Hierarchical Metamaterials Research Articles

Multispectral Hierarchical Metamaterials with Broadband Microwave Absorption, Gradient Infrared Emissivity, and High Visible Transparency

AbstractThe rapid progression of multispectral detectors poses a serious threat to weapon systems and personnel. The efficiency of stealth camouflage materials, however, has strong wavelength dependence, which limits their functionality to a specific spectral range. Here, a multispectral hierarchical metamaterial (MHM) with broadband microwave absorption, gradient infrared (IR) emissivity, and high visible transparency is proposed. The MHM design entails the integration of two distinct functional layers: the infrared camouflage layer (IRCL) and the radar absorbing layer (RAL). Specifically, leveraging the low‐pass and high‐impedance properties of capacitive frequency selective surfaces and adjustable filling ratio of low IR radiation materials, the IRCL achieves simultaneous high microwave transmission and gradient IR emissivity designs (emissivity gradients > 0.15 at 3–5 and 8–14 µm). The RAL achieves broadband microwave absorption across radar C, X, Ku, and Ka bands through a circuit‐analog absorber designed with lossy materials. Furthermore, prioritizing materials with high transparency enhances the average optical transmittance (>61.8%) of MHM in 380–760 nm. These distinctive features underscore the potential of the proposed MHM for advanced applications in camouflage and stealth technologies.

Hierarchical design of auxetic metamaterial with peanut-shaped perforations for extreme deformation: Self-similar or not?

Hierarchical designs have exhibited great potential in reducing structural weight and improving mechanical properties. However, the hierarchical design of perforated auxetic metamaterials with curved holes is rarely investigated and the choice of self-similar hierarchical design or not still confuses us. In this study, two types of hierarchical designs with self-similar and non-self-similar features for the auxetic metamaterial with peanut-shaped perforations are realized and compared. First, the printed hierarchical auxetic metamaterials via additive manufacturing technology are tested by quasi-static tension to explore their mechanical performance in different directions. Correspondingly, the computational homogenization model is established to characterize their full elastic properties and its effectiveness is verified by the experimental results. Subsequently, the deformation mechanisms of the proposed hierarchical metamaterials are numerically analyzed to address the superiority of self-similar design over the non-self-similar design. Finally, the influences of microstructural parameters and hierarchy order on the effective elastic constants of the proposed hierarchical metamaterial are considered and the optimal topology with extreme auxetic behavior is recommended. The results indicate that the proposed self-similar hierarchical design exhibits significant anisotropic feature, which can serve the multidirectional mechanical requirements, and the remarkable enhancement in auxeticity can be attributed to the synergistic deformation of tetrachiral sub-elements. Besides, the increase of hierarchy order does not continuously enhance the auxetic behavior of hierarchical metamaterial, although it can effectively change the porosity of structure. Through such investigations, a meaningful guidance of property map is provided for the hierarchical design of auxetic metamaterial perforated by curved cuts.

Lightweight self-similar hierarchical metamaterials with subwavelength and superwide bandgaps

Vibration isolation has always been a flourishing subject with practical interest because it helps in reducing structure vibration that has serious effects on moving vehicles and equipment operation, and it exists everywhere and incessantly in daily life. With the advantage of predictable and designable frequency bandgaps, elastic metamaterial has attracted a lot of research attention in the past decade and beyond. Inspired by the design of Chinese traditional window and kirigami pattern, this paper introduces a self-similar hierarchical elastic metamaterial that can offer superwide subwavelength bandgaps without increasing system weight. The comparison of band structures obtained by finite element simulation manifests significant effects of hierarchy design on lowering bandgap frequency and widening bandgap width. Through comprehensive analyses, the principles for maximizing bandgap width without increasing system weight are highlighted. The vibration response of supercells that consist of 2 × 3 unitcells is constructed for both the first- and second-order hierarchical structures are investigated. After analyzing the different working frequencies of supercells with distinct hierarchical ratios, the first-order and second-order hybrid hierarchical supercells containing unitcells with complementary bandgaps are designed. An excellent increase in effective and perfect attenuation width is demonstrated. The work presented herein provides a new and effective method for generating subwavelength and superwide bandgaps in lightweight structures. This advancement holds great promise for improving the application potential of elastic metamaterials.

Mechanical properties of hierarchical lattice via strain gradient homogenization approach

With the advancement of 3D printing technology, manufacturing metamaterials with extreme mechanical properties is becoming more feasible. Hierarchical lattices appear to be ideal candidates for obtaining desirable lightweight, high specific stiffness, and enhanced specific energy absorption. They can be constructed by architected substructures at multiple length scales. The interpretations of the underlying deformation mechanisms are necessary in order to manipulate with expected mechanical properties. In this paper, experiments were conducted to examine the effective mechanical behaviors of hierarchical lattice metamaterials. A strain gradient homogenization approach has been employed to correlate their morphological characteristics to the resulting material properties. The effective stiffness tensors are identified including the fourth-, fifth-, and sixth-order stiffness tensors. The higher-order inertial parameters are determined by a fitting procedure. Comparisons between direct finite element analyses and the homogenized strain gradient continua have been made for hierarchical lattice materials under static and dynamic loads. It is found that strain gradient homogenization approach can be an accurate, efficient and reliable way of predicting the mechanical behaviors of hierarchical lattice. A systematic analysis of geometrical parameters was conducted to uncover the underlying mechanisms responsible for the enhancement of effective properties. This work offers a novel approach for designing the mechanical properties of hierarchical metamaterials through precise control of secondary structure types and distributions.

Acoustically soft and mechanically robust hierarchical metamaterials in water

Acoustically soft and mechanically robust hierarchical metamaterials in water

Hierarchical Nanomaterials by Selective Deposition of Noble Metal Nanoparticles: Insight into Control and Growth Processes

AbstractComplex hierarchical metamaterials are currently the focus of many cutting‐edge studies due to their potential to advance such critically important areas of technology as energy storage and transformation, sensing, photovoltaics, nano‐medicine, antibacterial and self‐regenerating materials. However, the deterministic design of novel hierarchical metamaterials remains problematic due to the lack of efficient, highly reliable methods for controlling the internal structure and architecture of materials. A comprehensive advanced model is proposed to simulate the formation of complex hierarchical metamaterials with a controllable structure. The control is achieved via selective deposition of noble metal nanoparticles (Au, Au, Pd, Pt). Moreover, the novel method for the nanofabrication is theoretically examined and experimentally verified. This approach allows for the sophisticated spatiotemporal control of growth conditions and, as a result, achieving the targeted internal structure of metamaterials. This opens a way to the deterministic design and formation of complex multi‐material metamaterials on the basis of metal oxides and noble metal nanoparticles. Moreover, a fundamental insight related to the longstanding question about the prevalence of bottom‐up versus top‐down growth for various materials and systemswhich is challenging to directly verify experimentally is presented.

Robust elastic wave transport in zone-folding induced topological hierarchical metamaterials

The topologically protected elastic wave transport in hierarchical metamaterials for the in-plane mode and out-of-plane mode is investigated in this work. First of all, the influence of two key parameters (the hierarchical order and length ratio) on dispersion relation is studied in detail. It can be found that the introduction of structural hierarchy is beneficial for the formation of low-frequency Dirac cones (DCs). But the number of DCs is independent of the hierarchical order. Moreover, the frequency of DCs and band gaps can be tuned effectively by the length ratio. Tuning the lower-order length ratio is more effective to form low-frequency DCs. Based on above findings, we proposed novel topological hierarchical metamaterials analogue to quantum spin Hall effects (QSHEs) by zone-folding method. By shrinking or expanding the supercell, two types of supercells with distinct topological property are built. In addition, through the dispersion analysis and full-field numerical simulation, topological interface states for both wave modes are obtained successfully, and the robustness is verified also. To overcome the limited frequency range of topological interface states, we try to introduce the temperature-sensitive epoxy into the topological hierarchical metamaterial. Fortunately, the frequency of topological interface states can be tuned in a wide range, and the energy concentration cannot be affected by the temperature. This work will broaden the applied range of hierarchical metamaterials, and is expected to meet the tremendous needs for multifunctional materials in engineering practice.

Harnessing structural hierarchy and multi-material approaches to improve crushing performance of re-entrant honeycombs

This study proposes to improve the crushing performance of re-entrant honeycombs by considering both mechanistic and material ingredients. First, a set of novel hierarchical configurations possessing hexachiral auxetic subordinate cells was designed by replacing the solid cell walls of the conventional re-entrant honeycomb. Then the voids of the modified re-entrant honeycombs and the proposed hierarchical metamaterials were filled with a flexible material by using a multi-material 3D printer. Parametric numerical analyses were performed using validated Finite Element models to identify optimal metamaterial architectures. A set of samples, including traditional and developed configurations, were 3D printed and subjected to uniaxial compression loading. The deformation mechanism, compressive strength, and energy absorption of the samples were compared at different strain levels. The results show that introducing hexachiral hierarchies along the ribs prolongs the duration of plastic deformation and keeps the auxeticity of the samples at larger strains. This provides a stable and long post-yield plateau in the compressive stress-strain curve that brings considerable improvement in energy absorption and compressive strength. In addition, multi-material approaches with the combination of rigid photopolymer and flexible rubber-like material also contribute to stabilizing the deformation mechanism of both conventional and developed hierarchical re-entrant auxetic configurations. The proposed hierarchical auxetic structures present more specific compressive strength and specific energy absorption (up to ~150 %) compared to conventional re-entrant auxetic honeycombs. Overall, the proposed hybrid designed strategies can be leveraged to manipulate the collapse mechanism and improve crushing performance.

Wide-temperature-range multispectral camouflage enabled by orientation-gradient co-optimized microwave blackbody metastructure coupled with conformal MXene coating.

Cloaking against electromagnetic detection is a well-researched topic; yet achieving multispectral camouflage over a wide temperature range remains challenging. Herein, an orientation-gradient co-optimized graded Gyroid-shellular (GGS) SiOC-based metastructure with a conformal MXene coating (M@SiOC) is proposed to achieve wide-temperature-range microwave/infrared/visible-light-compatible camouflage. Firstly, the combination of coordinate transformation and genetic algorithm endows the GGS architecture with optimal orientation and gradient, allowing superior microwave blackbody-like behavior. Secondly, a microwave-transparent, low-infrared-emissivity MXene metasurface is constructed in situ to permit wide-temperature-range infrared camouflage. Finally, the outstanding spectral selectivity of MXene enables camouflage against 1.06 μm-lidar and visible-light detection. As a result, the as-fabricated [110]-oriented GGS M@SiOC metamaterials exhibit outstanding wide-temperature-range multispectral camouflage: (i) ultrabroadband microwave absorption exceeding 80% in the X-Ku band from room temperature (RT) to 500 °C with absorption above 86.0% (91.4% on average) at 500 °C; (ii) excellent long-wavelength infrared camouflage for object temperatures from RT to 450 °C, reaching an infrared signal intensity of 78.5% for objects at 450 °C; and (iii) camouflage against both 1.06 μm-lidar and dark environment. Compared with traditional hierarchical metamaterials necessitating complex micro/nano-fabrication processes, this work provides a novel pathway toward the realization of structurally integrated multispectral stealth components by combining flexible metastructure design and high-fidelity additive manufacturing.

Asymmetric electric field distribution enhanced hierarchical metamaterials for radar-infrared compatible camouflage

Metamaterials are widely used in electromagnetic radiation and camouflage for their flexible wavefront manipulation and polarization over a broad spectrum ranging from microwaves to optics. However, multispectral compatible camouflage faces significant challenges due to tremendous scale differences of unit cells and desired radiative properties in various spectral regimes. This study assembles a micron-scale infrared emitter, a millimeter-scale microwave absorber, and a metal reflector to propose a hierarchical metamaterial that reduces microwave scattering and reflects low-infrared waves. As a proof of concept, laser etching micro-manufactures an upper infrared shielding layer with a periodic metal pattern. At the same time, bottom square frustum metastructure composites are fabricated and optimized based on genetic algorithms. Under the normal incidence transverse electromagnetic wave with a 90° azimuth angle, the hierarchical strategy and infrared unit create an asymmetric electric field distribution of local near-field coupling, which is conducive to generating additional resonance for broadening the absorption bandwidth. Experiments verify the multispectral camouflage, which shows a high absorption efficiency of more than 90%, ranging from 3.6 to 6.2 and from 8.4 to 18 GHz with a total thickness of 4.05 mm (0.049λmax). Due to the non-reflection of surrounding thermal signals in the infrared 2-22 μm region, low-infrared emissivity (0.29) metamaterials can adapt to various thermal backgrounds. This methodology can provide a novel route for fabricating multispectral camouflage devices.

Geometry of sliding lamellae dictates the constitutive properties of nacre-like hierarchical materials

The mechanical properties of nacre (mother-of-pearl), which are superior to those of its constituent materials, derive from a micro-architecture formed by the arrangement into parallel laminae of individual aragonite tiles with surface asperities, bonded by organic interlayers. A mechanical model is developed to determine how the contact profile that defines the geometry of the tile surface affects the constitutive response of hierarchical metamaterials of this type when they are strained in the lamellar plane. We consider the structured character of the deformation, consisting of elastic distortion of the tiles and the inelastic contribution from the disarrangements produced by relative sliding of the lamellar interfaces, which is formulated within the thermodynamic framework for irreversible processes in generalized materials. The resistance to sliding associated with constrained shear-induced dilatation of the tiles and the bridging of the organic interlayers are represented by a generalized cohesive-frictional law, effective at the level of averaged separation plane, providing a phenomenological approach that by-passes the difficulty in analytically solving the contact problem at asperities. The nominal stress–strain curves of the nacreous structure are shown to be highly dependent, qualitatively and quantitatively, on the geometry of the contact profiles. The model not only produces results that are in excellent agreement with experiments on nacre, but it can also describe complex stress–strain curves with pinched hysteresis loops having branches of various shapes, as well as serrated inelastic regimes. The versatility of this theoretical approach offers promise as a design tool for innovative metamaterials.

Design, manufacture, and characterisation of hierarchical metamaterials for simultaneous ultra-broadband sound-absorbing and superior mechanical performance

ABSTRACT For engineering applications, sound-absorbing materials are supposed to withstand potential impact loading conditions. However, there is a lack of attempts on multifunctional metamaterials for both acoustic and mechanical purposes. Herein, a hierarchical metamaterial manufactured by fused deposition modelling (FDM) that exhibits simultaneous acoustic and mechanical energy-absorbing capacities is proposed in this work. The metamaterial obtains a successively increasing absorption bandwidth with the growth of the hierarchical order. Ultra-broad half-absorption band from 0.96 to 6.00 kHz is obtained for the fourth order. The unique resonant responses are demonstrated analytically, numerically, and experimentally via properly modulating the structural features. The enhancement mechanism is physically revealed by analysing the impedance matching and resonant damping states. Moreover, compared with its original counterpart, the specific energy absorption (SEA) of the first-order and the second-order hierarchical metamaterials increases by 228% and 434%, respectively. This work provides an effective approach for designing multifunctional metamaterials.

Polarization insensitive hierarchical metamaterial for broadband microwave absorption with multi-scale optimization and integrated design

The structural destructive resonance caused by the single resonant thickness of flat microwave absorbers results in narrow absorption, hindering the progress of stealth materials. Multi-scale optimization and metastructure design are effective in the improvement of multiple resonance thickness as well as wavefront transmission, allowing for greater freedom in the realization of broadband. Herein, hierarchical metamaterials constructed from pyramid metastructure composites and Huygens' metasurface on the basis of Fibonacci spiral element are reported here, with effective absorption bandwidth (reflection loss ≤ −10 dB) ranging from 4.8 to 18 GHz in terms of subwavelength thickness. The hybrid absorber also exhibits robustness with incident angle across 0°–50° for transverse magnetic polarization. The gradient impedance model based on pyramid composites comprising spherical carbonyl iron particles and graphene sheets will serve as a driver for the enhancement of the electromagnetic wave transmission and the booster of impedance matching. Huygens’ resonance of HMS induces the magnetic field convergence effect due to the simultaneous balance of effective surface current and magnetic current, which facilitates the absorption of lossy composites for further broadening absorption bandwidth. This integrated design could be widely applied to other absorbent materials of choice.

Mechanical performance of bio-inspired hierarchical honeycomb metamaterials

Natural materials with hierarchical structures usually have superior mechanical properties. Herein, inspired by the macro–micro coupling deformation characteristics of biomaterials, novel hierarchical auxetic-hexagonal honeycombs (AuxHex) metamaterials with various substructures, including equilateral triangles and double arrowheads lattice cells, were constructed. A universal analysis model of the plastic collapse stress was first established, considering the deformation behavior of both the primary and secondary structures. This mechanism-based method gets rid of redundant numerical fitting parameters, and is applicable to different hierarchical lattice structures. Typical hierarchical AuxHex specimens were prepared using selected laser melting and stainless steel. In-plane compression tests and finite element simulation results demonstrated that, in contrast to the regular structures, hierarchical honeycombs exhibit enhancement in their load-bearing capacities and energy absorption ability. The specific modulus of T-AuxHex and A-AuxHex were increased by about 180% and 45%, the specific strength rose by approximately 50% and 15%, and the specific energy absorption was improved by about 160% and 50%. The effects of geometrical parameters were systematically discussed to reveal the mechanisms underlying the enhancement of the above mechanical characteristics. The proposed theoretical model provides a new method for designing the mechanical properties of hierarchical metamaterials by tailoring the type and distribution of secondary structures.

Topology optimization of anisotropy hierarchical honeycomb acoustic metamaterials for extreme multi-broad band gaps

Acoustic metamaterials (AMMs), especially based on hierarchical honeycomb structure and topology-optimized design with suitable mechanical properties and low-frequency band gaps (BGs), have been studied recently. The present work reports a series of anisotropy hierarchical honeycomb structure lattices composed of the cell walls and vertices of regular hexagonal lattice replacement honeycombs of various sizes, as well as improved BG evaluation indicators. The band structures of three different types of unfilled hierarchical honeycomb lattices are calculated and the mechanism of BGs generation is analyzed. To obtain multi-broad BGs in the low-frequency range, the scatterers filling schemes are optimized by using a genetic algorithm (GA). Additionally, the effects of structural/material parameters on the BG characteristics of the optimized structures are discussed. Finally, the transmission loss (TL) experiment verified the optimization of the structures. This paper aims to promote the application of hierarchical honeycomb metamaterials with low-frequency vibration isolation in the industrial field.

Cross-Wavelength Hierarchical Metamaterials Enabled for Trans-Scale Molecules Detection Simultaneously.

Metamaterials have attracted increasing attention in sensing applications. However, the critical feature sizes of meta‐atom span several orders of magnitude in length scale, almost all the metamaterials are designed to operate at limited bands. It is challenging for a single type of meta‐atom with ultra‐broadband adaptability. Inspired by the natural hierarchical architectures, herein, the authors introduce a new constructing scheme of cross‐wavelength hierarchical metamaterials with a single type of meta‐atom that can realize enhancement of terahertz (THz) resonance and surface‐enhanced Raman scattering (SERS) at the same time. By combining multiple subwavelength structures at different hierarchical levels into a single meta‐atom, the obtained metamaterial can operate in two frequencies and realize multiple functionalities. Armed with this hierarchical metamaterial, detecting analytes as small as sub‐nanoscale chemical molecules or as big as microscale biomolecules simultaneously can be realized in one single metamaterial for the first time. As a proof‐of‐concept example, a smart sensory packaging is developed, which allowed them to real‐time monitor the kinetic growth of pathogenic bacteria and their metabolites in food without opening the packaging. They believe that their work will provide a valuable example that satisfies the unmet need for multiscale functional meta‐devices.

Three-dimensional hierarchical metamaterials incorporating multi-directional programmable thermal expansion

The dimensional stability under the temperature variation is of great significance for the temperature-sensitive structures, motivating the development of metamaterials with the programmable coefficient of thermal expansion (CTE). Here, all the configurations, totally including 51 types for the bi-material pyramid unit cells, were comprehensively devised to attain the widely programmable CTE in single direction. Furthermore, by using an originally developed matrix transformation method, multiple classes of the pyramid-based hierarchical metamaterials were systematically devised. These hierarchical metamaterials incorporated the unidirectional, transversal and isotropic CTEs in the multiple directions. The closed-form expressions of the CTE and relative density for the devised pyramid unit cells and hierarchical metamaterials were analytically established. The theoretical analysis was well verified by the performed numerical modeling, and confirmed that the large ranges of the programmable CTEs could be obtained by rationally adjusting the material and geometry parameters. Besides, the comprehensive comparison of the specific CTE identified that the programmable CTE and low relative density could be well balanced through the devised hierarchical metamaterials. The coupling effect of both material and geometrical parameters on the programmable CTE was figured out, providing a proper guideline to design the metamaterials with both light weight and desirable CTE.

In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials

In this review paper, some relevant models, algorithms, and approaches conceived to describe the bone tissue mechanics and the remodeling process are showcased. Specifically, we briefly describe the hierarchical structure of the bone at different levels and underline the geometrical substructure characterizing the bone itself. The mechanical models adopted to describe the bone tissue at different levels of observation are introduced in their essential aspects. Furthermore, the modeling of the evolution, including the growth and resorption of bone, is treated by analyzing the main approaches employed, namely the mechanical feedback concept and the structural optimization perspective. In this regard, the most prominent ways to model the biomechanical stimulus are summarized. The modeling of the interaction with prostheses or grafts commonly used in reconstructive surgery is also recalled. The main aim of this survey consists thereby in providing the appropriate knowledge to mimic the deeply structured hierarchy of the bone tissue for synthesizing innovative and highly performing bio-inspired metamaterials.

Designing Mechanical Metamaterials with Kirigami-Inspired, Hierarchical Constructions for Giant Positive and Negative Thermal Expansion.

Advanced mechanical metamaterials with unusual thermal expansion properties represent an area of growing interest, due to their promising potential for use in a broad range of areas. In spite of previous work on metamaterials with large or ultralow coefficient of thermal expansion (CTE), achieving a broad range of CTE values with access to large thermally induced dimensional changes in structures with high filling ratios remains a key challenge. Here, design concepts and fabrication strategies for a kirigami-inspired class of 2D hierarchical metamaterials that can effectively convert the thermal mismatch between two closely packed constituent materials into giant levels of biaxial/uniaxial thermal expansion/shrinkage are presented. At large filling ratios (>50%), these systems offer not only unprecedented negative and positive biaxial CTE (i.e., -5950 and 10 710ppm K-1 ), but also large biaxial thermal expansion properties (e.g., >21% for 20 K temperature increase). Theoretical modeling of thermal deformations provides a clear understanding of the microstructure-property relationships and serves as a basis for design choices for desired CTE values. An Ashby plot of the CTE versus density serves as a quantitative comparison of the hierarchical metamaterials presented here to previously reported systems, indicating the capability for substantially enlarging the accessible range of CTE.

Additively manufactured bi-material metamaterial to program a wide range of thermal expansion

The current research on bi-material diamond metamaterials, which can be used to program the coefficient of thermal expansion (CTE) over a wide range, mainly focuses on the theoretical design, while the corresponding experimental range of the CTEs is far narrower. In this study, a bi-material diamond metamaterial was additively manufactured using two polymers: nylon and polyvinyl alcohol (PVA). Without any need for extra processes such as bonding, welding, and mechanical fitting, the additively manufactured metamaterial integrated the nylon and PVA, providing an integrated fabrication process to ensure the expected programmable CTE. The experimentally measured CTEs agreed well with the theoretical predictions. When the material layout was selected as MAT-1 = PVA and MAT-2 = nylon, programmable CTEs ranging from 217.72 to 694.00 ppm/°C were obtained, which were larger than the CTEs of the nylon and PVA. When the material layout was MAT-1 = nylon and MAT-2 = PVA, even though both the nylon and the PVA had positive CTEs, a wide range of negative CTEs (varying from −25.02 to −369.01 ppm/°C) was obtained. The foregoing wide ranges of programmable CTEs are remarkably larger than the literature results, indicating the enhanced programmability of the bi-material metamaterial and stabilizing the foundation for the further design of multilevel and hierarchical metamaterials.