Response Of Metamaterials Research Articles

Influence of right-angled elbows on the modal response of labyrinthine meta-materials

This article studies how right-angled 90 degrees elbows modify the resonance properties of labyrinths. The resonance properties are evaluated by considering the dispersion curves obtained by performing a band structure calculation. The response to the bandgaps width and positions in the presence of one, then two and finally a large number of elbows has then been studied to quantify the influence of the path tortuosity on the modal response of the labyrinth’s geometry. The end-goal is to provide the elementary understanding tools leading to more refined predictive models for labyrinthine acoustic metamaterials (LAM).

Novel metamaterial structures with negative thermal expansion and tunable mechanical properties

The thermal expansion and stiffness characteristics are significant in determining the responses of lightweight mechanical metamaterials in a thermal environment. This paper proposed a novel trapezoid unit with negative thermal expansion (NTE) by three conventional materials with positive thermal expansion, and constructed a series of lightweight metamaterials by sharing edges and sharing vertexes. The effective linear coefficients of thermal expansion (CTE) of these metamaterial structures are theoretically explored by considering axial and bending deformations. Based on Euler beam theory, the effective linear elastic stiffnesses of these metamaterials are given accurately by the stiffness matrix method. The accuracy of the theoretical effective CTE and stiffness is well verified by numerical modeling. The effective linear CTE, elastic stiffness, and Poisson's ratio of these metamaterials can be programmable by controlling geometrical parameters and material properties. The NTE effect can be achieved in ET, EQ, EH, and VT metamaterials due to the presence of re-entrant structures, in which the ET metamaterial can fulfill the maximum magnitude NTE. The NTE and negative Poisson's ratio can simultaneously be realized in EQ metamaterial. Significantly, a broader range of CTE from negative to positive values can be fulfilled in these metamaterials compared with the conventional triangle unit. Furthermore, the high specific stiffness with extremely low thermal stress can be obtained in EQ, VT, and VH metamaterials, which benefits the stability controlling and enhancing natural frequencies of structures in a thermal environment.

Elastic stability of a lattice of cross-braced shear deformable beams

A plane metamaterial made up of a periodic square grid of shear deformable beams has been braced by crossing cables. This coupling, widely adopted in structural engineering, is here applied with the aim of enhancing the stability performance of a periodic material. Under suitable assumptions, analytical solutions for a rich variety of critical modes and the stability domain are determined by the Bloch wave approach and the effectiveness of our analytical results has been verified by numerical simulations. Furthermore, the experimental response of a specimen, in which hierarchical beams composed by lower order elements are modeled as equivalent shear deformable beams, has shown a satisfactory agreement with our analytical solutions. We argue that our analytical model can be efficiently used to tailor the buckling response of various new metamaterials under general plane stress states.

Defect sensitivity mitigation in the compressive mechanical response of two-phase lattice metamaterials

Engineered materials commonly referred to as metamaterials are materials that offer appealing features such as customisable stiffness and strength, auxetic behaviour and energy absorption. This work focuses on the classical 2D lattice metamaterial configuration with regular triangular unit cell. A combination of two dissimilar materials is employed in the design process: the primary material that constitutes the lattice structure is composed of thermoplastic polyurethane (TPU), while an incompressible silicone serves as the secondary material, completely filling selected lattice cells. In order to investigate the mechanical response of such lattices to intrinsic defects, geometric imperfections are intentionally introduced. Three distinct types of geometric anomalies, i.e. curvature of some elements, lateral shift of some lattice nodes, and reduced beam thickness, are randomly introduced. Additively manufactured perfect and defective lattices are subjected to compressive loading for both empty and silicone filled cases. Overall, the results reveal that the lattices show a significant improvement with the assumed reinforcing filling pattern, helping to prevent the buckling of the beams under compression and enhancing the load bearing capacity of the structure at higher deformations. Finite element (FE) analyses are performed to validate the experimental results, demonstrating how the filling pattern enhances the mechanical response of the lattices.

Analytical characterization of the dynamic response of viscoelastic metamaterials

The band-gap frequencies of elastic metamaterials are ideally determined by a metamaterial architecture; yet, in practical situations, are often dependent on the material damping in their constituent(s). The analysis of viscoelastic metamaterials requires however substantial computational resources and, except for oversimplified cases, is solely done numerically. Here, we propose an analytical procedure based on the spectral element method (SEM) to analyze bulk metamaterials with viscoelastic damping as continuous systems. Due to intrinsic limitations of the SEM to deal with complex geometries, we develop a procedure to build an approximate model based on SEM frame elements. The viscoelastic behavior is included by means of complex viscoelasticity moduli expressed by the generalized Maxwell mechanical model. We validate this approach by analyzing metamaterial plates and verify the findings experimentally. We demonstrate that our SEM-based analytical model can accurately capture wave transmission around the first band-gap frequencies. Therefore, our extension of the SEM approach to analyze three-dimensional meta-structures is promising to characterize wave propagation in realistic viscoelastic structures (with any type of linear viscoelastic behavior) in an accurate and computationally efficient way.

Enhanced Optical Activity with Zero Circular Dichroism in a Dielectric Chiral Metasurface

AbstractEnhanced chiral optical responses of metamaterials have widespread applications in chiral biosensor and polarization optics. Metamaterials with intrinsic chirality are commonly composed of complicated 3D structures, which leads to significant fabrication challenges. Recent works involving planar chiral metasurfaces have demonstrated chiral optical response by symmetry breaking, but the intrinsic optical chirality at normal incidence is usually weak. Here, a dielectric chiral metasurface is designed and fabricated, and its strong intrinsic optical chirality in visible spectrum is experimentally demonstrated. Particularly, giant optical activity with zero circular dichroism can be obtained, implying that linear polarization of the incident light passing through the metasurface can be rotated. A phenomenological model is proposed to explain the chiral optical response of the metasurface based on the superposition of two chiral optical resonances in opposite handedness. The multipole decomposition of the electric fields corroborates how the high‐order multipoles are related to the chiral optical response. These results enable the development of flat compact devices to manipulate the polarization of light flexibly.

Soft Mechanical Metamaterials with Transformable Topology Protected by Stress Caching.

Maxwell lattices possess distinct topological states that feature mechanically polarized edge behaviors and asymmetric dynamic responses protected by the topology of their phonon bands. Until now, demonstrations of non-trivial topological behaviors from Maxwell lattices have been limited to fixed configurations or have achieved reconfigurability using mechanical linkages. Here, a monolithic transformable topological mechanical metamaterial is introduced in the form of a generalized kagome lattice made from a shape memory polymer (SMP). It is capable of reversibly exploring topologically distinct phases of the non-trivial phase space via a kinematic strategy that converts sparse mechanical inputs at free edge pairs into a biaxial, global transformation that switches its topological state. All configurations are stable in the absence of confinement or a continuous mechanical input. Its topologically-protected, polarized mechanical edge stiffness is robust against broken hinges or conformational defects. More importantly, it shows that the phase transition of SMPs that modulate chain mobility, can effectively shield a dynamic metamaterial's topological response from its own kinematic stress history, referred to as "stress caching". This work provides a blueprint for monolithic transformable mechanical metamaterials with topological mechanical behavior that is robust against defects and disorder while circumventing their vulnerability to stored elastic energy, which will find applications in switchable acoustic diodes and tunable vibration dampers orisolators.

Peridynamics modeling of cellular elastomeric metamaterials: Application to wave isolation

We investigate how embedded geometrical imperfections can be designed to obtain significant reduction in wave amplitude and large band gap in periodic cellular metamaterials. A finite deformation peridynamics (PD) theory is developed to predict the static and dynamic responses of elastomeric metamaterials. Periodically structured cracks and volumetric geometrical imperfections, e.g., circular and elliptical holes, are embedded in elastomeric materials. Elastic wave propagation through these structured materials is studied by performing numerical simulations using PD. Two main mechanisms are exploited to enhance the energy absorption capacity compared to conventional metamaterials, viz. reflection of wave from crack surfaces and energy absorption due to local elastic instability of the cell walls. Slightly compressible neo-Hookean material model is considered, and plane strain condition is assumed. Nonlinear PD equations for quasi-static condition are solved using the Newton-Raphson method. The present model is validated against finite element solutions considering deformation of a solid elastomeric body subjected to tensile load. The model is also validated with experimental results considering rupture of a double notched elastomeric specimen assuming plane stress condition. PD predictions of nominal stress vs. strain for configurations with holes under quasi-static condition are validated against the experimental observations and numerical simulations through the finite element software ANSYS®. Newmark-beta method is employed to solve the PD equation of motion. At every time step, Newton-Raphson method is used, and convergence is established. The dynamic response obtained from the PD model is validated against finite element solutions using ANSYS® for a solid body. Various novel geometries combining cracks and holes are systematically developed guided by prediction of energy absorption capacity and band gap characteristics through numerical simulations. Wave propagation through these configurations is examined and the effects of microstructure topology on band gap and amplitude reduction are shown. Significant reduction of wave amplitude and large band gap demonstrate remarkable efficacy of the present proposal.

Computational analysis of sub-wavelength scatterers exhibiting electro-momentum coupling

The macroscopic response of acoustic metamaterials with sub-wavelength asymmetry may be described by the so-called Willis constitutive relations, which include coupling between the acoustic pressure and momentum density. One method to describe the behavior of acoustically-small, Willis material building-blocks is via a polarizability matrix relating the monopole and dipole scattering moments to the local pressure and velocity fields, providing a metric for the design of microscale structures leading to macroscopically observable Willis coupling. Additionally, heterogeneous, piezoelectric media with sub-wavelength asymmetry have been shown to exhibit coupling between momentum density and electric fields, a material response known as electro-momentum coupling. Recent studies have generalized the polarizability concept to include coupling between acoustic and electromagnetic fields for theoretical point scatterers in two and three dimensions, and derived analytical bounds based on conservation of energy. In this work, we computationally study the coupled, acousto-electromagnetic polarizability of heterogeneous, piezoelectric scatterers and assess the practicability of achieving electro-momentum coupling in physically realizable geometries. Numerical results are obtained using a custom finite element approach, which includes the fully electrodynamic nature of the system and accounts for large differences in the characteristic wavelengths of the acoustic and electromagnetic fields. [This work was supported by DARPA.]

Evanescent waves in hybrid poroelastic metamaterials with interface effects

The propagation of evanescent waves in hybrid poroelastic metamaterials is investigated by considering interface effects. Hybrid metamaterials consist of a single-phased (acoustic or elastic) medium and a poroelastic medium. To establish the finite element model of elastic/poroelastic and fluid/poroelastic interfaces, weak integral forms of wave equations for elastic, fluid, and poroelastic media and boundary conditions at the interfaces between different media are first given. Next, the expressions for displacement and pressure in the frame of Bloch’s theorem are substituted into the dynamical equations to obtain general forms suitable for periodic metamaterials, from which the complex band structure and the frequency response of hybrid metamaterials are calculated. The influence of geometrical and material parameters, as well as the viscosity of the pore fluid on the propagation of elastic waves are discussed. The results and discussions show that flat bands and narrow locally resonant band gaps appear for elastic/poroelastic metamaterials. A quasi-resonance Bragg band gap is formed in the case of an elastic inclusion in a poroelastic matrix. Furthermore, a transition from an avoided crossing to a wave-number band gap is obtained by adjusting the geometrical and material parameters of the elastic inclusion. For the case of fluid inclusion in a poroelastic matrix with the open-pore interface, a cut-off frequency for the fast longitudinal wave is observed. However, only an avoided crossing is produced for the sealed-pore interface. For both cases, the phase velocity of the shear vertical (SV) wave decreases faster than that of the slow longitudinal wave as the radius of the inclusion increases. When the viscosity of the pore fluid is considered for elastic inclusion in a poroelastic matrix, the transmission dip at the ‘quasi-resonance Bragg’ band gap disappears. However, the transmission dip in the locally resonant band gap of the SV wave becomes slightly shallower and smoother than in the inviscid case. This study is relevant to practical applications of hybrid single-phased and poroelastic metamaterials, e.g., for coastal engineering and civil engineering.

Effect of geometry, anisotropy and composition on the third-order optical nonlinearities of multilayer hyperbolic metamaterials -INVITED

Quantum technologies require advanced optical metamaterials whose properties can be tailored and controlled as desired. Hyperbolic metamaterials have great potential for applications in nonlinear nanophoton-ics, such as all-optical switching, optical limiting, mode-locking and optical sensing. In this work, we show how to obtain strong third-order optical nonlinearities in hyperbolic multilayers exploiting the effect of bulk plas-mon polaritons. We demonstrate the tunability of these properties with angle and polarization, and we propose a model to predict them. We evidence the enhancement of the nonlinear response in low-loss metamaterials.

Symmetrization of Mechanical Response in Fibrous Metamaterials through Micro-Shear Deformability

The basic concept of this study consists of the investigation of symmetrization of the mechanical response in extension and compression for fibrous metamaterials endowed with a symmetric microstructure relative to the axial direction. It is known that generally, this response is non-symmetric due to the different deformation mechanisms activated in the two tests. If a further deformation mechanism based on the micro-shearing of connective elements is taken into account, the global mechanical response is observed to be symmetric for given sets of stiffnesses. The studied problem is addressed with the help of numerical simulations.

Maximizing the electromagnetic chirality of thin metallic nanowires at optical frequencies

Electromagnetic waves impinging on three-dimensional helical metallic metamaterials have been shown to exhibit chiral effects of large magnitude both theoretically and in experimental realizations. Chirality here describes different responses of scatterers, materials, or metamaterials to left and right circularly polarized electromagnetic waves. These differences can be quantified in terms of electromagnetic chirality measures. In this work we consider the optimal design of thin metallic free-form nanowires that possess measures of electromagnetic chirality as large as fundamentally possible. We focus on optical frequencies and use a gradient based optimization scheme to determine the optimal shape of highly chiral thin silver and gold nanowires. The electromagnetic chirality measures of our optimized nanowires exceed that of traditional metallic helices. Therefore, these should be well suited as building blocks of novel metamaterials with an increased chiral response. We discuss a series of numerical examples, and we evaluate the performance of different optimized designs.

Humidity-induced direct modification of the optical response of plasmonic nanorod metamaterials

Plasmonic nanorod metamaterials are often used as a high-performance optical sensing platform for the detection of biochemical and gas species. Here, we investigate the effect of environmental humidity on their optical response. Due to the high refractive index sensitivity, a significant change in the transmission is observed with ΔT/T reaching values of more than 5% when the relative humidity is changed from 11% to 75%. This is the result of the condensation of water molecules on a rough surface of the gold nanorods. This finding reveals the importance of protecting plasmonic nanostructures from relative humidity variations in many practical applications. By coating the nanorods with a monolayer of poly-L-histidine, the fractional change of transmission is doubled due to the hydrophilic property of the monolayer, which can be used for the development of high-sensitivity relative humidity and dew condensation sensors.

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.

Frictional instability: A nonlinear mechanism to control shear wave responses in rough contact-based metamaterials

Incorporating nonlinearity in periodic media not only enables enriched wave dynamics but also allows passive tunability of the wave responses. However, studies so far have been mostly focused on nonlinear mechanisms and responses of longitudinal wave propagation whereas shear propagation in the presence of strong nonlinearity is yet to be fully understood. In this talk, we study shear wave propagation through metamaterials with rough contacts including friction. The roughness of contacting surfaces results in structural instability causing the contacts to switch between different regimes—stick, partial slip, and gross slip—giving rise to strong nonlinearity. Moreover, due to the presence of friction, the contacts exhibit hysteretic nonlinearity, i.e., history-dependent response. In this study, we first experimentally evaluate the frictional properties of rough contacts by measuring high-frequency friction hysteresis loops. Then, we develop metamaterial with a periodic arrangement of these rough contacts and use the obtained frictional properties to numerically study nonlinear shear wave signatures. We evaluate higher harmonic generation and demonstrate how they can be tuned through excitation wave amplitude, external precompression, and surface roughness. These fundamental understandings can open new avenues for designing tailored material with memory-dependent nonlinearity for controlling shear wave propagation.

Data enhanced iterative few-sample learning algorithm-based inverse design of 2D programmable chiral metamaterials

Abstract A data enhanced iterative few-sample (DEIFS) algorithm is proposed to achieve the accurate and efficient inverse design of multi-shaped 2D chiral metamaterials. Specifically, three categories of 2D diffractive chiral structures with different geometrical parameters, including widths, separation spaces, bridge lengths, and gold lengths are studied utilising both the conventional rigorous coupled wave analysis (RCWA) approach and DEIFS algorithm, with the former approach assisting the training process for the latter. The DEIFS algorithm can be divided into two main stages, namely data enhancement and iterations. Firstly, some “pseudo data” are generated by a forward prediction network that can efficiently predict the circular dichroism (CD) response of 2D diffractive chiral metamaterials to reinforce the dataset after necessary denoising. Then, the algorithm uses the CD spectra and the predictions of parameters with smaller errors iteratively to achieve accurate values of the remaining parameters. Meanwhile, according to the impact of geometric parameters on the chiroptical response, a new functionality is added to interpret the experimental results of DEIFS algorithm from the perspective of data, improving the interpretability of the DEIFS. In this way, the DEIFS algorithm replaces the time-consuming iterative optimization process with a faster and simpler approach that achieves accurate inverse design with dataset whose amount is at least one to two orders of magnitude less than most previous deep learning methods, reducing the dependence on simulated spectra. Furthermore, the fast inverse design of multiple shaped metamaterials allows for different light manipulation, demonstrating excellent potentials in applications of optical coding and information processing. This work belongs to one of the first attempts to thoroughly characterize the flexibility, interpretability, and generalization ability of DEIFS algorithm in studying various chiroptical effects in metamaterials and accelerating the inverse design of hypersensitive photonic devices.

Quasi-static crushing response of a novel 3D re-entrant circular auxetic metamaterial

Auxetic metamaterials have numerous excellent characteristics, such as low mass density, high specific stiffness/ strength and high impact resistance, triggering many potential applications in engineering fields. In this work, we propose a new type of three-dimensional (3D) architectured re-entrant circular (REC) auxetic metamaterial by orthogonally overlapping the two-dimensional (2D) REC honeycomb. Crushing responses of the 3D REC metamaterial under quasi-static compression load were investigated through experimental tests and numerical simulations. The 3D REC sample was additively manufactured and tested under uniaxial quasi-static compression. Experimental and numerical results revealed that the 3D REC sample showed an “X” deformation mode, and fracture failures occurred at the joints of horizontal straight and sloped arc struts. Meanwhile, the numerical results have good agreements with the experimental results in terms of deformation mode, failure mechanism and crushing force. In addition, we investigated the effects of cell number, geometric parameters and friction coefficient on the deformation mode, crushing stress, specific energy absorption (SEA) and Poisson’s ratio of the REC metamaterials. Finally, the proposed metamaterial was compared with 2D REC honeycomb and 3D re-entrant (RE) structure under the condition of ensuring the same relative density. The numerical results demonstrated that the SEA value of 3D REC metamaterial is 7.41 times and 1.27 times that of 2D REC honeycomb and 3D RE structure respectively, which means that the three-dimensional design has better energy absorption capacity.

The substrate effect on optical response of plasmonic metamaterials

The substrate effect on optical response of plasmonic metamaterials

Bio-inspired auxetic mechanical metamaterials evolved from rotating squares unit

This work investigates the mechanical response of bio-inspired titanium mechanical metamaterials with negative Poisson's ratio evolved from rotating squares unit. The systems were designed and optimized using finite element analysis, with peculiar focus on the shape profile at the interconnection regions of the rotating units. The proposed solution consists of a combined auxetic rotating/chiral architecture with enhanced mechanical and topological properties which exhibits a 3% of global elastic strain of the structure and a Poisson's ratio equal to −0.94. Numerical results are in good agreement with those obtained from experimental tests on a 3D printed Onyx prototype. We also examined the effect on the structural response of the metamaterial subject to off-axis mechanical conditions revealing the strong correlation to the geometrically-related anti-tetrachiral honeycombs. The work confirms the great potential of biologically inspired auxetic metamaterials, which can be designed to obtain tailored mechanical properties while improving the elastic strains capabilities of the system.