Metamaterial Samples Research Articles

Quasi-static crushing response of a novel triaxial isotropy mechanical metamaterial with dual-platform property

A novel triaxial isotropy origami metamaterial with dual-platform is proposed by combining the tachi tubes and the honeycomb structures. Crushing responses of the hexahedral metamaterial under quasi-static compression load are investigated through experimental tests and numerical simulations. Experimental and numerical results reveal that the hexahedral metamaterial sample shows three deformation modes. Meanwhile, the numerical predictions of deformation modes and locations agree very well with the experimental results. Moreover, the effect of aspect ratio, thickness-to-span ratio, angle on the deformation mode, peak stress, plateau stress of different stages, and specific energy absorption (SEAM, SEAV) is investigated. Finally, the proposed metamaterial is compared with traditional honeycomb. The numerical results demonstrate that the SEAM of the hexahedral metamaterial is 90.6% of the traditional honeycomb in the Z-direction. However, during X/Y-direction compression, the energy absorption capacity of the hexahedral metamaterial is 13.0 and 12.2 times that of the traditional honeycomb, respectively.

Designing Connectivity-Guaranteed Porous Metamaterial Units Using Generative Graph Neural Networks

Abstract Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. This complete connectivity is crucial for manufacturability and structure-fluid interaction applications (e.g., fluid-filled lattices). In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units with the constraint of complete connectivity. First, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Second, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design framework is evaluated by comparing the performances of the obtained designs with those of known designs in the metamaterial database. Merits and shortcomings of the proposed framework are also discussed.

Design and experimental validation of a finite-size labyrinthine metamaterial for vibro-acoustics: enabling upscaling towards large-scale structures.

In this article, we present the design and experimental validation of a labyrinthine metamaterial for vibro-acoustic applications. Based on a two-dimensional unit cell, different designs of finite-size metamaterial specimens in a sandwich configuration including two plates are proposed. The design phase includes an optimization based on Bloch-Floquet analysis with the aims of maximizing the band gap and extruding the specimens in the third dimension while keeping the absorption properties almost unaffected. By manufacturing and experimentally testing finite-sized specimens, we assess their capacity to mitigate vibrations in vibro-impact tests. The experiments confirm a band gap in the low- to mid-frequency range. Numerical models are employed to validate the experiments and to examine additional vibro-acoustic load cases. The metamaterial's performances are compared with benchmark solutions, usually employed for noise and vibration mitigation, showing a comparable efficacy in the band gap region. To eventually improve the metamaterial's performance, we optimize its interaction with the air and test different types of connections between the metamaterial and the homogeneous plates. This finally leads to metamaterial samples largely exceeding the benchmark performances in the band gap region and reveals the potential of interfaces for performance optimization of composed structures.This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Bioinspired Design of 3D-Printed Cellular Metamaterial Prosthetic Liners for Enhanced Comfort and Stability.

Traditional prosthetic liners are often limited in customization due to constraints in manufacturing processes and materials. Typically made from non-compressible elastomers, these liners can cause discomfort through uneven contact pressures and inadequate adaptation to the complex shape of the residual limb. This study explores the development of bioinspired cellular metamaterial prosthetic liners, designed using additive manufacturing techniques to improve comfort by reducing contact pressure and redistributing deformation at the limb-prosthesis interface. The gyroid unit cell was selected due to its favorable isotropic properties, ease of manufacturing, and ability to distribute loads efficiently. Following the initial unit cell identification analysis, the results from the uniaxial compression test on the metamaterial cellular samples were used to develop a multilinear material model, approximating the response of the metamaterial structure. Finite Element Analysis (FEA) using a previously developed generic limb-liner-socket model was employed to simulate and compare the biomechanical behavior of these novel liners against conventional silicone liners, focusing on key parameters such as peak contact pressure and liner deformation during donning, heel strike, and the push-off phase of the gait cycle. The results showed that while silicone liners provide good overall contact pressure reduction, cellular liners offer superior customization and performance optimization. The soft cellular liner significantly reduced peak contact pressure during donning compared to silicone liners but exhibited higher deformation, making it more suitable for sedentary individuals. In contrast, medium and hard cellular liners outperformed silicone liners for active individuals by reducing both contact pressure and deformation during dynamic gait phases, thereby enhancing stability. Specifically, a medium-density liner (10% infill) balanced contact pressure reduction with low deformation, offering a balance of comfort and stability. The hard cellular liner, ideal for high-impact activities, provided superior shape retention and support with lower liner deformation and comparable contact pressures to silicone liners. The results show that customizable stiffness in cellular metamaterial liners enables personalized design to address individual needs, whether focusing on comfort, stability, or both. These findings suggest that 3D-printed metamaterial liners could be a promising alternative to traditional prosthetic materials, warranting further research and clinical validation.

Multistep and Elastically Stable Mechanical Metamaterials

Abstract Materials and structures with tunable mechanical properties are essential for numerous applications. However, constructing such structures poses a great challenge since it is normally very complicated to change the properties of a material after its fabrication, particularly in pure force fields. Herein, we propose a multistep and elastically stable 3D mechanical metamaterial having simultaneously tunable effective Young's modulus and auxeticity controlled by the applied compressive strain. Metamaterial samples are fabricated by 3D printing at the centimetric scale, with selective laser sintering, and at the micrometric scale, with two-photon lithography. Experimental results indicate an elementary auxeticity for small compressive strains but superior auxeticity for large strains. Significantly, the effective Young's modulus follows a parallel trend, becoming larger with increasing compressive strain. A theoretical model explains the variations of the elastic constants of the proposed metamaterials as a function of geometry parameters and provides a basic explanation for the appearance of the multistep behavior. Furthermore, simulation results demonstrate that the proposed metamaterial has the potential for designing metamaterials exhibiting tunable phononic band gaps. The design of reusable elastically stable multistep metamaterials, with tunable mechanical performances supporting large compression, is made possible thanks to their delocalized deformation mode.

Reconstruction and Generation of Porous Metamaterial Units via Variational Graph Autoencoder and Large Language Model

Abstract In this paper, we propose and compare two novel deep generative model-based approaches for the design representation, reconstruction, and generation of porous metamaterials characterized by complex and fully connected solid and pore networks. A highly diverse porous metamaterial database is curated, with each sample represented by solid and pore phase graphs and a voxel image. All metamaterial samples adhere to the requirement of complete connectivity in both pore and solid phases. The first approach employs a Dual Decoder Variational Graph Autoencoder to generate both solid phase and pore phase graphs. The second approach employs a Variational Graph Autoencoder for reconstructing/generating the nodes in the solid phase and pore phase graphs and a Transformer-based Large Language Model (LLM) for reconstructing/generating the connections, i.e., the edges among the nodes. A comparative study is conducted, and we found that both approaches achieved high accuracy in reconstructing node features, while the LLM exhibited superior performance in reconstructing edge features. Reconstruction accuracy is also validated by voxel-to-voxel comparison between the reconstructions and the original images in the test set. Additionally, discussions on the advantages and limitations of using LLMs in metamaterial design generation, along with the rationale behind their utilization, are provided.

Nonlinear absorption conversion of epsilon-near-zero multilayer metamaterial at optical frequencies

Modern all-optical logic switches demand selective, precise, and rapid transmission of optical information. In this study, we investigate an epsilon-near-zero (ENZ) metamaterial composed of silver (Ag) and magnesium fluoride (MgF2), which demonstrates a low conversion threshold, strong nonlinear response, and nonlinear absorption conversion. Particularly noteworthy is its highest nonlinear absorption (β≈-2 × 106 cm/GW) occurring at the ENZ point (695 nm) under deposited condition. This research marks the first discussion of nonlinear absorption conversion in the ENZ multilayer metamaterial. The deposited metamaterial sample exhibits saturation absorption (SA), attributed to ground state free electron bleaching, while annealed sample shows a transition from SA to reverse saturation absorption (RSA) due to a three-photon absorption effect. Annealing significantly reduces the laser power threshold required for this conversion process, indicating reduced risk of laser-induced damage. Furthermore, the wavelength shift of the largest RSA (γ≈1.93 × 104 cm3/GW2) in the annealed sample aligns with the expected redshift direction of the ENZ region (735 nm). Our metamaterial design achieves enhanced nonlinear absorption and low-power absorption conversion, which holds significant potential for applications in all-optical logic switches.

Design, measurement, and demonstrating of a metamaterials with broadband and high transmittance for measuring the thermal conductivity of clothing fabrics samples

An all dielectric metamaterial sensor with smooth spectral lines resonance characteristics over a large frequency range is demonstrated and verified. The average transmittance and reflectance of the metamaterial sample are 0.734 and 0.201 in the frequency range of 4–30 THz. The effects of three important factors on the thermal conductivity of the outdoor clothing fabric samples are measured by using this metamaterial sensor: thickness, ambient temperature, and fabric type. The thermal diffusion coefficient of the fabric samples is decreased with the thickness increasing, which is enhanced by increasing the temperature. In addition, due to differences in preparation processes and materials, the type of fabric sample can also directly affect the thermal conductivity performance. The measurement results verify the feasibility of the metamaterial sensor to measure the thermal conductivity of outdoor clothing fabric samples.

Design and validate a wide-bandwidth, high-performance tunable metamaterial based on cultural-innovation shell materials and its sensing applications

The application of metamaterials in controllable thermal emission devices is an interesting field. However, most of the demonstrated thermal emitters required continuous consumption of external energy (electrical or thermal) to provide an effective thermal emissivity. Here, a metamaterial containing phase change materials Ge2Sb2Te5 (GST) and shell materials with controllable thermal emission power was proposed and measured. Based on the completely amorphous state of the GST layer, an emissivity of 0.212 at wavelength 7.11 μm was achieved by this this metamaterial, while a thermal emission band (with an average amplitude of 0.857 and a bandwidth of 6.16 μm) was excited for the crystalline state. Moreover, numerous thermal emission states were excited by this metamaterial based on the intermediate states between completely amorphous and crystalline states of the GST layer. Tunability of the thermal emission window was obtained by this metamaterial sample. The temperature sensitivity of this metamaterial thermal emitter was 341 nm °C−1. By increasing the thickness of the GST or shell layers, the thermal emission performance of the metamaterial was enhanced. Since the phase transition of GST does not require the continuous consumption of external energy, the metamaterial has the potential to be used in the development of low-power heat emitters, as well as temperature sensors.

Acoustic metamaterial samples preparation for impedance tube measurements—The influence of different 3D printing techniques and mechanical post-processing on the simulation compliance

Prototyping of acoustic metamaterials frequently involves the use of additive manufacturing techniques. It offers the best price and the option for complex structure production, which is beneficial in the R&D process. Previously, some differences in acoustic metamaterial sound absorption measurement dispersions regarding using 3D printing techniques for sample preparation were noted. The sound absorption sensitivity on different printing settings or materials is usually omitted. The paper will present the research on the impedance tube measurements of absorbing metamaterial manufactured with different 3D printing methods and post-processed with mechanical and chemical treatment. Two approaches to metamaterial construction were analyzed in the current study—the single-solid metamaterial and the structure divided into parts, where the influence of assembly methods was investigated. To achieve the best compatibility with FEM or TMM modeling results, different post-processing techniques were involved, such as drilling, grinding, and sealant use. The presentation will describe the valuable paths used in sample preparation to achieve better compatibility between the measurements and simulations. The need for a comprehensive part preparation description in metamaterials research and papers will be discussed. [Work funded and supported by the Polish Government, National Centre of Research and Development, agreement no. LIDER/11/0065/L-12/20/NCBR/2021.]

Void-Engineered Metamaterial Delay Line with Built-In Impedance Matching for Ultrasonic Applications

Metamaterials exhibit unique ultrasonic properties that are not always achievable with traditional materials. However, the structures and geometries needed to achieve such properties are often complex and difficult to obtain using common fabrication techniques. In the present research work, we report a novel metamaterial acoustic delay line with built-in impedance matching that is fabricated using a common 3D printer. Delay lines are commonly used in ultrasonic inspection when signals need to be separated in time for improved sensitivity. However, if the impedance of the delay line is not perfectly matched with those of both the sensor and the target medium, a strong standing wave develops in the delay line, leading to a lower energy transmission. The presented metamaterial delay line was designed to match the acoustic impedance at both the sensor and target medium interfaces. This was achieved by introducing graded engineered voids with different densities at both ends of the delay line. The measured impedances of the designed metamaterial samples show a good match with the theoretical predictions. The experimental test results with concrete samples show that the acoustic energy transmission is increased by 120% and the standing wave in the delay line is reduced by over a factor of 2 compared to a commercial delay line.

A study of deformation mechanisms for a two-dimensional metamaterial

This paper presents a numerical study of a two-dimensional tetrachiral metamaterial and the effect of unit cell parameters on its mechanical behavior. Finite element simulations are performed using independently varied geometric parameters of the chiral unit cell. Chiral structures can induce the compression–torsion effect and the deflection in mechanical metamaterials. The sample deflection is affected by the following factors: ring deformation, ligament deformation, and structure twisting. The highest strain estimated by the deflection of the metamaterial sample from the initial position is observed at an optimal ratio of ligament length to ring size. The effect of structural parameters on the deformation, stress distribution, and effective elastic properties of a two-dimensional metamaterial sample under uniaxial compression is studied and analyzed. For all variable parameters, a qualitatively similar nature of the equivalent stress distribution is revealed. It is found that a decrease in the volume of the main material in the metamaterial sample entails a decrease in effective Young’s modulus. The parameters accounting for the auxetic properties of the metamaterial are obtained. Effective Poisson’s ratio is determined in the range from –0.1 to 0.95.

PROGRAMMABLE BEHAVIOR OF THE METAMATERIAL BY KINDS OF UNIT CELLS CONNECTION

The paper is devoted to the numerical analysis of uniaxial loading of a sample of the mechanical metamaterial. The structure of the mechanical metamaterial is constructed of a ring and four ligaments, which make up a tetrachiral structure. The peculiarity of such a structure consists in torsion of the sample under the force load. Two methods of connecting cells in the metamaterial are considered: "adjoining" and "overlapping". The "adjoining" method of joining cells increases the thickness of the internal structure of the sample, which allows us to consider it as a topological defect of the metamaterial. The "overlapping" method saves the base material from which the tetrachiral structure is constructed. Differences in the structure when constructing a three-dimensional sample result in a significant change in the characteristics of the sample. Numerical solution of the problem is performed in a three-dimensional formulation using the finite element method. The constitutive relation describing the behavior of the model corresponds to Hooke's law. Numerical simulation of uniaxial loading made it possible to obtain the results of mechanical response and to analyze the effective properties of metamaterials. A topological defect in the form of a thickening of the internal structure elements led to a difference in the linear dimensions of the two samples. The increased thickness of the unit cell connection elements resulted in a decrease in the effective density of the metamaterial sample. The same sample showed a triple increase in the value of the elastic modulus. The greater ability to resist deformation resulted in a reduced twist effect compared to the sample whose cells were joined by the "overlapping" method. The results obtained will make it possible to program the mechanical behavior and properties of the metamaterial sample.

Design and verification of a tunable single-band metamaterial based on Polymeric Methyl Methacrylate and its feasibility for temperature detection in smart packaging

Metamaterial absorbers with single resonance mode and narrow bandwidth are often used in sensing. A metamaterial absorber containing dielectric layers of the same thickness (Polymeric Methyl Methacrylate (PMMA) and strontium titanate (STO)) are proposed and confirmed. At room temperature (300 K), an individual absorption peak is excited, and the single resonance mode and narrow bandwidth characteristic are obtained. The amplitude and resonance frequency of the metamaterial samples can be controlled by changing the thickness of PMMA or STO. The metamaterial samples are placed in an environment with a gradual change in temperature. The results show that the absorptive properties of the metamaterial sample show remarkable repeatability in the process of temperature increase and decrease. Therefore, based on the properties of single resonance mode, narrow bandwidth, and reversibility, the metamaterial samples have the potential to be used in smart packaging sensing.

Broadband omnidirectional visible spectral metamaterials

Optical metamaterials offer the possibility of controlling the behavior of photons similarly to what has been done about electrons in semiconductors. However, most optical metamaterials are narrowband, and they achieve negative refraction within a small window of incident angles, making them impractical for common visible light systems that operate effectively over a wide range of frequencies and directions. Considerable resistive loss at the resonant frequency of these metamaterials further prevents them from being deployed in the real world. Here, we develop a novel metamaterial randomly assembled by a list of narrowband, omnidirectional, and ultralow-loss meta-cluster systems using a bottom-up approach. Weak interactions among numerous meta-cluster sets greatly broaden the effective bandwidth of the overall structure, exhibiting frequency selectivity and spatial modulation when responding to white-light illumination. We observe negative refraction in the 490–730 nm band, and observe an inverse Doppler effect at green, yellow, and red frequencies, across most of the visible spectrum. Our method allows for low-cost fabrication of sizable broadband omnidirectional three-dimensional metamaterial samples, which opens the door to the rapid development of optical metamaterials, micro–nano assembly and preparation, tunable optical device engineering, etc.

Topological Avenue for Efficient Decontamination of Large Volumes of Fluids via UVC Irradiation of Packed Metamaterials.

Nowadays, metamaterials application enjoys notoriety in fluid decontamination and pathogen annihilation, which are frequently present in polluted fluids (e.g., water, blood, blood plasma, air or other gases). The depollution effect is largely enhanced by UVC irradiation. The novelty of this contribution comes from the significant increase by packing of the total surface of metamaterials in contact with contaminated fluids. Packed metamaterial samples are subjected to UVC irradiation, with expected advantages for implant sterilization and long-term prevention of nosocomial infections over large clinical areas. The novel aspect of the investigation consists of a combination of big and small elements of the metamaterial to optimize the above effects connected with fluids and irradiation. The big elements allow the radiation to penetrate deep inside the fluid, and the small elements optimally disperse this radiation toward deeper regions of the metamaterial. A packing scheme of smaller, in-between large metamaterial spheres and fibres is proposed for promoting enhanced depollution against pathogen agents. It is demonstrated that the total surface of metamaterials in contact with contaminated fluids/surface is significantly increased as a result of packing. This opens, in our opinion, new auspicious perspectives in the construction of novel equipment with high sensibility in the detection and decontamination of microorganisms.

3D printing of fiber composite sandwich metamaterial with spiral resonators for attenuation of low-frequency structural vibration

This paper proposes a fiber composite sandwich metamaterial as a stiff structure with a low-frequency band gap. The proposed structure is a locally resonant metamaterial that inhibits the propagation of elastic waves with spiral resonators. The dispersion curves and stiffness of the metamaterial were obtained using the finite element method. The numerical analysis results indicated that the proposed sandwich structure contributes not only to the improvement of the specific stiffness but also to the widening of the band gap. From observations of the band gap boundary modes, an analytical model was developed to derive the lower and upper bound frequencies of the band gap. A metamaterial sample manufactured by 3D printing exhibited a frequency range with low vibration transmissibility, which agreed with the results of the frequency response analysis. The specific bending stiffness and band gap center frequency of the proposed metamaterial were compared with those of existing plate-type metamaterials.

Wave propagation behaviors of a low-symmetry reentrant chiral structure with mass inclusion in a single material

This work proposed a low symmetry characteristics metamaterial in a single material. The structural configuration of the metamaterial is composed of the reentrant structure, chiral structure and mass inclusion. The wave propagation characteristics are investigated in terms of the Bloch-Floquet wave propagation theorem. Firstly, the band diagram of the metamaterial is analyzed. The wave behaviors of the structure are changed due to the low symmetry characteristics. The irreducible Brillouin zone (IBZ) of the proposed structure is changed. The band diagram in the whole IBZ is analyzed to get the accurate distributions of the bandgaps. Some extremum values of the dispersion surface are deviated from the boundary of the IBZ. The formation mechanisms of bandgaps are illustrated based on the analysis of the vibration mode shapes. Then, the phase velocity and group velocity of the elastic wave are calculated, showing the strong anisotropic properties. Moreover, the effects of the geometrical parameters on the bandgaps are investigated. The locations and width of the bandgaps can be tuned for by the rational design. The existence of bandgaps of the metamaterial are validated by a finite element model. Finally, a metamaterial beam sample with seven cells is made and experiment test are conducted for the vibration attenuation performance and error analysis. The proposed structure can be used for vibration attenuation in the fields of underwater vehicles.

Compressive strength of metamaterial bones fabricated by 3D printing with different porosities in cubic cells

This research focuses on the compressive strength of metamaterial bones, fabricated by 3D printing with different porosities in cubic cells. For this objective, compressive testing was done on standard samples besides bones, both 3D-printed and real ones. To fabricate a metamaterial bone, the cubic cell was chosen in this research. Since the yield strength and the ultimate stress of the vertical solid standard specimen had better performance than the horizontal solid standard one, the vertical metamaterial sample with a cubic cell was designed for four porosity states of 25%, 30%, 50%, and 55%. The obtained results illustrated that 30% of porosity was introduced as the optimal specimen. Therefore, this percentage of porosity was used to fabricate a metamaterial bone. In addition, the rabbit tibia bone in two solid and metamaterial states was prepared by 3D printing and compared with the real rabbit bone. The results showed that the real bones withstood more force compared to the solid and metamaterial 3D-printed bone samples. The weight of the metamaterial bone decreased by 5.97%, compared to the solid bone specimen. Finally, the quality of 3D printing was checked by microscopy. Then, the quality of 3D printing decreased by increasing the thickness of the strut.

Metamaterial characterization from far-field acoustic wave measurements using convolutional neural network

Identifying the material properties of unknown media is an important scientific/engineering challenge in areas as varied as in-vivo tissue health diagnostics and metamaterial characterization. Currently, techniques exist to retrieve the material parameters of large unknown media from elastic wave scattering in free-space using analytical or numerical methods. However, applying these methods to small samples on the order of few wavelengths in diameter is challenging, as the fields scattered by these samples become significantly contaminated by diffraction from the sample edges. Here, we propose a method to extract the material parameters of small samples using convolutional neural networks trained to learn the mapping between far-field echoes and the material parameters. Networks were trained with synthetic time domain echo data obtained by simulating the free-space scattering of sound from unknown media underwater. Results show that neural networks can accurately predict effective material parameters such as mass density, bulk modulus, and shear modulus even when small training sets are used. Furthermore, we demonstrate in experiments executed in a water tank that the networks trained with synthetic data can accurately estimate the material properties of fabricated metamaterial samples from single-point echo measurements performed in the far-field. This work highlights the effectiveness of our approach to identify unknown media using far-field acoustic reflection dominated by diffraction fields and will open a new avenue toward acoustic sensing techniques.