Metamaterial Sheet Research Articles

A lightweight and transparent acoustic metamaterial sheet with designed structures for sound insulation applications

Normal sound insulation materials such as metal plates and rubber sheets follow the mass law. According to the mass law, a weight increase of sound insulators leads to high sound insulation. Therefore, novel lightweight and high-performance materials have been required in various fields such as mobility and electronics. We developed lightweight and transparent acoustic metamaterial sheets having blocklike weights with rodlike or cylindrical shapes periodically arranged on thin films. Upon sound incidence at a target frequency, the heavier weights and the lighter film cooperatively vibrate in opposite phase and with the same amplitude. The transmitted sound waves through those parts cancel each other out owing to the wave interference. As a result, the acoustic metamaterial sheets show high sound insulation performance beyond the mass law limit at the target frequencies. In this study, we report the structural design, sound insulation properties and mechanisms, and application of acoustic metamaterial sheets.

Development of Acoustic Metamaterial Sheets with Two-Dimensional Array of Hollow Local Resonators

Novel practical acoustic metamaterial sheets with hollow local resonators that can be processed with simple integral molding have been developed. This acoustic metamaterial is a variant of the acoustic metamaterial sheet reported by our group in 2021, which consists of two-dimensionally connected non-hollow-shaped stubs embedded with metal weights. Each hollow-shaped stub can work as a local resonator using the vibration mode of a circular membrane. This acoustic metamaterial can handle lower frequencies even with smaller and lighter stubs compared to those with the non-hollow-shaped stubs we previously reported. It has a particular advantage when used for objects with limited space and weight. It is also possible to control the resonant frequency by altering the material properties or adjusting the shape and size of the stub. It has been experimentally shown that significant sound insulation performance exceeding the mass law can be obtained around the resonant frequencies of the hollow stubs. We show the results of finite element method simulations, modal vibration testing, and transmission loss measurements.

Design of a Wideband Flower-like Shape Metamaterial Reflectarray Antenna

In this paper, a planar reflectarray antenna is designed. The designed structure consists of new types of metamaterial unit cells. Two different flower-like shaped unit cells were studied at the center frequency of 12.5 GHz. The reflectarray contains multi cells with varying sizes of flowers. A metal plate and an air gap layer are placed behind the metamaterial sheet. A standard Ku band horn antenna feeds the structure. The F/D ratio is unity for the designed reflect array. Compared to previous reflectarray antennas, the designed reflect array consists of a limited number of cells, i.e. 121. Also, a new method without any try-and-error process is presented. The width of the designed reflector is so compact. This proposed method can be used for a reflectarray antenna with gain in the range of 20 to 30dBi with acceptable radiation efficiency. The CST software is performed to simulate and optimize the proposed structure. There is a good agreement between simulation and measurement results.

Curvature screening in draped mechanical metamaterial sheets.

We develop a framework to understand the mechanics of metamaterial sheets on curved surfaces. Here we have constructed a continuum elastic theory of mechanical metamaterials by introducing an auxiliary, scalar gauge-like field that absorbs the strain along the soft mode and projects out the stiff ones. We propose a general form of the elastic energy of a mechanism based metamaterial sheet and specialize to the cases of dilational metamaterials and shear metamaterials conforming to positively and negatively curved substrates in the Föppl-Von Kármán limit of small strains. We perform numerical simulations of these systems and obtain good agreement with our analytical predictions. This work provides a framework that can be easily extended to explore non-linear soft modes in metamaterial elasticity in future.

Flexible Metamaterial Wrap for Improved Head Imaging at 3 T MRI With Low-Cost and Easy Fabrication Method.

Magnetic resonance imaging (MRI) requires spatial uniformity of the radiofrequency (RF) field inside the subject for maximum signal-to-noise ratio (SNR) and image contrast. Bulky high permittivity dielectric pads (HPDPs) focus magnetic fields into the region of interest (ROI) and increase RF field uniformity when placed between the patient and RF coils in the MR scanner. Metamaterials could replace HPDPs and reduce system bulkiness, but those in the literature often require a complicated fabrication process and cannot conform to patient body shape. Proposed is a flexible metamaterial for brain imaging made with a scalable fabrication process using conductive paint and a plastic laminate substrate. The effects of single and double-sided placement of the metamaterial around a human head phantom were investigated in a 3 T scanner. When two metamaterial sheets were wrapped around a head phantom (double-sided placement), the total average signal in the resulting image increased by 10.14% compared to placing a single metamaterial sheet underneath the phantom (single-sided placement). The difference between the maximum and minimum signal intensity values decreased by 57% in six different ROIs with double-sided placement compared to single-sided placement.

Programmable shape-morphing of rose-shaped mechanical metamaterials

Shape morphing is one of the most attractive functionalities of materials that are desired in many applications, including robotic grippers, medical stents, wearable electronics, and so on. Shape morphing can be implemented by using mechanical metamaterials that combine building blocks with properly designed mechanical or material properties. The design approaches are, however, mostly ad hoc or require materials with special properties. This work proposes two automated design strategies for programmable shape morphing and validates them on structures 3D-printed from a widely available commercial Stereolithography Durable resin. We proposed a so-called rose-shaped metamaterial with reduced stress concentration due to the absence of sharp corners and with a large range of tailorable Poisson’s ratios, from −0.5 to 0.9, governed by a single design parameter. We programmed the shape of the rose-shaped metamaterial sheets aiming at high shape comfortability or uniform effective stiffness. The shape-morphing performance is demonstrated in the linear (0.1% strain) and non-linear (20% strain) deformation regimes, and it agrees well with the tensile test results. Our findings show the potential to develop complex practical metamaterial structures at comparatively low costs.

A Solution for the Plane Wave Diffraction by the Discontinuity Between Two Co-Planar Metamaterial Sheets

A high-frequency approach is described to investigate the scattering by a junction between double negative metamaterial (DNG MTM) sheets. These last are lit by an incident plane wave and have same thickness, but different electric and magnetic parameters, thus assuring discontinuities of reflected and transmitted fields across the junction. The proposed methodology permits to evaluate the diffraction contribution as the sum of two independent terms arising from the scattering process including electric and magnetic equivalent sources under the physical optics (PO) approximation. The formulation of this wave contribution permits its use in the enclosure of the uniform geometrical theory of diffraction (UTD). Useful approximations and integral representations are adopted together with asymptotic evaluations to obtain the diffraction matrix elements. Accordingly, these last account for convenient reference systems, the approximated equivalent currents, and the typical function of the UTD. A full-wave numerical tool is exploited to assess the correctness of the proposed formulation.

A practically designed acoustic metamaterial sheet with two-dimensional connection of local resonators for sound insulation applications

A novel practical design of sheet-like acoustic metamaterials is described, which comprise a two-dimensional array of mutually connected cylindrical stubs with embedded metallic weights that can be processed with a simple integral molding. We investigate the elastic wave band dispersion of the acoustic metamaterial sheets to design the connected structure of the stubs so that each stub can work as spring–mass local resonators to open the out-of-plane acoustic bandgaps. For properly integrated materials, remarkable noise insulation performance over the mass law at the resonant frequencies is experimentally demonstrated. The sound insulation mechanism is numerically analyzed in association with the sound fields, the vibrational fields, and the dynamic effective mass using the finite element method by coupling the structures with acoustics. Furthermore, we show that the insulation frequency is tunable over a wide range of frequency by designing the physical and structural parameters of the resonator. The practically designed acoustic metamaterial sheets will pave the way for industrial use of acoustic metamaterials as advanced lightweight and compact sound insulators that can be tailored to meet individual needs on problems related to noise.

Achieving selective snapping-back and enhanced hysteresis in soft mechanical metamaterials via fiber reinforcement

When a soft mechanical metamaterial, consisting of a regular array of representative volume elements (RVEs), is stressed up to a large strain, the delicately tailored behavior of the RVE does not prevail in the metamaterial due to the boundary effect and manufacturing imperfections. A metamaterial sheet comprising RVEs designed for snapping-back behavior exhibits random snapping-through instability when uniaxially stretched. We conceptualize that loss of representativeness of RVE can be avoided by introducing fiber reinforcement to regulate boundary conditions. Through a combination of experiments and numerical simulation, we demonstrate that fiber reinforcements tune behavior of a metamaterial sheet from random snapping-through to sequential and even selective snapping-back instability by introducing small structural variations. Ideal snapping-back instability, characterized by sharp variations of forces in both loading and unloading processes, is captured, while the latter is typically hard to observe in real experiments. Enhanced energy dissipation rate from 25.3% for the case without fiber to 46.4% for the case with fiber-reinforcement is recorded in experiments, when the metamaterial sheet is stretched up to 200% and then released to restore its original length.

Metamaterial Magnetic Sheet at 3.7-T MRI for Animal Imaging

Animal models have been utilized for many decades to examine human diseases and symptoms via magnetic resonance imaging (MRI) techniques. To avoid the fatal effects of the strong static magnetic field (B0) when imaging the mouse brain at higher Tesla values in MRI, i.e., 7-T, we propose a compact metamaterial magnetic sheet which can improve the image resolution for simulation of the mouse brain even at lower Tesla values in MRI systems. The magnetic sheet operates at 3.7-T MRI working frequency and provides a passband within its interfaces to restore the formation of scattering of an evanescent radio-frequency (RF) field radiating from the MRI gradient coils towards the sheet. We show in the optimized simulated test bed setup that the magnetic sheet localizes and adjusts the response of the evanescent RF field and improves the transient transverse magnetic field B1 and signal-to-noise ratio at the designated region of interest, i.e., mouse brain (Mb), where B1 at the mouse brain is the response of the static magnetic field B0 generated by the magnetic resonance gradient coils. The unique concept proposed here is that negative permeability (−μ) controls the metamaterial magnetic sheet to improve image resolution inside the human brain without increasing B0 intensity at the brain, in order to avoid thermal heating of the brain tissues.

Dome-Patterned Metamaterial Sheets.

The properties of conventional materials result from the arrangement of and the interaction between atoms at the nanoscale. Metamaterials have shifted this paradigm by offering property control through structural design at the mesoscale, thus broadening the design space beyond the limits of traditional materials. A family of mechanical metamaterials consisting of soft sheets featuring a patterned array of reconfigurable bistable domes is reported here. The domes in this metamaterial architecture can be reversibly inverted at the local scale to generate programmable multistable shapes and tunable mechanical responses at the global scale. By 3D printing a robotic gripper with energy‐storing skin and a structure that can memorize and compute spatially‐distributed mechanical signals, it is shown that these metamaterials are an attractive platform for novel mechanologic concepts and open new design opportunities for structures used in robotics, architecture, and biomedical applications.

Mechanics of axisymmetric sheets of interlocking and slidable rods

In this work, we study the mechanics of metamaterial sheets inspired by the pellicle of Euglenids. They are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of these structures using the special Cosserat theory of rods and by assuming axisymmetric deformations of the tubular assembly. Through an asymptotic expansion, we investigate both structures that comprise a discrete number of rods and the limit case of a sheet composed by infinitely many rods. We apply our theoretical framework to investigate the stability of these structures in the presence of an axial load. Through a linear analysis, we compute the critical buckling force for both the discrete and the continuous case. For the latter, we also perform a numerical post-buckling analysis, studying the non-linear evolution of the bifurcation through finite elements simulations.

Novel origami-inspired metamaterials: Design, mechanical testing and finite element modelling

Two novel, origami-inspired, metamaterials were designed, mechanically tested, and modelled. One novel origami model was folded using a triangular based crease pattern and the other was folded using a rectangular based crease pattern. The origami-inspired metamaterial sheets were fabricated from polylactic acid using fused deposition additive manufacturing. Several configurations, parameterized by varying the fold angle, were mechanically tested under compression and impact loads. It was found that the specific elastic compression modulus of these novel designs was higher, ranging from 594 MPa/kg to 926 MPa/kg, than existing origami-inspired structures made based on the popular Ron-Resch design, which had specific elastic compression moduli between 15 MPa/kg to 365 MPa/kg. A finite element model further analysed the stress distribution of the core structures under compression loads. The impact testing results showed that the pattern of the tessellated cores affected the amount of impact force transferred through the samples, whereas the fold angle of the origami-inspired design had little impact on the results. The rectangular structure was shown to transfer approximately 50–75% of the force transferred by the triangular structure under impact loads.

Highly stretchable two-dimensional auxetic metamaterial sheets fabricated via direct-laser cutting

The design and production of multifunctional materials possessing tailored mechanical properties and specialized characteristics is a major theme in modern materials science, particularly for implementation in high-end applications in the biomedical and electronics industry. In this work, a number of metamaterials with perforated architectures possessing the ability to exhibit a plethora of 2D auxetic responses with negative Poisson's ratios ranging from quasi-zero to large negative values (lower than −3.5), stiffnesses, stretchability and surface coverage properties were manufactured. These systems were produced through the introduction of microstructural cuts in a rubber sheet using direct laser cutting, and analysed using a dual approach involving experimental tests and Finite Element Analysis. In addition to examining the mechanical properties of the perforated metamaterials, the influence of edge effects and material thickness on the deformation behaviour of these systems were investigated, with re-entrant systems shown to possess anomalous deformation profiles which are heavily dominated by the boundary regions. These findings highlight the effectiveness of this method for the fabrication of auxetic metamaterial sheets as well as the large variety of mechanical properties, deformation mechanisms and load responses which may be obtained through what may be effectively described as simply the introduction of patterned cuts in a thin sheet.

Tunable shear stiffness in a metamaterial sheet

In this paper a metamaterial sheet constituted by a periodic pattern of square tensegrity cells (T-bar) subjected to a uniform equibiaxial pressure is studied. In particular, a minimal mass lattice is analytical determined by imposing stability and material failure conditions. Interestingly, the shear stiffness of this optimized lattice is very small in comparison to the other moduli and exhibits a linear dependence on the applied load. This behavior suggests the interesting possibility of tailoring new materials with force tunable shear modulus.

Core Concept: Mechanical metamaterials bend the rules of everyday physics.

Chiara Daraio played for Italy’s junior national basketball team in the 1990s. But when a Swiss running-shoe maker called her up in 2015, it wasn’t to talk about her athletic talents. Mechanical metamaterials, such as this Islamic-art–inspired metamaterial sheet, can pop into new configurations when stretched. Image courtesy of Ahmad Rafsanjani and Damiano Pasini (McGill University, Montreal). The company, called On, was looking for new ways to cushion its clients’ feet by using 3D printing. On had heard about some strange materials Daraio and like-minded researchers had been fabricating in their labs: weird stuff that stretches and squishes in counterintuitive ways. “The sports equipment industry is relatively quick on the uptake,” says Daraio, a professor of mechanical engineering and applied physics at Caltech. “It has been proactive in trying to use these materials.” The soles on Nike’s recent line, Free footwear, offer an illustration. The bottoms of these sneakers don’t look particularly special, just polymer cut into triangles. But the shapes are informed by science. Every time wearers take a step, their foot widens from the impact, stretching the shoes. Nike’s sole responds by both widening and lengthening, to help absorb impact. That shouldn’t happen. Think of a rubber band pulled outward between your fingers; it narrows in the middle. Soft materials stretched wider should shrink in length. But the shoes exhibit bizarre behavior, thanks to materials made of simple patterns of repeating geometric shapes. And shoes are just the beginning, says Daraio. “A new field is emerging that creates unusual materials using simple geometrical architectures,” she says. There’s a name for this stuff: metamaterials, from the Greek word “meta,” meaning “higher” or “beyond.” The term was originally coined to describe things that interact with electromagnetic waves in counterintuitive ways—not because of their composition, per se, but because of their …

Generation of surface plasmon-polaritons by edge effects

By using numerical and analytical methods, we describe the generation of fine-scale lateral electromagnetic waves, called surface plasmon-polaritons (SPPs), on atomically thick, metamaterial conducting sheets in two spatial dimensions (2D). Our computations capture the two-scale character of the total field and reveal how each edge of the sheet acts as a source of an SPP that may dominate the diffracted field. We use the finite element method to numerically implement a variational formulation for a weak discontinuity of the tangential magnetic field across a hypersurface. An adaptive, local mesh refinement strategy based on a posteriori error estimators is applied to resolve the pronounced two-scale character of wave propagation and radiation over the metamaterial sheet. We demonstrate by numerical examples how a singular geometry, e.g., sheets with sharp edges, and sharp spatial changes in the associated surface conductivity may significantly influence surface plasmons in nanophotonics.

Split-ring-based metamaterial for far-field subwavelength focusing based on time reversal

In this paper, split-ring-based metamaterial sheets are designed for the purpose of achieving far-field subwavelength focusing, with the aid of a time-reversal technique. The metamaterial sheets are inserted into a subwavelength array consisting of four element antennas, with the element spacing being as small as 1/15 of a wavelength. Experiments are performed to investigate the effect of the metamaterial sheets on the focusing resolution. The results demonstrate that in the presence of the metamaterial sheets, the subwavelength array exhibits the ability to achieve super-resolution focusing, while there is no super-resolution focusing without the metamaterial sheets. Further investigation shows that the metamaterial sheets are contributive to achieving super-resolution by weakening the cross-correlations of the channel impulse responses between the array elements.

Abnormal Radiation Pattern of Metamaterial Waveguide

The idea to inverse the radiation pattern of the microwave antenna due to appli- cation of the isotropic metamaterial screen with negative refractive index in S band is demon- strated at the flrst time in this investigation. The electromagnetic simulation of waveguide antenna patterns by moment's methods demonstrates an agreement modeling antenna patterns with measured antenna diagrams for values of metamaterial efiective parameters (permittivity and permeability) extracted from measured S-parameters of metamaterial sheet sample.

Metamaterials and superresolution: From homogenization to rigorous approach

The paper touches upon the correspondence between the widely used homogenized approach and integral equation technique in simulating electromagnetic excitation of metamaterials. The attention is drawn to metamaterials with helix-type inclusions, their properties are briefly discussed. Special attention is paid to the thin metamaterial sheets as they are the primary candidates to manufacture the so-called “superlenses” that can reveal the resolution overcoming the well-known diffraction limit (about half a wavelength). Experimental results are compared to computer simulation using both homogenized model and a rigorous approach. A physical interpretation is suggested of the development of an image with superresolution in a real device.