Multiple Unit Cells Research Articles

Flexural wave band gaps in metamaterial beams with membrane-type resonators: theory and experiment

This paper deals with flexural wave band gaps in metamaterial beams with membrane-type resonators. The proposed membrane-type resonator consists of a tensioned elastic membrane and a mass block attached to the center of the membrane. Numerical models based on finite element method are presented to predict the dispersion relation, band gaps and eigen-modes. It has shown that the metamaterial beams exhibit unique wave physics. A broad Bragg band gap (BBG) and two low-frequency locally resonant band gaps (LRBGs) can be observed due to the structural periodicity and locally resonant behavior respectively. The first LRBG can be ascribed to the combined resonance of the membranes and the masses, while the second LRBG is caused by the resonance of the membranes. The study of the effective property shows that negative mass density occurs in the LRBGs. The effects of membrane tension and mass magnitude (the weight of mass block) on the LRBGs are further analyzed. It is shown that both the two LRBGs move to high-frequency with the increase of the membrane tension. However, as the mass magnitude increases, the first LRBG moves to low-frequency and the second LRBG almost remains unchanged. It is further demonstrated that, when a larger unit cell with multiple kinds of masses (a larger unit cell incorporating multiple basic unit cells but with different weights of mass blocks within each basic unit cell) are used, the first LRBG can be broadened, which can be employed to achieve broadband vibration attenuation. Moreover, experimental measurements of vibration transmittance are conducted to validate the theoretical predictions. Good agreements between the experimental results and the theoretical predictions are observed.

Resilient 3D hierarchical architected metamaterials

Hierarchically designed structures with architectural features that span across multiple length scales are found in numerous hard biomaterials, like bone, wood, and glass sponge skeletons, as well as manmade structures, like the Eiffel Tower. It has been hypothesized that their mechanical robustness and damage tolerance stem from sophisticated ordering within the constituents, but the specific role of hierarchy remains to be fully described and understood. We apply the principles of hierarchical design to create structural metamaterials from three material systems: (i) polymer, (ii) hollow ceramic, and (iii) ceramic-polymer composites that are patterned into self-similar unit cells in a fractal-like geometry. In situ nanomechanical experiments revealed (i) a nearly theoretical scaling of structural strength and stiffness with relative density, which outperforms existing nonhierarchical nanolattices; (ii) recoverability, with hollow alumina samples recovering up to 98% of their original height after compression to ≥ 50% strain; (iii) suppression of brittle failure and structural instabilities in hollow ceramic hierarchical nanolattices; and (iv) a range of deformation mechanisms that can be tuned by changing the slenderness ratios of the beams. Additional levels of hierarchy beyond a second order did not increase the strength or stiffness, which suggests the existence of an optimal degree of hierarchy to amplify resilience. We developed a computational model that captures local stress distributions within the nanolattices under compression and explains some of the underlying deformation mechanisms as well as validates the measured effective stiffness to be interpreted as a metamaterial property.

Lattice Entertain You: Paper Modeling of the 14 Bravais Lattices on YouTube

A system for the construction of double-sided paper models of the 14 Bravais lattices, and important crystal structures derived from them, is described. The system allows the combination of multiple unit cells, so as to better represent the overall three-dimensional structure. Students and instructors can view the models in use on the popular internet channel YouTube at no cost.

Hybrid silencers with micro-perforated panels and internal partitions

A sub-structuring approach, along with a unit cell treatment, is proposed to model expansion chamber silencers with internal partitions and micro-perforated panels (MPPs) in the absence of internal flow. The side-branch of the silencer is treated as a combination of unit cells connected in series. It is shown that, by connecting multiple unit cells with varying parameters, the noise attenuation bandwidth can be enlarged. With MPPs, the hybrid noise attenuation mechanism of the silencer is revealed. Depending on the size of the perforation hole, noise attenuation can be dominated by dissipative, reactive, or combined effects together. For a broadband sound absorption, the hole size, together with the perforation ratio and other parameters, can be optimized to strike a balance between the dissipative and reactive effect, for ultimately achieving the desired noise attenuation performance within a prescribed frequency region. The modular nature of the proposed formulation allows doing this in a flexible, accurate, and cost effective manner. The accuracy of the proposed approach is validated through comparisons with finite element method and experiments.

A 36‐Fold Multiple Unit Cell and Switchable Anisotropic Dielectric Responses in an Ammonium Magnesium Formate Framework

AbstractAn ammonium Mg formate framework, prepared by using di‐protonated 1,3‐propanediamine (pnH22+), has a rare three‐dimensional binodal (412⋅63)(49⋅66)3 Mg‐formate framework with elongated cavities accommodating pnH22+⋅⋅⋅H2O⋅⋅⋅pnH22+ assemblies. It displays a para‐electric to antiferroelectric phase transition at 275 K, with a 36‐fold multiple unit cell from the high‐temperature cell of 1703 Å3 to the low‐temperature one of 60 980 Å3. The change results from the disorder–order transition of the pnH22+ cations and H2O molecules. The motions of these components freeze in a stepwise fashion on going from the high‐temperature disorder state to the low‐temperature ordered state, triggering the switch from high to low dielectric constants, and the spatial limitation of such motions contributes the strong dielectric anisotropy.

A 36-fold multiple unit cell and switchable anisotropic dielectric responses in an ammonium magnesium formate framework.

An ammonium Mg formate framework, prepared by using di-protonated 1,3-propanediamine (pnH2(2+)), has a rare three-dimensional binodal (4(12)⋅6(3))(4(9)⋅6(6))3 Mg-formate framework with elongated cavities accommodating pnH2(2+)⋅⋅⋅H2O⋅⋅⋅pnH2(2+) assemblies. It displays a para-electric to antiferroelectric phase transition at 275 K, with a 36-fold multiple unit cell from the high-temperature cell of 1703 Å(3) to the low-temperature one of 60,980 Å(3). The change results from the disorder-order transition of the pnH2(2+) cations and H2O molecules. The motions of these components freeze in a stepwise fashion on going from the high-temperature disorder state to the low-temperature ordered state, triggering the switch from high to low dielectric constants, and the spatial limitation of such motions contributes the strong dielectric anisotropy.

Large-Scale Fluidic Tuning of Subwavelength Periodic Structures

In this letter, we present a technique to fluidically tune the responses of periodic structures with multiple unit cells and finite dimensions. The periodic structures are composed of subwavelength constituting unit cells. This technique is applied to a two-dimensional high-impedance surface with multiple unit cells, and the response of the structure is continuously tuned. The technique is based on embedding metal and glass balls inside several parallel channels within a dielectric substrate supporting the structure. In each channel, a periodic arrangement of metal and glass balls is assembled and is allowed to move freely within the channel. By moving this periodic train of balls over small distances with respect to the fixed periodic structure, the response of the structure is continuously tuned. Three-dimensional (3-D) printing technology is used to implement the dielectric substrate with embedded fluidic channels. An architecture for the fluid distribution network is proposed that ensures the movement of balls in all channels is synchronized. A prototype with 16 parallel channels accommodating several unit cells in each channel is fabricated, and synchronized movement of the balls is verified experimentally when the balls in channels are embedded in mineral oil and pressure driven. Using this substrate and an array of subwavelength capacitive patches fabricated on a thin dielectric substrate, a fluidically tunable high-impedance surface is designed and experimentally characterized.

Local and Global Stress–Strain Behaviors of Transformation-Induced Plasticity Steel Using the Combined Nanoindentation and Finite Element Analysis Method

Transformation-induced plasticity (TRIP) steels have excellent strain hardening exponents and resistibility against tensile necking using the strain-induced martensite formation that occurs as a result of the plastic deformation and strain on the retained austenite phase. Detailed studies on the microstructures and local mechanical properties, as well as global mechanical properties, are necessary in order to thoroughly understand the properties of TRIP steels with multiple phases of ferrite, bainite, retained austenite, and martensite. However, methods for investigating the local properties of the various phases of the TRIP steel are limited due to the very complicated and fine microstructures present in TRIP steel. In this study, the experimental and numerical methods, i.e., the experimental nanoindenting results and the theoretical finite element analyses, were combined in order to extract the local stress–strain curves of each phase. The local stress–strain curves were in good agreement with the values presented in the literature. In particular, the global plastic stress–strain behavior of the TRIP steel was predicted using the multiple phase unit cell finite element analysis, and this demonstrated the validity of the obtained properties of each local phase. The method of extracting the local stress–strain curves from the nanoindenting curves and predicting the global stress–strain behavior assists in clarifying the smart design of multi-phase steels.

Probing excitonic dark states in single-layer tungsten disulphide.

Transition metal dichalcogenide (TMDC) monolayers have recently emerged as an important class of two-dimensional semiconductors with potential for electronic and optoelectronic devices. Unlike semi-metallic graphene, layered TMDCs have a sizeable bandgap. More interestingly, when thinned down to a monolayer, TMDCs transform from indirect-bandgap to direct-bandgap semiconductors, exhibiting a number of intriguing optical phenomena such as valley-selective circular dichroism, doping-dependent charged excitons and strong photocurrent responses. However, the fundamental mechanism underlying such a strong light-matter interaction is still under intensive investigation. First-principles calculations have predicted a quasiparticle bandgap much larger than the measured optical gap, and an optical response dominated by excitonic effects. In particular, a recent study based on a GW plus Bethe-Salpeter equation (GW-BSE) approach, which employed many-body Green's-function methodology to address electron-electron and electron-hole interactions, theoretically predicted a diversity of strongly bound excitons. Here we report experimental evidence of a series of excitonic dark states in single-layer WS2 using two-photon excitation spectroscopy. In combination with GW-BSE theory, we prove that the excitons are of Wannier type, meaning that each exciton wavefunction extends over multiple unit cells, but with extraordinarily large binding energy (∼0.7electronvolts), leading to a quasiparticle bandgap of 2.7electronvolts. These strongly bound exciton states are observed to be stable even at room temperature. We reveal an exciton series that deviates substantially from hydrogen models, with a novel energy dependence on the orbital angular momentum. These excitonic energy levels are experimentally found to be robust against environmental perturbations. The discovery of excitonic dark states and exceptionally large binding energy not only sheds light on the importance of many-electron effects in this two-dimensional gapped system, but also holds potential for the device application of TMDC monolayers and their heterostructures in computing, communication and bio-sensing.

Simulation of the cross-correlated positions of in-plane tow centroids in textile composites based on experimental data

In-plane centroids of textile composites are simulated as cross-correlated random fields. Each tow position is defined as an average trend quantified from experimental data, added with zero-mean deviations produced as a stochastic field. Realisations of these fields are generated using a framework based on the Karhunen–Loève series expansion that is calibrated with experimental information from prior work. Positional deviations are obtained that are correlated along the tow and between neighbouring tows.The application is a 2/2 twill woven carbon fibre reinforced epoxy consisting of multiple unit cells. Generated in-plane deviations of the warp and weft tows resemble the experimental fluctuations with similar wavelengths. Simulation of thousand specimens demonstrates that the virtual in-plane positions possess the experimental standard deviation and correlation lengths on average.

Phase coexistence in Ti6Sn5 intermetallics

Here we report the structural characterization of a complex Ti–Sn intermetallic compound, Ti6Sn5. From X-ray diffraction, the resulting compound was observed to exist in both orthorhombic and hexagonal phases. Analysis by electron microscopy revealed that “planar-like” defects form throughout the material. Atomic resolution aberration-corrected scanning transmission electron microscopy reveals that these “planar-like” defects represent the coexistence of the orthorhombic and hexagonal phases within single grains. The resulting interwoven phases range in thickness from a fraction to multiple unit cells and exhibit coherent phase boundaries with the matrix grain.

Analysis and modeling of localized faceting on 4H-SiC epilayer surfaces

Comparing with the well-established theory of periodic surface faceting, the formation mechanism of localized surface faceting is not yet clear. We investigate the localized surface faceting of 4H silicon carbide (4H-SiC) epilayers using atomic force microscopy (AFM). The AFM measurements reveal that this phenomenon gives rise to the appearance of isolated macrosteps with multiple unit cell heights. A model for the localized surface faceting is presented based on the AFM cross-sectional height profile. In this model, the isolated macrostep appears in the form of the double-hill–valley structure. We formulize the total surface free energy in the model and explain the important structural features of isolated macrosteps observed by AFM. A generalized model for the localized surface faceting with multiple-hill–valley structure is further proposed to analyze the transition from the localized surface faceting to the periodic surface faceting. Our results provide a basis for understanding the localized surface faceting phenomenon of 4H-SiC epilayers.

An accurate macro-cell-method for extracting dispersion characteristics of 1D reciprocal microwave structures with finite periodicity

A novel macro-cell-method (MCM) has been proposed, which is capable of accurately extracting the dispersion characteristics of 1D reciprocal microwave structures with finite periodicity. In practice a single macro-cell consists of multiple periodic unit cells, therefore the electromagnetic coupling effects among unit cells can be rigorously considered. The eigen transfer factors ξN and 1/ξN corresponding to the forward and backward Bloch waves can be calculated in terms of the Bloch theory. Imposing complex logarithmic operation to ξN, the attenuation constant α can be univocally determined, while multiple integer branches exist in the solution of the phase shift constant β due to the multiroots property of the complex logarithm function. The rational integer branch is uniquely selected by comparing β from the MCM with that extracted from the unwrapping-method (UPM), regarding β from the UPM as the approximate value. Compared to the conventional eigenmode-method, UPM and single-cell-method, the MCM has no requirements to the coupling intensity among unit cells comprising finitely periodic structures, and with such good generality and accuracy, the MCM can be an effective tool for characterizing 1D reciprocal finitely periodic structures, facilitating their wide applications in microwave engineering.

Modeling the diffusion-free liquid phase residence time distribution of Taylor flow by the unit cell concept: Progress and limitations

In this paper we study the diffusion-free liquid phase residence time distribution (RTD) of laminar Taylor flow in square mini-channels numerically and analytically. We evaluate the RTD caused by the non-uniform laminar velocity field for co-current upward and downward Taylor flow from detailed numerical simulations obtained with a volume-of-fluid method by diffusion-free Lagrangian tracking of a set of virtual particles. The numerical RTD curves are used to develop a compartment model for the RTD of a Taylor flow unit cell (which consists of one gas bubble and one liquid slug) in the fixed frame of reference. While the new model is conceptually similar to models from literature, it is refined with respect to (i) the delay time (i.e. the residence time of the fastest liquid elements, modeled by a plug flow reactor) and (ii) the difference in slope of the RTD at small and large residence times (modeled by two parallel continuous stirred tank reactors with different mean residence time). It is shown that the refined model fits the numerical unit cell RTD reasonably well for different flow conditions. From the unit cell RTD model, the RTD for two and three unit cells in series is computed by a convolution procedure. The agreement between the numerical and the convolution-based RTD for multiple unit cells is not satisfactory and indicates the inappropriateness of the convolution procedure for computing the diffusion-free RTD of multiple unit cells in Taylor flow. The failure of the convolution procedure is attributed to the dividing streamline, which separates in Taylor flow the liquid phase in two regions, one with recirculating and one with bypass flow. In the absence of diffusion, the diving streamline is never crossed. As a consequence, locations of tracer particles in neighboring unit cells are not independent which invalidates the unit cell convolution approach.

Scaling‐Up Microbial Fuel Cells: Configuration and Potential Drop Phenomenon at Series Connection of Unit Cells in Shared Anolyte

To scale-up microbial fuel cells (MFCs), installing multiple unit cells in a common reactor has been proposed; however, there has been a serious potential drop when connecting unit cells in series. To determine the source of the loss, a basic stack-MFC (BS-MFC) has been devised, and the results show that the phenomenon is due to ions on the anode electrode traveling through the electrolyte to be reduced at the cathode connected in series. As calculated by means of the percentage potential drop, the degree of potential drop decreased with an increase in the unit-cell distance. When the distance was increased from 1 to 8 cm, the percentage potential drop in BS-MFC1 decreased from 46.76 ± 0.90 to 45.08 ± 0.70 % and in BS-MFC2 from 46.41 ± 0.95 to 43.82 ± 2.23 %. As the p-value of the t-test was lower than 0.05, the difference was considered significant; however, if the unit cells are installed far enough from each other to avoid the potential drop phenomenon, the system will be less dense, consequently reducing the ratio of electrode area per volume of anode compartment and decreasing the power density of the system. Finally, this study suggests design criteria for scaling-up MFC systems: Multiple-electrode-installed MFCs are modularized, and the unit cells are connected in series across the module (connecting each unit cell does not share the anolyte).

Nonharmonic phonons in MgB2at elevated temperatures

Inelastic neutron scattering was used to measure phonon spectra in MgB_2 and Mg_(0.75)Al_(0.25)B_2 from 7 to 750 K to investigate anharmonicity and adiabatic electron-phonon coupling. First-principles calculations of phonons with a linear response method were performed at multiple unit cell volumes, and the Helmholtz free energy was minimized to obtain the lattice parameters and phonon dynamics at elevated temperature in the quasiharmonic approximation. Most of the temperature dependence of the phonon density of states could be understood with the quasiharmonic approximation, although there was also significant thermal broadening of the phonon spectra. In comparison to Mg_(0.75)Al_(0.25)B_2, in the energy range of 60 to 80 meV the experimental phonon spectra from MgB_2 showed a nonmonotonic change with temperature around 500 K. This may originate from a change with temperature of the adiabatic electron-phonon coupling.

Extraction algorithm for retrieving the effective constitutive parameters of metamaterials based on TE10 rectangular waveguide

A novel retrieval method of the effective constitutive parameters of metamaterials based on TE10 rectangular waveguide is proposed, which is adopted to extract effective relative permittivity ε and permeability μ for the composite ferrite and wire array metamaterial in multiple symmetrical unit cell configuration. Much attention has been paid to choose the correct branch of the real part of the propagation constant β for the metamaterial with multiple unit cells, and in terms of the relationship between the measured values and theoretical values in the measurement theory, β values in the case of multiple unit cells are determined by taking the extracted β values for a single unit cell as the measured values for the multiple unit cells case. Owing to the coupling effect between the unit cells of the metamaterial with multiple unit cells, the electromagnetic wave mainly behaves as the periodic Bloch wave, which is usually negligible for a single unit cell, so the extracted effective constitutive parameters for a single unit cell generally can not be assigned as those for the metamaterial with multiple unit cells directly. However, β values for a single unit cell is generally prone to be extracted, which can be the first step to extract the β values in multiple unit cells case. It is pointed out that the extracted effective constitutive parameters can be physically meaningful only if attenuation coefficients of higher Bloch wave modes are larger than that of the fundamental Bloch mode in the periodic metamaterial, and under this condition, higher Bloch wave modes will get further attenuated with increase of the unit cell number, leaving only the fundamental mode propagation, which makes the extracted ε and μ more stable and convergent.

The cages, dynamics, and structuring of incipient methane clathrate hydrates

Interest in describing clathrate hydrate formation mechanisms spans multiple fields of science and technical applications. Here, we report findings from multiple molecular dynamics simulations of spontaneous methane clathrate hydrate nucleation and growth from fully demixed and disordered two-phase fluid systems of methane and water. Across a range of thermodynamic conditions and simulation geometries and sizes, a set of seven cage types comprises approximately 95% of all cages formed in the nucleated solids. This set includes the ubiquitous 5(12) cage, the 5(12)6(n) subset (where n ranges from 2-4), and the 4(1)5(10)6(n) subset (where n also ranges from 2-4). Transformations among these cages occur via water pair insertions/removals and rotations, and may elucidate the mechanisms of solid-solid structural rearrangements observed experimentally. Some consistency is observed in the relative abundance of cages among all nucleation trajectories. 5(12) cages are always among the two most abundant cage types in the nucleated solids and are usually the most abundant cage type. In all simulations, the 5(12)6(n) cages outnumber their 4(1)5(10)6(n) counterparts with the same number of water molecules. Within these consistent features, some stochasticity is observed in certain cage ratios and in the long-range ordering of the nucleated solids. Even when comparing simulations performed at the same conditions, some trajectories yield swaths of multiple adjacent sI unit cells and long-range order over 5 nm, while others yield only isolated sI unit cells and little long-range order. The nucleated solids containing long-range order have higher 5(12)6(2)/5(12) and 5(12)6(3)/4(1)5(10)6(2) cage ratios when compared to systems that nucleate with little long-range order. The formation of multiple adjacent unit cells of sI hydrate at high driving forces suggests an alternative or addition to the prevailing hydrate nucleation hypotheses which involve formation through amorphous intermediates.

Composite corrugated structures for morphing wing skin applications

Composite corrugated structures are known for their anisotropic properties. They exhibitrelatively high stiffness parallel (longitudinal) to the corrugation direction and arerelatively compliant in the direction perpendicular (transverse) to the corrugation. Thus,they offer a potential solution for morphing skin panels (MSPs) in the trailing edgeregion of a wing as a morphing control surface. In this paper, an overview of thework carried out by the present authors over the last few years on corrugatedstructures for morphing skin applications is first given. The second part of the paperpresents recent work on the application of corrugated sandwich structures. Panelsmade from multiple unit cells of corrugated sandwich structures are used as MSPsin the trailing edge region of a scaled morphing aerofoil section. The aerofoilsection features an internal actuation mechanism that allows chordwise length andcamber change of the trailing edge region (aft 35% chord). Wind tunnel testing wascarried out to demonstrate the MSP concept but also to explore its limitations.Suggestions for improvements arising from this study were deduced, one of whichincludes an investigation of a segmented skin. The overall results of this studyshow that the MSP concept exploiting corrugated sandwich structures offers apotential solution for local morphing wing skins for low speed and small air vehicles.

Toward Distinct Element Method Simulations of Carbon Nanotube Systems

We propose distinct element method modeling of carbon nanotube systems. The atomic-level description of an individual nanotube is coarse-grained into a chain of spherical elements that interact by parallel bonds located at their contacts. The spherical elements can lump multiple translational unit cells of the carbon nanotube and have both translational and rotational degrees of freedom. The discrete long ranged interaction between nanotubes is included in a van der Waals contact of nonmechanical nature that acts simultaneously with the parallel bonds. The created mesoscopic model is put into service by simulating a realistic carbon nanotube ring. The ring morphology arises from the energy balance stored in both parallel and van der Waals bonds.