the torsion-bending coupling (TBC) effect of the special metamaterials. To explain the main characteristics of the TBC effect, the deformation mechanism of the metamaterials is analyzed. Combining the finite element method (FEM) and the spherical fitting algorithm, the relationship between the bending angle and the load of the metamaterials after deformation is analyzed and verified by experiments. Finally, a metamaterial module that could be freely transformed between planar and spherical surfaces is envisaged. A faster and greener solution is proposed for the construction of curved surfaces of engineering structures in the future, which promotes the subsequent applications of metamaterials to engineering practice.

Design and analysis of three-dimensional chiral metamaterials for enhanced torsional compliance

Three-dimensional (3D) chiral structures are a subset of mechanical metamaterials known for their distinctive deformation characteristics, including the presence of auxetic and compression–torsion coupling behaviors. In this study, a novel 3D chiral metamaterial with high torsional compliance was designed. A gammadion-shaped chiral cell comprising inclined ligaments was incorporated into the chiral structure for enhanced torsional compliance. Finite element analyses (FEAs) were performed to demonstrate that the proposed chiral structure outperformed other chiral structures in terms of torsional compliance. Furthermore, FEAs were performed to investigate the influence of the slenderness ratio and ligament diameter of the chiral structure, on attaining a maximum torsional compliance of 18.6° N−1. These 3D chiral structures were fabricated using additive manufacturing techniques, and experimental validations were performed to observe and confirm the compression–torsion coupling behaviors. To further expand the utility of these 3D chiral structures, statistical analyses were conducted to establish regression models for effective density and torsional compliance, as functions of the slenderness ratio and ligament diameter. These regression models can enhance the applicability of the proposed chiral structures in the development of versatile functional components that require compression–torsion coupling behaviors.

Developing three-dimensional mechanical metamaterials with tailorable bandgaps for impact mitigation

A novel three-dimensional mechanical metamaterial with low frequency bandgaps and negative Poisson’s ratio is designed, consisting of a conventional three-dimensional reentrant structure and periodic resonators, with the aim of achieving vibration isolation and impact mitigation. The bandgap characteristic of the proposed metamaterial is determined computationally, and its dispersion diagram exhibits both partial bandgaps and a complete bandgap within a frequency band of interest. The mechanism for bandgap occurrence is characterised as the local resonance of ligaments and resonators, according to a vibration mode analysis. The wave attenuation capacity of the proposed metamaterial is derived numerically and experimentally from semi-infinite and finite-size metamaterial models, showing a good agreement with the predicted bandgap. Additionally, a thorough study on the design flexibility indicates that the bandgap characteristic can be directly tailored by changing the geometrical parameters of the proposed metamaterial. This allows further optimisation of the metamaterial for potential applications. The dynamic performance of the proposed metamaterial under an impact load is investigated by a finite element model. This demonstrates that the metamaterial reduces the transmitted force by a factor of 1.6 (for peak value) and 2.0 (for root mean square value) under a pulse impact with a duration of 0.88 ms. The impact mitigation result obtained from the impact test confirms that the metamaterial shows a mitigation capacity which is approximately 20% better than that of the conventional reentrant structure.

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.

Mechanical behaviors of three-dimensional chiral mechanical metamaterials

Chiral and achiral mechanical metamaterials are designed via spherical tiling. The 3D chiral designs show an interesting coupled compression-twisting behavior, while the 3D achiral designs show auxetic behavior. Also, besides the cellular-type chiral and achiral designs, composite-type of each design are created by adding soft matrix to the cellular designs. The designs are fabricated via multi-material 3D printing. Mechanical uni-axial compression experiments are performed on the 3D printed specimens and the experimental results are compared with finite element (FE) simulations. By jointly tailoring the chiral geometry and material combination, the effective mechanical properties and the deformation mechanisms can be tuned in a large range. In addition, a continuum-level material model was developed to predict the constitutive relationship. The results show that the material model can well predict the effective mechanical properties of the chiral 3D mechanical metamaterials.

Thermally Reconfigurable, 3D Chiral Optical Metamaterials: Building with Colloidal Nanoparticle Assemblies.

The three-dimensional, geometric handedness of chiral optical metamaterials allows for the rotation of linearly polarized light and creates a differential interaction with right and left circularly polarized light, known as circular dichroism. These three-dimensional metamaterials enable polarization control of optical and spin excitation and detection, and their stimuli-responsive, dynamic switching widens applications in chiral molecular sensing and imaging and spintronics; however, there are few reconfigurable solid-state implementations. Here, we report all-solid-state, thermally reconfigurable chiroptical metamaterials composed of arrays of three-dimensional nanoparticle/metal bilayer heterostructures fabricated from coassemblies of phase change VO2 and metallic Au colloidal nanoparticles and thin films of Ni. These metamaterials show dynamic switching in the mid-infrared as VO2 is thermally cycled through an insulator-metal phase transition. The spectral range of operation is tailored in breadth by controlling the periodicity of the arrays and thus the hybridization of optical modes and in position through the mixing of VO2 and Au nanoparticles.

General three-dimensional thermal illusion metamaterials

Abstract Thermal illusion aims to create fake thermal signals or hide the thermal target from the background thermal field to mislead infrared observers, and illusion thermotics was proposed to regulate heat flux with artificially structured metamaterials for thermal illusion. Most theoretical and experimental works on illusion thermotics focus on two-dimensional materials, while heat transfer in real three-dimensional (3D) objects remains elusive, so the general 3D illusion thermotics is urgently demanded. In this study, we propose a general method to design 3D thermal illusion metamaterials with varying illusions at different sizes and positions. To validate the generality of the 3D method for thermal illusion metamaterials, we realize thermal functionalities of thermal shifting, splitting, trapping, amplifying and compressing. In addition, we propose a special way to simplify the design method under the condition that the size of illusion target is equal to the size of original heat source. The 3D thermal illusion metamaterial paves a general way for illusion thermotics and triggers the exploring of illusion metamaterials for more functionalities and applications.

Analytical equivalent circuits for three-dimensional metamaterials and metagratings

Analytical equivalent circuits for three-dimensional metamaterials and metagratings

Linkage-based three-dimensional kinematic metamaterials with programmable constant Poisson’s ratio

Metamaterials constructed from the tessellation of units have extraordinary physical properties and material functions. Most mechanical metamaterials are based on the large structural deformation of units, while the transmission and synchronization of these motion deformations among units are poor which leads to difficulty in designing and controlling the properties. In this study, a modular mechanism based on the kinematics of Sarrus linkage is constructed, and this mechanism is tessellated to a metamaterial with constant negative Poisson’s ratios and a clearly defined deformation path. By varying the specific parameters of the modular mechanism, Poisson’s ratios of the metamaterial can be programmed and almost constant. Hence, a novel approach to constructing metamaterials based on the kinematics of linkages is proposed in this work.

Three-Dimensional Gradient Metamaterial Devices Coupled with Phononic Crystals for Acoustic Enhancement Sensing

Conventional acoustic systems exhibit a difficulty in sensing weak acoustic fault signals in complex mechanical vibration environments. Therefore, it is necessary to develop an acoustic sensing mode and a corresponding functional device with pressure amplification. This paper proposes a three-dimensional device, coupling gradient acoustic metamaterials (GAM) with phononic crystals (GAM–PC). The strong wave compression effect coupled with the phononic crystal equivalent medium mechanism is utilized to achieve the enhancement of weak acoustic signal perception at the target frequency. The superior amplification capability of the GAM–PC structure for the amplitude of loud signals is verified by numerical simulations and experiments. Moreover, the GAM–PC structure has a narrower bandwidth per slit, making it more frequency selective. Furthermore, the structure can separate different frequency components. This work is expected to be applied to signal monitoring in environments with strong noise.

Post-fabrication tuning of origami-inspired mechanical metamaterials based on Tachi-Miura Polyhedron

We investigate the reconfigurability and tunability of the tessellation of Tachi-Miura Polyhedron (TMP), an origami-based cellular structure composed of bellows-like unit cells. Lattice-based three-dimensional mechanical metamaterials have recently received significant scientific interest due to their superior and unique mechanical performance compared to conventional materials. However, it is often challenging to achieve tunability and reconfigurability from these metamaterials, since their geometry and functionality tend to be pre-determined in the design and fabrication stage. Here, we utilize TMP's highly versatile phase-transforming and tessellating capabilities to design reconfigurable metamaterial architecture with tunable mechanical properties. The theoretical analyses and experiments with heat processing discover the wide range of the in-situ tunability of the metamaterial – specifically orders of magnitude change in effective density, Young's modulus, and Poisson's ratio – after its fabrication within the elastic deformation regime. We also witness a rather unique behavior of the inverse correlation between effective density and stiffness. This mechanical platform paves the way to design the metamaterial that can actively adapt to various external environments.

Three-dimensional metamaterials exhibiting extreme isotropy and negative Poisson's ratio

This research will develop a new set of mechanical metamaterials with simultaneous ideal elastic isotropy and extreme negative Poisson's ratio through a topology optimization approach. Firstly, we propose a new method to generate a three-dimensional ground structure with geometric cubic symmetry. Secondly, a more efficient topology optimization method is developed by utilizing a small number of both integer and continuous design variables for topological description of the design based on the discrete ground structure. Thirdly, two new geometric constraints are incorporated into the mathematical formulation to ensure creation of designs that are practical. Finally, the genetic algorithm is used to solve this type of mixed-integer programming problems. Several numerical examples have been used to demonstrate the generation of a series of three-dimensional microarchitectures from a single integrated design. The microlattices can also be customized to obtain a broad range of negative Poisson's ratios across different relative densities. The effective material properties and macroscopic deformation behaviors of the designs are numerically validated using commercial software.

On vibration isolation performance and crashworthiness of a three-dimensional lattice metamaterial

This work investigates the vibration isolation performance and crashworthiness of a novel three-dimensional (3D) lattice metamaterial, whose unit cell is constructed by combining a hollow rhombic dodecahedron and six cylindrical tubes. The transmission of elastic waves in the 3D metamaterial can be suppressed for the existence of band gaps in the metamaterial. Meanwhile, the 3D metamaterial can absorb the crushing energy through plastic deformation when a collision occurs. The influence of structural parameters on the band gap features and crashing behaviors of the novel 3D metamaterial are examined. It is shown that the structural parameters play a vital role in determining the band gap features and crashing behaviors. Thus, the required vibration isolation performance and crashworthiness can be obtained by adjusting the structural parameters reasonably. Finally,multi-objective optimization is performed from the comprehensive aspects of vibration isolation performance and crashworthiness to obtain the optimal design of the novel 3D metamaterial. This work provides a new possibility for the development of multifunctional metamaterials with vibration isolation performance and crashworthiness simultaneously.

Coexisting hinge and vertical disclination states in a higher-order acoustic Dirac semimetal

The concept of crystalline disclinations in solid-state physics has gained attention in recent years, particularly with a focus on two-dimensional ${C}_{n}$-symmetric topological crystalline insulators. Research in this area has revealed novel topological phases different from the traditional bulk-boundary correspondence, expanding the topological material family. However, there remains a need to investigate the bulk-disclination correspondence in three-dimensional topological semimetals. We present an example of a higher-order Dirac semimetal in acoustic crystals with central disclinations. Our simple model not only exhibits hinge modes in the vertical direction but also supports a robust one-dimensional disclination hinge state along the central bulk-hollow path. Simulations demonstrate that our structure is capable of realizing backscatter-free disclination and higher-order hinge waves under the same architecture. Our findings offer insight for potential applications in acoustic devices for sound wave propagation and manipulation, as well as for exploring more exotic high-performance three-dimensional acoustic metamaterials.

Mechanics Characteristics of a 3D Star-Shaped Negative Poisson's Ratio Composite Structure.

A negative Poisson's ratio honeycomb material has the characteristics of anti-conventional deformation behavior and high impact resistance, which is a new lightweight microstructure material with broad application prospects. However, most of the current research is still at the microscopic level and two-dimensional level, and little research has been carried out for three-dimensional structures. Compared with the two-dimensional level, three-dimensional negative Poisson's ratio structural mechanics metamaterials have the advantages of a lighter mass, higher material utilization, and more stable mechanical properties, and they have great potential for development in the fields of aerospace, the defense industry, and vehicles and ships. This paper presents a novel 3D star-shaped negative Poisson's ratio cell and composite structure, inspired by the octagon-shaped 2D negative Poisson's ratio cell. The article carried out a model experimental study with the help of 3D printing technology and compared it with the numerical simulation results. The effects of structural form and material properties on the mechanical characteristics of 3D star-shaped negative Poisson's ratio composite structures were investigated through a parametric analysis system. The results show that the error of the equivalent elastic modulus and the equivalent Poisson's ratio of the 3D negative Poisson's ratio cell and the composite structure is within 5%. The authors found that the size of the cell structure is the main factor affecting the equivalent Poisson's ratio and the equivalent elastic modulus of the star-shaped 3D negative Poisson's ratio composite structure. Furthermore, among the eight real materials tested, rubber exhibited the best negative Poisson's ratio effect, while the copper alloy showed the best effect among the metal materials, with a Poisson's ratio between -0.058 to -0.050.

Broadband seismic isolation effect of three-dimensional seismic metamaterials in a semi-infinite foundation: modelled by fast multipole indirect boundary element method

In this study, a fast multipole indirect boundary element method (FM-IBEM) is developed for studying the scattering of seismic waves by 3-D seismic metamaterials (SMs), and a 3-D rock soil composite seismic metamaterial (RSCSM) is proposed. Based on the indirect boundary element method, the fast multipole expansion technique is adopted to reduce the calculation time and memory requirements, and effectively solve the broadband scattering problem of seismic waves by large-scale SMs. The bandgap characteristics of three-dimensional SM are studied in detail, and the effects of the geometric and material parameters on the isolation effect of SMs are investigated. The results show that RSCSM can attenuate the ultralow frequency of a seismic wave, the bandgap width is 0.5–19 Hz, and the isolation effect is 37%. The cell size and material parameters significantly affect the bandgap characteristics of the RSCSM. This type of seismic metamaterial provides a new technique for seismic wave isolation and could be applied in engineering structures.