Design Of Metamaterials Research Articles

Novel 4D-printed multi-stable metamaterials: programmability of force-displacement behaviour and deformation sequence.

The unique properties of metamaterials are determined by the configuration and spatial arrangement of artificially designed unit structures. However, the configuration and mechanical properties of conventional metamaterials are challenging to reverse and adjust. Based on curved beams, two types of novel three-dimensional (3D) multi-stable metamaterials with reconfigurable deformation and tunable mechanical properties are designed and fabricated using a four-dimensional (4D) printing method. The effects of temperature and curved-beam thickness on the force-displacement curves and multi-stable snapping sequence of the 3D multi-stable metamaterials are investigated by finite-element analysis (FEA) and experiments. In addition, based on the designed four-branch multi-stable metamaterials, three- and six-branched multi-stable structures are designed by changing the number of curved-beam branches. It is shown that, owing to shape memory effects, the 3D multi-stable metamaterials can realize mechanical programmability, and the multi-stable deformation sequence can be precisely regulated by varying the temperature and curved-beam thickness. These 4D-printed multi-stable metamaterials provide valuable contributions to the design of programmable multi-stable metamaterials and their applications in soft robots and intelligent structures. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 1)'.

Innovative applications for civil structures of the Municipality of Finiq using topology optimization and additive manufacturing

The Municipality of Finiq is located in the South of Albania, inside the Vlora’s County and it is just 9 kilometers from the City of Saranda. The village of Finiq is particularly important because of the presence of The Archaeological Park at the top of the hill, which has received this status in 2005. Inside the Municipality there are a lot of attractive sites, such as The Blue Eye, the main lake of the Municipality, the Monastery of St. Nikolla, located in Mesopotam, etc., making the Municipality dominated by nature (e.g. long lots of fields, hills, rivers, and lakes) and monuments that represent the cultural heritage of the municipality. Within this context some villages arise, which are characterized mostly by infrastructures and civil structures in reinforced concrete, this is strictly due to the fact that these buildings were built in the last decades, instead of what can be observed outside the Municipality, e.g. Gjirokaster. The structures of the Municipality’s villages are mostly under construction, some are unfinished, abandoned, or damaged. Despite the trend of reinforced concrete building construction does not tend to decrease, the world of civil engineering is trying to find new solutions, that are also environmentally compatible and sustainable. This necessity is motivated by the fact that the industry of concrete is the most energy-intensive industry in the world. In particular, two main aspects that the research is investigating to address these issues are the use of new manufacturing technologies, e.g. 3D printing, combined also with new computational methodologies, such as topology optimization, and the development of innovative materials, e.g. architected meta-materials. The aim of this paper is to suggest innovative approaches and methodologies in the fields of structural mechanics for civil structures. The proposed approach wants to be applied not only to buildings under construction but also to the existing ones, which could be restored or completed in some specific structural and non-structural parts. In particular, we propose new topology optimization strategies that allow us to obtain an efficient material layout with maximized performance under predefined constraints. This design method is not only used to optimize the structural behavior of the structures but also for the optimization of specific features of the structures, e.g. thermal and acoustic optimization. The interest in this computa- tional method has grown due to the development of innovative techniques of manufacturing, i.e. additive manufacturing. In particular, there are different types of manufacturing that could be used for construction, which differ with respect to the material adopted, e.g. steel, concrete, or stone-like materials. The proposed method will be supported by several examples to under- stand the potentiality of the approach considering the role of additive manufacturing. Indeed, the development of new manufacturing methods has reduced the distance between the Theoretical and practical representation of the optimized layout. In conclusion, the proposed approach allows to obtain novel 3D printable structures characterized by a more efficient use of material, contributing to the realization of the concept of circular economy within the construction industry.

Multifunctionality in vanadium dioxide-integrated metamaterials for switching between dual-band perfect absorption and asymmetric transmission

In this work, we present a theoretical proposal for an actively tunable metamaterial design that integrates vanadium dioxide (VO2). This VO2-integrated design demonstrates the ability to switch between dual-band perfect absorption and asymmetric transmission (AT) functionalities in the near-infrared and mid-infrared spectral ranges. By utilizing the unique properties of VO2, our proposed device achieves broadband absorption across approximately 2.47 μm with polarization independence when VO2 is in its metallic state. Furthermore, it exhibits narrowband absorption with polarization correlation, reaching a linear dichroism value of approximately 0.704. On the other hand, when VO2 is in its insulating state, the metamaterial structure realizes AT of 0.418 for circularly polarized light. We provide physical insight into the operating mechanisms through impedance matching analysis and electric field distributions. The integration of VO2 in this dynamically tunable, multifunctional metamaterial design offers a novel approach to developing reconfigurable nanophotonic and nanosystem technologies.

Thermal Metamaterials with Configurable Mechanical Properties.

Thermal metamaterials are typically achieved by mixing different natural materials to realize effective thermal conductivities (ETCs) that conventional materials do not possess. However, the necessity for multifunctional design of metamaterials, encompassing both thermal and mechanical functionalities, is somewhat overlooked, resulting in the fixation of mechanical properties in thermal metamaterials designed within current research endeavors. Thus far, conventional methods have faced challenges in designing thermal metamaterials with configurable mechanical properties because of intricate inherent relationships among the structural configuration, thermal and mechanical properties in metamaterials. Here, a data-driven approach is proposed to design a thermal metamaterial capable of seamlessly achieving thermal functionalities and harnessing the advantages of microstructural diversity to configure its mechanical properties. The designed metamaterial possesses thermal cloaking functionality while exhibiting exceptional mechanical properties, such as load-bearing capacity, shearing strength, and tensile resistance, thereby affording mechanical protection for the thermal metadevice. The proposed approach can generate numerous distinct inverse design candidate topological functional cells (TFCs), designing thermal metamaterials with dramatic improvements in mechanical properties compared to traditional ones, which sets up a novel paradigm for discovering thermal metamaterials with extraordinary mechanical structures. Furthermore, this approach also paves the way for investigating thermal metamaterials with additional physical properties.

A multi-step auxetic metamaterial with instability regulation

A stable deformation mode is highly desired for mechanical metamaterials, especially when coupled with a negative Poisson’s ratio. However, such metamaterials often face challenges in terms of scalability toward large deformation or strain. In response, we propose a multi-step hierarchical auxetic metamaterial design paradigm, incorporating a series of incrementally scaled-down structures with same scale factor α into a re-entrant framework. This design enables instability regulation and multi-step deformation capabilities while preserving auxetic behavior, even under significant strain. Such multi-step metamaterials exhibit excellent properties, including tailored multi-phase compression modulus and strength, along with an enhanced energy absorption capacity that is as large as 2.1 times that of the original auxetic metamaterial. Experiments and simulations demonstrate that the deformation mechanism and compression response of the proposed multi-step auxetics are strongly influenced by the reduction factor and the order of the inner structure. A particularly intriguing observation is that the incorporation of embedded microstructures can restore stable deformation, even in the presence of significant initial instability, particularly with a reduction factor of 1/5. At high relative density, its specific energy absorption stands out favorably compared to other configurations, highlighting the success of the recoverable buckling mechanism. This work paves the way for designing multi-step mechanical metamaterials for use in impact resistance and body protection.

Broadband metamaterial linear polarization converter designed by a hybrid neural network with data augmentation

Deep learning techniques provide a new approach to the design and optimization of electromagnetic metamaterials. This study used a convolutional neural network and long short-term memory (CNN–LSTM) hybrid network to design and optimize a broadband metamaterial reflective linear polarization converter. The data augmentation method was also employed in few-shot learning to reduce optimization costs and improve model prediction performance. With the inverse prediction, a linear polarization converter that perfectly covers the Ku-band was obtained and fabricated with flexible printed circuit technology. Both simulation and experimental results indicate that this network can accurately predict the structural parameters. The polarization converter not only achieves remarkable broadband polarization conversion efficiency spanning the 2.2–18 GHz range but also maintains precise cross-polarization control across the entire Ku-band. The mean polarization conversion ratio in the Ku-band was calculated to be an impressive 99.69%. Finally, the mechanism of polarization conversion and the influence of each structural parameter on its performance further verify the optimality of the inverse design model. The use of CNN–LSTM deep learning methods significantly simplified the design process of electromagnetic metamaterials, reducing design costs while ensuring high design precision and excellent performance.

Design of metamaterial thermoelectric generators for efficient energy harvesting

Thermoelectric generators (TEGs) are widely recognized as clean energy solutions that can convert low-grade waste heat into electricity through a temperature gradient. Despite their significant potential, challenges such as low conversion efficiency and high costs have limited their practical applications. In this paper, we present an innovative metamaterial design concept for TEGs with significantly improved efficiency. A Finite Element Model is validated using Bi0.5Sb1.5Te3 bulk samples fabricated via the drop-cast method. This model can predict open-circuit voltage and output power as a function of an arbitrary metamaterial design using the commercial software ANSYS®. Four different metastructure designs, including 2D Triangular Honeycomb, Re-entrant, body-centered cubic (BCC), and triply periodic minimal surface (TPMS) structures, are systematically investigated. Through experiments and numerical analysis, the effects of annealing temperature, porosity, and unit cell numbers (UCNs) on the performance of TE legs are explored. It is found that 2D Triangular Honeycomb and BCC structures outperform other configurations due to their capacity to maintain a higher thermal gradient. Optimizing their porosity and UCNs can further enhance the output power. Compared to the traditional designs with bulk TE legs, implementing a 2D metastructure design with 30 % porosity and UCNs of 4 × 4 × 4 can lead to approximately a 100 % increase in power output.

Design of broad quasi-zero stiffness platform metamaterials for vibration isolation

Adaptability and reliability are challenges in designing vibration isolation structures, and mechanical metamaterials featuring broad quasi-zero stiffness (QZS) platforms are among the most promising candidates for addressing this issue. This paper proposes a novel design of vibration isolation metamaterials featuring a broad QZS platform to achieve vibration control in complex environments. The metamaterial unit cells are designed by integrating horizontal and diagonal beams based on the mechanism combining Euler buckling and flexural deformation. Herein, the component made of diagonal beams is configured to exhibit negative stiffness behavior, while the designed support components aim to relax the boundary constraints of the diagonal beam component, thereby mitigating the negative stiffness effect. By tuning the synergistic effects between horizontal and diagonal beams, QZS features can be achieved over a broad range of displacements. A combination of theoretical analysis, finite element method and experiment is employed to investigate the payload and QZS features of metamaterials comprehensively. Notably, the designed unit cell maintained a considerably broad QZS platform, with static experiments revealing that this platform accounts for approximately 55 % of the total loading range. Furthermore, the designed metamaterials exhibit excellent vibration isolation performance in the low-frequency range, with vibration experiments demonstrating that the unit cell can effectively shield vibrations across almost the entire range when the support mass corresponds to the QZS payload. The geometric parameters of the metamaterial configuration that influence the range of the QZS platform are also explored. In conclusion, the proposed mechanical metamaterials have a tunable and broad QZS platform with considerable potential for use in customized low-frequency vibration isolation applications.

Square & H metasurfaces for SPR Increasing in long Wave-IR absorber

In the long-wave infrared (LWIR) spectrum, this paper suggests an electromagnetic (EM) waveband absorber design based on metamaterials. Germanium, gold, and magnesium oxide layers are arranged in a layered structure from top to bottom in the suggested model. Our proposed metamaterial structure’s upper surface is composed of metallic metasurfaces with H and square forms from various studies. The finite element method is used to evaluate the metamaterials’ electromagnetic properties in terms of absorbance and reflectance. It is observed that there is a particular size of the metamaterial at which extremely localized electromagnetic resonance occurs. Quantitative findings indicate that the suggested metamaterial design’s average absorption reaches 90 % in the 10 μm to 14 μm range across a wide variety of incidence angles (00 to 400 & 00 to 800) for both transverse electric (TE) and transverse magnetic (TM) polarization. It is evident from these data that the suggested model configuration has broad potential applications in manyoptoelectronic fields of study.

Computational design of mechanical metamaterials.

In the past few years, design of mechanical metamaterials has been empowered by computational tools that have allowed the community to overcome limitations of human intuition. By leveraging efficient optimization algorithms and computational physics models, it is now possible to explore vast design spaces, achieving new material functionalities with unprecedented performance. Here, we present our viewpoint on the state of the art of computational metamaterials design, discussing recent advances in topology optimization and machine learning design with respect to challenges in additive manufacturing.

Computational design of art-inspired metamaterials.

Computational design of art-inspired metamaterials.

Damage-programmable design of metamaterials achieving crack-resisting mechanisms seen in nature

The fracture behaviour of artificial metamaterials often leads to catastrophic failures with limited resistance to crack propagation. In contrast, natural materials such as bones and ceramics possess microstructures that give rise to spatially controllable crack path and toughened material resistance to crack advances. This study presents an approach that is inspired by nature’s strengthening mechanisms to develop a systematic design method enabling damage-programmable metamaterials with engineerable microfibers in the cells that can spatially program the micro-scale crack behaviour. Machine learning is applied to provide an effective design engine that accelerate the generation of damage-programmable cells that offer advanced toughening functionality such as crack bowing, crack deflection, and shielding seen in natural materials; and are optimised for a given programming of crack path. This paper shows that such toughening features effectively enable crack-resisting mechanisms on the basis of the crack tip interactions, crack shielding, crack bridging and synergistic combinations of these mechanisms, increasing up to 1,235% absorbed fracture energy in comparison to conventional metamaterials. The proposed approach can have broad implications in the design of damage-tolerant materials, and lightweight engineering systems where significant fracture resistances or highly programmable damages for high performances are sought after.

Computational challenges in additive manufacturing for metamaterials design.

Computational challenges in additive manufacturing for metamaterials design.

Designing a TPMS metamaterial via deep learning and topology optimization

Data-driven models that act as surrogates for computationally costly 3D topology optimization techniques are very popular because they help alleviate multiple time-consuming 3D finite element analyses during optimization. In this study, one such 3D CNN-based surrogate model for the topology optimization of Schoen’s gyroid triply periodic minimal surface unit cell is investigated. Gyroid-like unit cells are designed using a voxel algorithm and homogenization-based topology optimization codes in MATLAB. A few such optimization data are used as input–output for supervised learning of the topology-optimization process via the 3D CNN model in Python code. These models could then be used to instantaneously predict the optimized unit cell geometry for any topology parameters. The high accuracy of the model was demonstrated by a low mean square error metric and a high Dice coefficient metric. The model has the major disadvantage of running numerous costly topology optimization runs but has the advantages that the trained model can be reused for different cases of TO and that the methodology of the accelerated design of 3D metamaterials can be extended for designing any complex, computationally costly problems of metamaterials with multi-objective properties or multiscale applications. The main purpose of this paper is to provide the complete associated MATLAB and PYTHON codes for optimizing the topology of any cellular structure and predicting new topologies using deep learning for educational purposes.

A new seismic metamaterial design with ultra-wide low-frequency wave suppression band utilizing negative Poisson's ratio material

In this paper, we present a new seismic metamaterial (SM) for the suppression of Lamb waves and surface waves utilizing the negative Poisson's ratio (NPR) foam. The periodic cell of the metamaterial is composed of a square cylinder made of steel in the center and NPR foam connecters at the corners. Utilizing the unique resonance properties of the NPR material, an ultra-low-frequency broadband wave suppression is achieved. First, the characteristics of bandgaps (BGs) of the proposed structure with different materials were analyzed using the finite element (FE) method. It shows that the application of the NPR foam can significantly broaden the BGs compared with the case using traditional rubber. The vibration modes were analyzed to investigate the mechanism of BG generation, and the results show that the broad BG is achieved via the unique local resonance mechanism of the NPR foam. Subsequently, the frequency-domain analysis was carried out to verify the shielding effect of the designed SM on Lamb waves, using a periodic structure consisting of 10 × 6 unit cells. It shows that the designed SM can effectively attenuate Lamb waves in the range of 3–44 Hz with attenuation up to −590 dB at 32 Hz. A parametric analysis shows that the NPR foam with small thickness, high modulus, low mass density, and low Poisson's ratio can broaden the first complete BG. In addition, the acoustic cone method was combined with the frequency-domain analysis to calculate the BGs of the proposed structure against the surface wave, using a periodic structure consisting of 20 unit cells. It shows that the surface wave can be significantly attenuated within the BG. Finally, real seismic excitations were applied for time-domain analyses, and the simulation results show that the proposed structure can effectively shield the low-frequency seismic surface waves in the range of 0.1–20 Hz. The design scheme proposed in this paper is simple in structure and easy to implement, and is believed to possess bright application potentials in seismic protection.

New topology design of 3D chiral metamaterials with compression-twist coupling effect

Chiral structure can be used for compression-twist coupling (CTC) metamaterials, exhibiting twist deformation under axial compression. In this study, a series of chiral CTC metamaterials were designed based on the 3D tetra-chiral structure, including cube-type and cylinder-type structures. The CTC properties of these metamaterials were investigated in detail by finite element simulations and experiments. The results show that the proposed chiral configurations have better CTC effects than the original 3D tetra-chiral structure. Furthermore, a wide range of adjustable torsion angles can be achieved by changing the geometrical parameters. Finally, the energy absorption properties of these structures were also discussed.

Enhancing mechanical properties of additively manufactured voronoi-based architected metamaterials via a lattice-inspired design strategy

Voronoi-based architected metamaterials have gained significant recognition as promising candidates for bone defect repair implants. However, the demanding requirements for reliable and adjustable load-bearing capacity pose challenges in applying irregular Voronoi-based architected metamaterials in implant applications. In this study, we propose a lattice-inspired design methodology for these metamaterials, enabling precise control over topologies and porosities to enhance their mechanical properties. We demonstrate the influence of unit cell topology on the printability, mechanical properties, and permeability of lattice-inspired Voronoi-based metamaterials (LIVMs) fabricated via laser powder bed fusion (LPBF) additive manufacturing. The LPBF-printed LIVMs exhibited yield strengths ranging from 3.35 to 17.59 MPa and specific energy absorption ranging from 3.81 to 14.29 J/g. Through finite element modeling and experimentation, we show that the deformation behavior of LIVMs with various topologies plays a crucial role in enhancing mechanical performance through mechanisms such as homogeneous load transfer between unit cells and multistage-contact strengthening within a unit cell. Additionally, we analyze the impact of unit cell type and porosity on the mass-transport behavior of LIVMs using computational fluid dynamics simulations. The LIVMs achieved experimental permeability values ranging from 3.88 × 10−9 to 16.83 × 10−9 m2 (consistent with trabecular bones), indicating that multiple fluid flow channels can be utilized to enhance mass transport by distributing flow pressure and increasing fluid mobility. The proposed design method effectively achieves a favorable combination of superior mechanical properties and tunable permeability in Voronoi-based architected metamaterials. These findings provide valuable theoretical guidance for the development of architected metamaterials for bone implant applications.

Distribution of Single-Particle Resonances Determines the Plasmonic Response of Disordered Nanoparticle Ensembles.

Understanding how colloidal soft materials interact with light is crucial to the rational design of optical metamaterials. Electromagnetic simulations are computationally expensive and have primarily been limited to model systems described by a small number of particles-dimers, small clusters, and small periodic unit cells of superlattices. In this work we study the optical properties of bulk, disordered materials comprising a large number of plasmonic colloidal nanoparticles using Brownian dynamics simulations and the mutual polarization method. We investigate the far-field and near-field optical properties of both colloidal fluids and gels, which require thousands of nanoparticles to describe statistically. We show that these disordered materials exhibit a distribution of particle-level plasmonic resonance frequencies that determines their ensemble optical response. Nanoparticles with similar resonant frequencies form anisotropic and oriented clusters embedded within the otherwise isotropic and disordered microstructures. These collectively resonating morphologies can be tuned with the frequency and polarization of incident light. Knowledge of particle resonant distributions may help to interpret and compare the optical responses of different colloidal structures, correlate and predict optical properties, and rationally design soft materials for applications harnessing light.

Genetic algorithm-enabled on-demand co-design of optically transparent metamaterial for multispectral stealth applications

This paper proposes a genetic algorithm (GA)-enabled co-design method for the development of metamaterials with on-demand microwave reflectivity and infrared (IR) emissivity. First, we proposed a multilayered metamaterial based on metasurface with hexagonal patch and ring patterns. An equivalent circuit model (ECM) was then established to model the microwave reflectivity of the metamaterial. To achieve broadband low microwave reflectivity, a GA based on this ECM was adopted to optimize the structural parameters of the metamaterial. A co-design task was accomplished by setting a judgment condition in the algorithm for low IR emissivity. With the help of GA, a metamaterial with broadband low microwave reflectivity and low IR emissivity was designed. Subsequently, a prototype metamaterial was fabricated by patterning optically transparent indium tin oxide films. The calculated, simulated, and measured results agreed well. The co-designed metamaterial had an IR emissivity of 0.15 within the spectral range of 3–14 µm, −10 dB microwave reflectivity at frequencies of 3.1–32.2 GHz, and transparency in the visible band. The proposed co-design method will benefit the design and application of multispectral stealth metamaterials.

A novel windmill-shaped auxetic structure with energy absorption enhancement

The traditional anti-tetra-missing rib structure often suffers from uneven stress deformation and poor energy absorption, which limits its engineering applications. To address these limitations, this paper proposed a novel windmill-shaped auxetic structure by incorporating reinforcing ligaments into the traditional anti-tetra-missing rib structure. The incorporation of these reinforcing ligaments ensures that both the outer and inner ligaments of the windmill-shaped auxetic structure are adequately supported, leading to more uniform structural deformation and enhanced energy absorption capabilities. Further modifications, such as reducing the length of the outer and inner ligaments and increasing their thickness within a reasonable range, significantly enhance the energy absorption capacity. These findings provide a theoretical basis for the design and practical application of auxetic metamaterials.