Behavior Of Metamaterials Research Articles

L-PBF for the production of metallic phononic crystal: design and functional characterization

Vibration abatement often requires the adoption of peculiar solutions and/or foundations. This paper presents an innovative solution to this problem, consisting in a phononic meta-material realized via Laser Powder Bed Fusion (L-PBF) capable to prevent the propagation of vibrations within specific frequency ranges. The integration of this meta-material within existing supporting structures can, therefore, greatly reduce the needing of foundations capable to stop vibrations. After a description of the design procedure of the meta-material that shows how to satisfy the constraints imposed by L-PBF technology, the manufactured sample is described and analyzed to predict its band-gaps. Finally, the theoretical results are compared with experimental measurements. These results show a good agreement between expected and actual meta-material behavior.

Time domain homogenisation of elastic and viscoelastic metamaterials

The mechanical behaviour of metamaterials typically depends on their microstructural configuration and composition, in addition to their relative density. The design of these materials requires extensive experiments or complex finite element models which tend to be numerically demanding. In order to understand, control and optimise the macroscopic mechanical behaviour, in this paper numerical homogenisation is applied to a simple square unit cell with a single inclusion using a combination of elastic and viscoelastic responses on the micro level. Through a systematic analysis of unit cell behaviour with increasingly complex microstructural configurations, it is shown how certain macroscale constitutive laws can be obtained in a controlled and controllable manner.

From rigid to amorphous folding behavior in origami-inspired metamaterials with bistable hinges

The folding behavior of origami-inspired metamaterials is often described by linear rotational springs and rigid faces. However, other folding modes and multistability appears when assuming elastic faces, specially when assuming (non-euclidean) crease patterns in 2D or 3D where a high number of hinges meet at their vertices. Instead, here we study multistability by exploring the use of non-linear material behavior implemented as bistable hinges. By drawing a similitude to atomic crystals, we are able to classify the complex folding behavior that non-linear elastic origami metamaterials undergo, where we identify transitions from rigid to elastic to amorphous behavior upon increasing the strength of the bistability. As a result, our study gives a better understanding and provides a tool to control multistable metamaterials for future applications.

A miniaturized tri-band antenna loaded with d-shaped meta-structures

This paper presents a miniaturised tri-band antenna for WLAN, airport surveillance radar/aviation services, and Wi-MAX systems. The proposed radiator consists of an inset-fed rectangular-shaped radiator and a ground, which is loaded with two different sized 1 × 2 arrays of d-shaped meta-structure (DS-MS). The loading of the ground surface with DS-MSs changes the surface current circulation, lowering the operating frequency and generating additional operating bands. The effective material attributes of the DS-MR are computed to check it’s metamaterial behaviour over stop bands. The developed antenna is unilayer and operates in three bands with centre frequencies of 2.44 GHz, 2.82 GHz, and 3.52 GHz. The total volume of the proposed tri-band radiator is 35 × 25 × 1.6 mm3.

A compact dual-band antenna with an elliptical-shaped meta-resonator array

A planar miniaturised dual-band patch antenna for WLAN and Wi-MAX systems is investigated in this paper. The prospective design is made of an inset-fed square patch radiator and a defected ground plane, which is loaded with a 2 × 2 array of elliptical-shaped-meta-resonator (ES-MR). The loading of ES-MR results in size miniaturisation and dual-band operation. The medium parameters of the ES-MR are calculated to evaluate its metamaterial behaviour, and the antenna operates at 2.46 GHz and 3.50 GHz. The overall footprint of the developed dual-band radiator is 30 × 35 × 1.60 mm3.

The extreme mechanics of viscoelastic metamaterials

Mechanical metamaterials made of flexible building blocks can exhibit a plethora of extreme mechanical responses, such as negative elastic constants, shape-changes, programmability, and memory. To date, dissipation has largely remained overlooked for such flexible metamaterials. As a matter of fact, extensive care has often been devoted in the constitutive materials’ choice to avoid strong dissipative effects. However, in an increasing number of scenarios, where metamaterials are loaded dynamically, dissipation cannot be ignored. In this Research Update, we show that the interplay between mechanical instabilities and viscoelasticity can be crucial and that they can be harnessed to obtain new functionalities. We first show that this interplay is key to understanding the dynamical behavior of flexible dissipative metamaterials that use buckling and snapping as functional mechanisms. We further discuss the new opportunities that spatial patterning of viscoelastic properties offer for the design of mechanical metamaterials with properties that depend on the loading rate.

Compression Deformation Prediction of Chiral Metamaterials: A Compression–Shear Coupling Model

A category of metamaterials consisting of chiral cytosolic elements assembled periodically, in which the introduction of a rotatable annular structure gives metamaterials the ability to deform in compression–shear, has been a focus of research in recent years. In this paper, a compression–shear coupling model is developed to predict the compressive deformation behaviour of chiral metamaterials. This behaviour will be analysed by coupling the rotation of the annular node and the bending characteristics of ligament beam, which are obtained as a function of the length of ligament beam and the angle of rotation at the end of the beam. The shape function of the ligament beam under large deformation is obtained based on the elliptic integral theory; the function characterises the potential relationship between key parameters such as displacement and rotation angle at any point on the ligament beam. By simulating the deformation of cells under uniaxial compression, the reasonableness of the large deformation model of the ligament beam is verified. On this basis, a chiral cell-compression mechanical model considering the ductile deformation of the annular node is established. The compression–shear deformation of two-dimensional planar chiral metamaterials and three-dimensional cylindrical-shell chiral metamaterials was predicted; the offset displacements and torsion angles agreed with the experimental and finite element simulation results with an error of less than 10%. The developed compression–shear coupling model provides a theoretical basis for the design of chiral metamaterials, which meet the need for the precise control of shapes and properties.

Structural periodicity dependent scattering behavior in parity-time symmetric elastic metamaterials

We investigate the effect of structural periodicity on elastic longitudinal and flexural wave propagation in parity-time ($\mathcal{PT}$) symmetric prototypical elastic metamaterial rods and beams. Through theoretical analysis and numerical demonstration, we reveal the link between the observed band structure of infinite periodic $\mathcal{PT}$ symmetric elastic metamaterials and the unique scattering properties of the corresponding finite periodic $\mathcal{PT}$ symmetric systems. In particular, we study the coherent perfect absorber and laser (CPAL). There is an observed periodic-like occurrence of the CPAL formation when varying the cell number in the finite periodic metamaterial that correlates to the band structure of the infinite periodic system. For this, we provide simple equations to estimate the periodicity and the minimum cell number. Using a piezoelectric-aided elastic metamaterial consisting of piezoelectric patches and active circuits, we propose a feasible configuration to realize tunable flexural wave CPALs in a periodic-structured $\mathcal{PT}$ symmetric metamaterial beam, and demonstrate that the CPAL can be induced in the Bragg's bandgap.

Effects of geometry and boundary constraint on the stiffness and negative Poisson's ratio behaviour of auxetic metamaterials under quasi-static and impact loading

Auxetic metamaterials exhibit a negative Poisson's ratio and superior energy dissipation characteristics under dynamic (impact) loading. This makes them attractive candidates for components that provide crash or impact protection (such as crumple zones) in automotive and aerospace applications. However, little prior work on the effect of boundary constraint on the behaviour of these structures exists. Therefore, the primary goal of this investigation is to assess the effect of boundary constraint on the energy-absorbing properties of auxetic metamaterials. Specifically, auxetic metamaterials (lattice structures) were fabricated from stainless steel powders via 3-D laser printing (selective laser melting). Additional structures were printed with constraining walls attached in order to evaluate the effects of boundary constraint on the auxetic behaviour. A comprehensive investigation of the mechanical performance of the structures was then carried out under both quasi-static and dynamic (impact) loading conditions. Poisson's ratio and elastic modulus values were determined from the experimental results and compared with theoretical calculations. Dissipation of vertical forces into the lateral boundaries was confirmed by about 20% less negative Poisson's ratios, for otherwise identical auxetic structures. In addition, dynamic loading simulations have shown that with optimized geometric parameters, auxetic metamaterials are capable absorbing over 90% of the energy of an impact. However, critical overestimation of the energy absorbing abilities of auxetic crash protectors could occur if the effects of lateral constraint are not carefully considered.

CRLH-TL Based Reconfigurable Antennas With Multiple Parameter Reconfigurability

In this communication, two composite right-/left-handed transmission line (CRLH-TL)-based reconfigurable antennas with multiple-parameter reconfiguration capability have been presented. In antenna I, the polarization is switched between circular polarization and linear polarization. In antenna II, a split-ring resonator (SRR) is introduced that is connected with the ground through another p-i-n diode D2. In the D2 OFF-state, the metamaterial behavior of the SRR establishes. Due to negative permeability at the frequency of operation, it produces magnetic coupling with the antenna and the antenna starts radiating at a new band (5.2 GHz), forming dual-band characteristics with circular polarization. Antenna II is capable of providing band/frequency and polarization/band, frequency, and polarization reconfiguration using different ON/OFF combination states of diodes D1 and D2. The antennas are suitable for 2.4/5.2 GHz WLAN and 3.5/3.6 GHz WiMAX applications.

Nonlinear strain gradient and micromorphic one-dimensional elastic continua: Comparison through strong ellipticity conditions

We discuss the strong ellipticity (SE) conditions for strain gradient and micromorphic continua considering them as an enhancement of a simple nonlinearly elastic material called in the following primary material. Recently both models are widely used for description of material behavior of beam-lattice metamaterials which may possess various types of material instabilities. We analyze how a possible loss of SE results in the behavior of enhanced models. We shown that SE conditions for a micromorphic medium is more restrictive than for its gradient counterpart. On the other hand we see that a violation of SE for a primary material affects solutions within enhanced models even if the SE conditions are fulfilled for them.

Inverse metamaterial design combining genetic algorithms with asymptotic homogenization schemes

In the current work, a numerical method for the inverse engineering of metamaterials is elaborated. The method is based on the combination of asymptotic homogenization schemes with genetic algorithms and it makes use of the complete set of parameters contained in the target compliance tensor. As such, it can be used to compute lattice unit-cell patterns that meet target macroscale elastic, shear, Poisson’s ratio and normal to shear strain coupling performances for the first time. The elaborated formulation applies to both constant and variable target relative density metamaterial designs, identifying metamaterial architectures within and beyond orthotropy. Different relevant case-study examples are provided, highlighting the potential of the formulation to capture a wide range of effective metamaterial behaviors. The accuracy of the results is additionally verified through commercial code, dedicated Abaqus finite element models, as well as through experimental testing of 3D-printed, periodic metamaterial samples. The scheme has a substantially low computational cost, so that a wide range of inverse engineering tasks can be performed within a computing time of a few minutes, using regular power, personal computing machines.

A toy model for the effective density of acoustic metamaterials

We propose a simple mechanical system that can be used as a toy model for calculating the effective density of acoustic metamaterials. Through analytical calculations, it gives a better understanding of how the effective density can become negative, when the system responds elastically instead of inertially. We show that this toy model can reproduce, qualitatively, the acoustical behaviour of some real acoustic metamaterials.

Pattern transformation induced waisted post-buckling of perforated cylindrical shells

A comprehensive investigation on the extremely large post-buckling deformation of perforated cylindrical shells is conducted using experiments and verified with an analytical shell model and nonlinear finite element simulations. A “waisted” post-buckling configuration, which is characterized by uniform shrinking in the middle section of the perforated cylindrical shell, is identified. The waisted behavior is attributed to the triggering of a pattern transformation under compressive load that shows special hyperelastic metamaterial characteristics. The load-carrying capacity of waisted post-buckling suffers a sudden drop and then recovers when the holes are completely collapsed and closed. Plenty of design parameters can be utilized to enrich variations of the waisted post-buckling responses. The negative Poisson's ratio induced by pattern transformation plays a key role in forming the waisted post-buckling modes. This special hyperelastic metamaterial behavior can be easily achieved by fixing the boundaries and adjusting the geometric parameters of the shell. By comparing the characteristics of a porous cylindrical shell with those appeared for an equivalent porous panel, it is highlighted that pattern transformation can occur in a thinner porous cylindrical shell without lateral support. The waisted post-buckling modes of a perforated cylindrical shell are stable, and the shell is invulnerable to the progressively increasing applied loads. In comparison, an ordinary cylindrical shell may snap from one mode to another in the post-buckling process. Moreover, we find that some non-closed cylindrical panels can also buckle into the waisted-like modes. These findings can be applied to the construction of functional devices for soft robotics, actuators, and structural protection for facilities, etc.

Stiffness and strength evaluation of lattice-based mechanical metamaterials by decoupled two-scale analysis

There is an emerging class of artificial materials, so-called mechanical metamaterials. By deliberately designing microscopic internal mechanisms, these materials exhibit exotic properties, which distinguish the mechanical metamaterials from natural materials. As additive manufacturing technology has been rapidly developed and its manufacturing quality has been improved, those conceptual artificial materials are ready to fabricate. This paper presents a decoupled two-scale analysis framework to efficiently evaluate the stiffness and strength characteristics of lattice-based mechanical metamaterials. Structural characteristics of lattice-based mechanical metamaterials are effectively captured by accommodating a computational homogenization method to lattice-based structures. In the computational homogenization procedure, a unit cell of the periodically distributed structure is modeled as representative finite elements. Equivalent stiffness properties of the unit cell are calculated based on the computational homogenization procedure. The equivalent structural properties are then used to perform macroscopic structural analysis of lattice-based structures in an effective manner. Similarly, a local/microscopic stress distribution within the periodic lattice unit cell is recovered by transforming macroscopic sectional loads, which are obtained from the macroscopic structural analysis, through a stress amplification matrix. The microscopic stress distribution obtained with the two-scale analysis can be used for strength evaluation. Subsequently, numerical results are validated by comparing them with experimental results providing actual behaviors of lattice-based mechanical metamaterials. This work presents the novel use of the multi-scale analysis scheme combining the computational homogenization method and the stress field transformation method enabling structural evaluations to design mechanical metamaterials with structural integrity. This study also demonstrates the feasibility and capability of the presented approach to effectively predict stiffness and strength characteristics of lattice-based structures.

Formation of quasi-static stop band in a new one-dimensional metamaterial

The main objective of this paper is to propose a new metamaterial capable of generating a quasi-static stop band from zero frequency. The metamaterial is modeled by a lattice system made of mass-in-mass units. The unit cell of the proposed metamaterial contains a resonator connected to bar-spring mechanism embedded in a host mass and also linked to a fixed substrate. The stop band behavior of the new metamaterial is first investigated on basis of a lumped-parameter infinite lattice model. The equations of motion are derived using the Lagrangian approach, and then Bloch’s theorem is used to derive the dispersion relation. Analytical expressions of the stop band edge frequencies are derived in closed-form. The proposed metamaterial is then studied on a finite lattice model to verify the stop band behavior predicted using the infinite lattice model. A closed-form expression of the transmittance is derived using the matrix method. It is shown that there are two frequency regions in the transmittance spectrum of the finite chain in which the amplitude is considerably attenuated which correspond to the stop bands predicted in the dispersion curve of the infinite chain. Finally, a parametric study is performed to investigate the effects of various design parameters of the proposed metamaterial.

An Oval-Square Shaped Split Ring Resonator Based Left-Handed Metamaterial for Satellite Communications and Radar Applications.

Development of satellite and radar applications has been continuously studied to reach the demand in the recent communication technology. In this study, a new oval-square-shaped split-ring resonator with left-handed metamaterial properties was developed for C-band and X-band applications. The proposed metamaterial was fabricated on 9 × 9 × 0.508 mm3 size of Rogers RO4003C substrate. The proposed metamaterial structure was designed and simulated using Computer Simulation Technique (CST) Microwave Studio with the frequency ranging between 0 to 12 GHz. The simulated result of the proposed design indicated dual resonance frequency at 5.52 GHz (C-band) and 8.81 GHz (X-band). Meanwhile, the experimental result of the proposed design demonstrated dual resonance frequency at 5.53 GHz (C-band) and 8.31 GHz (X-band). Therefore, with a slight difference in the dual resonance frequency, the simulated result corresponded to the experimental result. Additionally, the proposed design exhibited the ideal properties of electromagnetic which is left-handed metamaterial (LHM) behavior. Hence, the metamaterial structure is highly recommended for satellite and radar applications.

CPW-fed metamaterial inspired compact multiband antenna for LTE/5G/WLAN communication

Abstract In this work, metamaterial (MTM) inspired a compact CPW-fed antenna with triple operating band is proposed. A rectangular Split Ring Resonator (SRR) is unified in a circular slot of the polygon-shaped radiator in MTM inspired antenna. The antenna exhibits three operating band which are based on metamaterial characteristics of unit cell. The CPW-fed antenna is ensuing 10 dB impedance bandwidth varies from 2.28 to 2.38 GHz, 3.07 to 3.78 GHz, and 5.05 to 7.03 GHz, whereas notch band exist from 2.39 to 3.06 GHz frequency. Metamaterial behaviour leads into the bandwidth enhancement as well as miniaturization in lower operating band with electric length of 0.14λ 0 × 0.21λ 0. The antenna archives the peak gain of 1.49 dB at 2.34 GHz, 2.04 dB at 3.32 GHz, and 4.14 dB at 6.5 GHz frequency. The measured results authenticate the simulated outcomes and consequently the proposed antenna can be pertinent in LTE, WLAN, and 5G communications.

Quasi-static compression and dynamic crushing behaviors of novel hybrid re-entrant auxetic metamaterials with enhanced energy-absorption

Auxetic metamaterials with excellent mechanical properties have attracted considerable attention for use in various applications, especially for energy-absorption. In this work, novel vertical strut combined auxetic metamaterials are proposed to enhance their energy-absorption performances. Specifically, a vertical strut and hexagon combined structure (VSHCS) is developed by overlapping the two convex corners of a hexagonal unit with two concave corners of a vertical strut combined structure (VSCS). The finite element model (FEM) is validated by employing the quasi-static compression experiment of 3D-printed VSCS honeycomb samples. The quasi-static compression and dynamic crushing behaviors of VSHCS are investigated through simulation and theoretical analysis. To clarify the deformation mechanisms, the deformation modes, structure effect, stress-strain curves, and energy-absorption ability are comprehensively examined under different velocities. The VSHCS exhibits a hierarchical deformation mode, corresponding to two-stage stress-strain curves with double-plateau stresses. The results indicate that the VSHCS possesses higher mean plateau stress and specific energy-absorption (SEA) than re-entrant, VSCS, and non-auxetic hexagonal structures. The enhancement can be attributed to the novel structural design, unique two-order deformation modes, and plastic hinge dissipation.

Widening, transition and coalescence of local resonance band gaps in multi-resonator acoustic metamaterials: From unit cells to finite chains

Local resonance band gaps in acoustic metamaterials are widely known for their strong attenuation yet narrow frequency span. The latter limits the practical ability to implement subwavelength band gaps for broadband attenuation and has motivated novel metamaterial designs in recent years. In this paper, we investigate the behavior of acoustic metamaterials where unit cells house multiple resonating elements stacked in different configurations, aimed at instigating a wide array of wave propagation profiles that are otherwise unattainable. The dispersion mechanics of the multi-resonator metamaterials are developed using purely analytical expressions which depict and explain the underlying dynamics of such systems both at the unit cell level as well as the frequency response of their finite realizations. The framework reveals the mechanism behind the transition of the lower and upper band gap bounds in metamaterials with parallel resonators resulting in a significant band gap widening. The analysis also illustrates the ability of metamaterials with dual-periodic super cells to exhibit a range of dispersion transitions culminating in collapsing solutions of acoustic and optical bands, enabling a coalescence of local resonance band gaps, vanishing resonances, and a number of intriguing scenarios in between.