Periodic Metamaterials Research Articles

The Influence of Additive Manufacturing Processes on the Performance of a Periodic Acoustic Metamaterial

Advancements in 3D print technology now allow the printing of structured acoustic absorbent materials at the appropriate microscopic scale and sample sizes. The repeatability of the fundamental cell unit of these metamaterials provides a pathway for the development of viable macro models to simulate built-up structures based on detailed models of the individual cell units; however, verification of such models on actual manufactured structures presents a challenge. In this paper, a design concept for an acoustic benchmark metamaterial consisting of an interlinked network of resonant chambers is considered. The form chosen is periodic with cubes incorporating spherical internal cavities connected through cylindrical openings on each face of the cube. This design is amenable to both numerical modelling and manufacture through additive techniques whilst yielding interesting acoustic behaviour. The paper reports on the design, manufacture, modelling, and experimental validation of these benchmark structures. The behaviour of the acoustic metamaterial manufactured through three different polymer-based printing technologies is investigated with reference to the numerical models and a metal powder-based print technology. At the scale of this microstructure, it can be seen that deviations in surface roughness and dimensional fidelity have a comparable impact on the experimentally measured values of the absorption coefficient.

Periodic topological lattice with different indentation hardness on opposite surfaces

Different surface properties are needed simultaneously in many applications, especially under an indentation load or impact load. This study proposes one class of novel periodic topological mechanical metamaterials, 2D topological honeycomb structure and 3D topological lattice, whose opposite surfaces have significantly different indentation hardness. The difference of hardness is predicted by theoretical analysis and validated by simulations and experiments, which can be up to 7 times. In comparison with the traditional honeycomb structure with the same parameters, the topological honeycomb structure exhibits higher resistance to indentation loads and it can reduce the influence range and degree of indentation loads at the same time. A design guide of parameters is proposed to achieve a more significant difference of hardness between the opposite surfaces. General design rules at the level of both basic unit piece and lattice structure are proposed, which renders the topological lattice to have outstanding designability to meet different demands in applications. The topological lattice concept will open new avenues to design asymmetric structures and expand the existing design space of mechanical metamaterials.

Realization of THz dualband absorber with periodic cross-shaped graphene metamaterials**Project supported by the Key Science and Technology Research Project of Henan Province, China (Grant Nos. 162102210164 and 1721023100107) and the Natural Science Foundation of Henan Educational Committee, China (Grant No. 17A140002).

A dualband terahertz (THz) absorber including periodically distributed cross-shaped graphene arrays and a gold layer spaced by a thin dielectric layer is investigated. Numerical results reveal that the THz absorber displays two perfect absorption peaks. To elucidate the resonant behavior, the LC model is introduced to fit the spectra. Moreover, the strength and linewidth of the absorption peak can be effectively tuned with structural parameters and the relaxation time of graphene. Owing to its rotational symmetry, this THz absorber exhibits polarization insensitivity. Our designed absorber is a promising candidate in applications of tunable optical sensors and optical filters.

Shear resistance of an auxetic chiral mechanical metamaterial

The shear resistance of 3D printed periodic auxetic chiral mechanical metamaterial was quantified via a picture-frame apparatus. The experimental set-up allowed the accurate measurement of the effective shear modulus of the material. Also, a rigid-rod-rotational spring model shows that the effective shear modulus of the material is directly related to the chiral geometry and the rotational rigidity of the center joints and the corner joints in the chiral cell. To facilitate practical design, design guidelines were developed through an integrated analytical, numerical and experimental approach. The influences of the chiral geometry and the joint rigidity on the shear resistance of the periodic auxetic chiral mechanical metamaterial were quantified. The design guidelines were verified by systematic finite element (FE) simulations.

Thermal conductivity of architected cellular metamaterials

Periodic architected cellular metamaterials, as a novel class of low-density materials, possess unprecedented multifunctional properties mainly due to their underlying microarchitecture. In this paper, we study the thermal conductivity of cellular metamaterials and evaluate their performance for thermal management applications. To understand the relations between the microarchitecture and the thermal response, we analyze the thermal conductivity of a wide range of cellular metamaterials with strategically developed microarchitectures from two-dimensional (2D) cells with Supershape pores to three-dimensional (3D) thin-walled open lattices and shellular materials. We implement standard mechanics homogenization on the periodic representative volume elements (RVEs) of these cellular metamaterials to examine the effect of pore architecture (relative density, pore shape, pore orientation, and pore elongation) on their effective thermal conductivity. The numerical results show how the thermal conductivity of an isotropic material can be modified by pore introduction and how the pore architecture could lead to an anisotropic effective thermal conductivity tensor. To examine the impact of having 2D Supershape cuts on 3D RVEs, thin-walled open lattices are designed as an assembly of thickened 2D RVEs with Supershape pores. A mathematical model is derived based on the effective thermal properties of the constituent 2D RVEs to predict the effective thermal properties of these lightweight cellular materials. Effective thermal conductivity of shellular materials based on triply periodic minimal surfaces is also compared with those of the previously introduced architectures. Unlike the shellular materials, which only cover a narrow region of thermal conductivity versus relative density chart, cellular materials with a wide range of anisotropic effective thermal conductivities can be engineered by using 2D Supershape pores on 2D or 3D thin-walled cells. Finally, we show how the concept of architected functionally graded cellular materials can be used to tune the heat flow within cellular media to guide it in a specific direction to control the temperature inside advanced 3D printed materials. As a case study, the optimum spatial distribution of pore rotation angle is found to maximize or minimize the heat flow passing through different sides of a square-shaped porous slab. This paper opens an avenue for developing thermal metamaterials with programmable anisotropic thermal properties.

Left-handed band in an electromagnetic metamaterial induced by sub-wavelength multiple scattering

Due to the deep sub-wavelength unit cell in metamaterials, the quasi-static approximation is usually employed to describe the propagation. By making pairs of resonators, we highlight that multiple scattering also occurs at this scale and results in the existence of a dipolar resonance, which leads to a negative index of refraction when we consider several resonators. We experimentally verify the possibility of obtaining a negative index of refraction in periodic metamaterials in two different ways and eventually demonstrate the subwavelength recovery of several point sources in both cases.

Randomness in periodic metamaterials

The most straightforward way to design artificial structures is to use periodicity and leverage its potential mathematical and physical consequences to our favor. However, strict periodicity, which is usually employed in designing artificial materials, is not practically feasible and most often some degrees of randomness are introduced in the fabrication process, which degrade the performance. In this presentation, using the Furstenberg theory on the product of random matrices and Monte Carlo simulations we explore the effect of randomness in the transmission performance of periodic structures designed to realize density-near-zero (DNZ) metamaterials. We show that DNZ propagation is very sensitive to randomness, and we unravel the physics behind this sensitivity with analytical theory and full-wave simulations.

Experimental demonstration of Luneburg lens based on hyperuniform disordered media

Hyperuniformity provides a means of categorizing many nanostructures including nano-composite materials, and the design methodology based on hyperuniform randomness often leads to devices with extraordinary characteristics. In this work, we numerically and experimentally demonstrate that a Luneburg lens made of hyperuniform disordered composite materials can dramatically reduce back scattering in comparison with its counterpart design based on periodic metamaterials. Two sample Luneburg lenses made of scatterers with hyperuniform disordered and periodic distributions have been designed and fabricated, respectively. Measurements are carried out in a two-dimensional near-field microwave scanning apparatus. Both experimental and simulation results agree with theoretical prediction demonstrating almost identical in-band focusing but rather contrast out-of-band wave scattering characteristics.

Targeted Double Negative Properties in Silver/Silica Random Metamaterials by Precise Control of Microstructures

The mechanism of negative permittivity/permeability is still unclear in the random metamaterials, where the precise control of microstructure and electromagnetic properties is also a challenge due to its random characteristic. Here silver was introduced into porous SiO2 microsphere matrix by a self-assemble and template method to construct the random metamaterials. The distribution of silver was restricted among the interstices of SiO2 microspheres, which lead to the precise regulation of electrical percolation (from hoping to Drude-type conductivity) with increasing silver content. Negative permittivity came from the plasma-like behavior of silver network, and its value and frequency dispersion were further adjusted by Lorentz-type dielectric response. During this process, the frequency of epsilon-near-zero (ENZ) could be adjusted accordingly. Negative permeability was well explained by the magnetic response of eddy current in silver micronetwork. The calculation results indicated that negative permeability has a linear relation with ω0.5, showing a relaxation-type spectrum, different from the “magnetic plasma” of periodic metamaterials. Electromagnetic simulations demonstrated that negative permittivity materials and ENZ materials, with the advantage of enhanced absorption (40dB) and intelligent frequency selection even in a thin thickness (0.1 mm), could have potentials for electromagnetic attenuation and shielding. This work provides a clear physical image for the theoretical explanation of negative permittivity and negative permeability in random metamaterials, as well as a novel strategy to precisely control the microstructure of random metamaterials.

Targeted Double Negative Properties in Silver/Silica Random Metamaterials by Precise Control of Microstructures.

The mechanism of negative permittivity/permeability is still unclear in the random metamaterials, where the precise control of microstructure and electromagnetic properties is also a challenge due to its random characteristic. Here silver was introduced into porous SiO2 microsphere matrix by a self-assemble and template method to construct the random metamaterials. The distribution of silver was restricted among the interstices of SiO2 microspheres, which lead to the precise regulation of electrical percolation (from hoping to Drude-type conductivity) with increasing silver content. Negative permittivity came from the plasma-like behavior of silver network, and its value and frequency dispersion were further adjusted by Lorentz-type dielectric response. During this process, the frequency of epsilon-near-zero (ENZ) could be adjusted accordingly. Negative permeability was well explained by the magnetic response of eddy current in silver micronetwork. The calculation results indicated that negative permeability has a linear relation with ω0.5, showing a relaxation-type spectrum, different from the “magnetic plasma” of periodic metamaterials. Electromagnetic simulations demonstrated that negative permittivity materials and ENZ materials, with the advantage of enhanced absorption (40dB) and intelligent frequency selection even in a thin thickness (0.1 mm), could have potentials for electromagnetic attenuation and shielding. This work provides a clear physical image for the theoretical explanation of negative permittivity and negative permeability in random metamaterials, as well as a novel strategy to precisely control the microstructure of random metamaterials.

Modelling of elastic metamaterials with negative mass and modulus based on translational resonance

A new elastic metamaterial model is proposed based on translational resonance to obtain simultaneously negative mass and negative modulus within specific frequency ranges, which consists of a series properly arranged stiff and soft components. Two different translational resonances exist in the proposed metamaterial representative cell. One resonance contributes directly to the negative effective modulus and the coupled effect of the two resonances can generate negative effective mass. The unique feature of the representative cell endows the model with great flexibility to generate negative effective parameters in different frequency ranges from various selections of materials and different geometrical parameters. The effect of the structural parameters of the representative cell on the frequency ranges with single negativity (negative mass or negative modulus) or double negativity (negative mass and negative modulus) has been evaluated in detail. Periodic metamaterials are formed by connecting multiple representative cells, and wave propagation in such metamaterials is studied. In the frequency ranges with single negative parameters, strong wave mitigation is observed, as expected. In the frequency ranges with double negative parameters, negative phase velocity is clearly shown. Typical examples are presented to illustrate the dynamic property of the current metamaterial.

Architected cellular piezoelectric metamaterials: Thermo-electro-mechanical properties

Advances in additive manufacturing have recently made possible the manufacturing of smart materials with arbitrary microarchitectures, which leads to developing lightweight smart metamaterials with unprecedented multifunctional properties. In this paper, asymptotic homogenization (AH) method is developed for predicting the effective thermo-electro-mechanical properties of architected cellular piezoelectric metamaterials. The effect of pore microarchitecture (relative density and cell topology) and polarization direction on elastic, dielectric, piezoelectric, pyroelectric and thermal properties of periodic cellular piezoelectric metamaterials is explored. The pore topology is determined by Fourier series expansion. Alternative pore microarchitectures are considered by tailoring shape parameters, scaling factor, and rotation angle of the constitutive pore. Smart cellular metamaterials made of both single-phase (BaTiO3) and bi-phase (BaTiO3-expoy) piezoelectric materials are considered. Apart from effective thermo-electro-mechanical properties, a series of figures of merit for the cellular piezoelectric metamaterials, i.e. piezoelectric coupling constant, acoustic impedance, piezoelectric charge coefficient, hydrostatic figure of merit, current responsivity, voltage responsivity and pyroelectric energy harvesting figures of merit, are presented and the reason for difference between the figures of merit of different types of piezoelectric metamaterials is discussed. The figures of merit shed lights on the effect of microarchitecture on optimizing the multifunctional performance of smart cellular metamaterials for applications as structurally efficient multifunctional energy harvesters. It is found that the piezoelectric and pyroelectric figures of merit of cellular piezoelectric metamaterials can be significantly improved compared to the commonly used honeycomb cellular materials and composite materials with solid circular inclusion if an appropriate microarchitecture is selected for the pore. For example, piezoelectric charge coefficient (dh) for a transversely polarized single-phase cellular piezoelectric metamaterial with a solid volume fraction of 0.4 can be 350% higher than the corresponding figures of merit of honeycomb piezoelectric material; voltage responsivity of transversely polarized bi-phase cellular piezoelectric metamaterials with an inclusion volume fraction of 0.3 can be also 249% higher than the corresponding value of composite materials with a solid circular inclusion.

Metamaterial filter design via surrogate optimization

Recently, an increasing research effort has been dedicated to analyse transmission and dispersion properties of periodic metamaterials containing resonators, and to optimize the amplitude of selected acoustic band gaps between consecutive dispersion curves in the Floquet-Bloch spectrum. Potential novel applications of this research are in the design of passive mechanical filters/diodes. The present work proposes a way to interpolate the objective functions in such band gap optimization problems, using Radial Basis Functions. The study is motivated by the high computational effort often needed for an exact evaluation of the original objective functions, when using iterative optimization algorithms. By replacing such functions with surrogate objective functions, well-performing suboptimal solutions can be obtained with a small computational effort. Numerical results demonstrate the feasibility of the approach.

Ultra-broadband, polarization-independent, wide-angle absorption in impedance-matched metamaterials with anti-reflective moth-eye surfaces.

We computationally study periodic impedance-matched metal-dielectric metamaterials and the advantage of imprinting moth-eye surfaces on them. Impedance-matched metamaterials are known to act as strong, polarization-independent, broadband absorbers. However, in the infrared region far from the metal's plasma frequency, the reflection from metal layers dominates over the absorption. Using anti-reflective moth-eye surfaces we show that it is possible to obtain absorption independent of polarization or incidence angle, over an exceptionally broad frequency range from 400 nm to 6 μm.

Theory of the Hall effect in three-dimensional metamaterials

We apply homogenization theory to calculate the effective electric conductivity and Hall coefficient tensor of passive three-dimensionally periodic metamaterials subject to a weak external static homogeneous magnetic field. We not only allow for variations of the conductivity and the Hall coefficient of the constituent material(s) within the metamaterial unit cells, but also for spatial variations of the magnetic permeability. We present four results. First, our findings are consistent with previous numerical calculations for finite-size structures as well as with recent experiments. This provides a sound theoretical justification for describing such metamaterials in terms of effective material parameters. Second, we visualize the cofactor fields appearing in the homogenization integrals. Thereby, we identify those parts of the metamaterial structures which are critical for the observed effective metamaterial parameters, providing a unified view onto various previously introduced single-constituent/multiple-constituent and isotropic/anisotropic architectures, respectively. Third, we suggest a novel three-dimensional non-magnetic metamaterial architecture exhibiting a sign reversal of the effective isotropic Hall coefficient. It is conceptually distinct from the original chainmail-like geometry, for which the sign reversal is based on interlinked rings. Fourth, we discuss two examples for metamaterial architectures comprising magnetic materials: yet another possibility to reverse the sign of the isotropic Hall coefficient and an approach to conceptually break previous bounds for the effective mobility.

Size effects in nonlinear periodic materials exhibiting reversible pattern transformations

This paper focuses on size effects in periodic mechanical metamaterials driven by reversible pattern transformations due to local elastic buckling instabilities in their microstructure. Two distinct loading cases are studied: compression and bending, in which the material exhibits pattern transformation in the whole structure or only partially. The ratio between the height of the specimen and the size of a unit cell is defined as the scale ratio. A family of shifted microstructures, corresponding to all possible arrangements of the microstructure relative to the external boundary, is considered in order to determine the ensemble averaged solution computed for each scale ratio. In the compression case, the top and the bottom edges of the specimens are fully constrained, which introduces boundary layers with restricted pattern transformation. In the bending case, the top and bottom edges are free boundaries resulting in compliant boundary layers, whereas additional size effects emerge from imposed strain gradient. For comparison, the classical homogenization solution is computed and shown to match well with the ensemble averaged numerical solution only for very large scale ratios. For smaller scale ratios, where a size effect dominates, the classical homogenization no longer applies.

A parametric class of composites with a large achievable range of effective elastic properties

In this paper, we study an instance of the G-closure problem for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two isotropic materials. We focus on the case when one material has zero stiffness, i.e., single-material structures with voids. This problem is important, in particular, in the context of designing small-scale structures for metamaterials that can be manufactured using additive fabrication. A range of effective metamaterial properties can be obtained this way using a single base material.We demonstrate that two closely related simple parametric families based on the structure proposed by Sigmund in [26] attain good coverage of the space of isotropic properties satisfying Hashin–Shtrikman bounds. In particular, for positive Poisson’s ratio, we demonstrate that Hashin–Shtrikman bound can be approximated arbitrarily well, within limits imposed by numerical approximation: a strong evidence that these bounds are achievable in this case. For negative Poisson’s ratios, we numerically obtain a bound which we hypothesize to be close to optimal, at least for metamaterials with rotational symmetries of a regular triangle tiling.

Negative refraction in metamaterials based on dielectric spherical particles

Negative refraction (NR) metamaterials are featured with unique physical properties and potential to realize full control of electromagnetic waves, which have attracted much attention since the last decade. However, few researches focus on the realization of three-dimensional dielectric NR metamaterials in optic frequency, and the current design methods need further development. In this paper, a three-dimensional all-dielectric NR metamaterial with two NR bands has been realized based on proper excitation of electric and magnetic multipoles. It is also predicted that the coupling of magnetic dipole and electric dipole can lead to the NR bands in near-infrared frequencies, and NR in the visible frequencies can be achieved by the coupling of magnetic quadrupole and electric dipole. Band structures and equal-frequency surfaces of proposed metamaterial arranged in the periodic cubic lattice are solved by adopting the plane wave expansion method, and then the results verify the existence of these two NR frequency bands in periodic metamaterials. In this way, the characteristic parameters such as transmission and absorption of light in two NR bands are also analyzed. In the meantime, the finite-deference time-domain method is used to intuitively display the phenomenon of NR and investigate the effects of disorder in particle arrangement. Besides, it is found that the proposed metamaterials have fine robustness to the disorder in particle arrangement, and these two NR bands can be tuned by adjusting volume fraction. In brief, this work provides means for preliminary designing, profound analysis and intuitively exhibition of NR metamaterials based on dielectric particles.

Electrodynamic multiple-scattering method for the simulation of optical trapping atop periodic metamaterials

We present a new theoretical tool for simulating optical trapping of nanoparticles in the presence of an arbitrary metamaterial design. The method is based on rigorously solving Maxwell’s equations for the metamaterial via a hybrid discrete-dipole approximation/multiple-scattering technique and direct calculation of the optical force exerted on the nanoparticle by means of the Maxwell stress tensor. We apply the method to the case of a spherical polystyrene probe trapped within the optical landscape created by illuminating of a plasmonic metamaterial consisting of periodically arranged tapered metallic nanopyramids. The developed technique is ideally suited for general optomechanical calculations involving metamaterial designs and can compete with purely numerical methods such as finite-difference or finite-element schemes.

Acoustics of locally bilinear periodic metamaterials

The scope of traditional metamaterials is expanded by analyzing bilinear discontinuities in an otherwise continuous medium. This amplitude independent nonlinearity is sought for its practicality and utility. Wave propagation has to be solved for in the time domain due to the difference in energy transfer from compression to rarefaction across an interface. Various sizes, orientations and shapes of the discontinuities are analyzed on a unit cell level. Periodic chains with the same type of material discontinuity have recently been shown to exhibit a rich dispersion behavior, such as negatively sloped dispersion branches [Titovich (2017), J. Acoust. Soc. Am. 141(5), 3698]. These waves are now investigated in a continuum, where the discontinuity is modelled as displacement-dependent complex impedance relating the interface tractions. The onset of chaotic behavior as well as its effect on absorption is discussed. Also, the ability of such periodic discontinuities to produce nonlinear non-reciprocity is invest...