Unit Cell Analysis Research Articles

Non-dimensional linear analysis of one-dimensional wave propagation in tensegrity structures

This study presents a methodology for analyzing wave propagation in tensegrity lattices within a non-dimensional framework. Two strategies are employed to predict pass bands and bandgaps. The first examines wave dispersion through a single representative unit cell, using dispersion curves to identify bandgaps and pass bands. The second models the structure as a finite system, using modal analysis to compute the steady-state response to harmonic loads and plot the frequency response function. Two unit cells are analyzed: a two-dimensional D-bar unit and a three-dimensional tensegrity prism. The study investigates axial and in-plane bending wave propagation in a D-bar chain and axial wave propagation in a prism chain. After non-dimensionalizing the equations of motion, key parameters such as ratios of stiffness per unit length, mass per unit length, and prestress are identified. Its is shown that varying these parameters shifts the bandgap locations and widths. Prestress has minimal effect in the D-bar case, while a slight shift in the first bandgap is observed in the prism. The predictions from unit cell and finite structure analyses show good agreement.

Elevating NIR photonic integration with tantalum-niobium pentoxide

In this study, we present a novel material platform based on tantalum-niobium pentoxide (TaNbO5) for integrated photonics applications. TaNbO5 demonstrates exceptional attributes suitable for both linear and nonlinear optics across a wide range of near-infrared wavelengths. Our analysis of the TaNbO5 unit cell revealed crucial lattice parameters and a direct band gap value of 2.268 eV. At a wavelength of 1550 nm, TaNbO5 exhibits a refractive index of 2.22, an extinction coefficient of 5.24 × 10−4, and other optical properties. We determine a 0.8 μm cut-off core width for single-mode TaNbO5 waveguides, which achieve efficiencies exceeding 99% for single-mode configurations and 98% for multimode structures. When coupled with conventional waveguides, TaNbO5 waveguides demonstrate excellent transmission characteristics. Notably, at a wavelength of 1.55 μm, the single-mode waveguide exhibits minimal excess loss. These findings highlight the significant potential of TaNbO5 waveguides for various near-infrared applications, emphasizing their versatility and promising performance.

Effect of nonlocality on the dispersion relations of mechanical metamaterials

The advent of mechanical metamaterials, with their unconventional and programmable properties, has revolutionised the field of engineering across length scales. Their design remains an area of interest to researchers requiring careful analysis of unit cells so as to achieve desired mechanical and wave dispersion behaviour. While metamaterials are known to extract their unique properties from the internal geometry of the unit cells, the contributions of the constituent materials are typically accounted for via their local material properties in the form of Young’s modulus and Poisson’s ratio. In this article, we demonstrate that material nonlocality of the constituents can also play a crucial role in modulating the nontrivial properties of metamaterials. Such nonlocality can arise from various sources, such as finer scale inhomogeneity like defects, inclusions etc. Towards this, we propose a nonlocal continuum model by upscaling a discrete potential through a stochastic gradient estimator (SGE) interpreted herein as a generalised Cauchy–Born rule. The nonlocal parameters can also be estimated from experimental data by solving an inverse problem, similar to the estimation of constitutive parameters in classical continuum mechanics. The proposed model accurately captures the dispersion behaviour at the continuum level as compared to its discrete counterpart. We further incorporate the model within the transfer matrix method to derive the dispersion relations of a metabar as a function of the constituent material nonlocality. We envisage that the present study introduces a new handle in the form of constituent material nonlocality for designing architected metamaterials with unprecedented mechanical functionalities.

Investigating mechanical properties and bending behavior of an auxetic plate with 4-star unit cell

This study derives the constitutive relationships between stress resultants and strain measures for 4-star auxetic structures using force-moment analysis of a representative unit cell and the Castigliano strain energy method. To validate the accuracy of the constitutive model, bending analysis is performed for a 4-star auxetic rectangular plate under Levy boundary conditions. The analytical and numerical results show excellent agreement, confirming the validity of the constitutive relations extracted from the generic 4-star unit cell. This work establishes a theoretical framework for designing 4-star auxetic metamaterials and demonstrates their potential for diverse engineering applications.

Mechanical metamaterial design with the customized low-frequency bandgap and negative Poisson's ratio via topology optimization

The precise control of both the mechanical deformation and wave propagation characteristics of metamaterial through design holds significant importance and presents a challenging task. This paper proposes a novel two-stage topological optimization design method for customizing both negative Poisson's ratio and locally resonant bandgap in the mechanical metamaterial. In the optimized model, the negative Poisson’s ratio structure is firstly obtained by optimizing the material distribution within the matrix region, then the metamaterial with the customized negative Poisson’s ratio and bandgap range is obtained through the second stage optimization. In the analysis of the metamaterial unit cell, the topology-dependent Poisson’s ratio is calculated based on the equivalent elastic matrix obtained through the homogenization method. The range of bandgap is estimated using the effective mass analytical model of the spring-mass system. Thus, the range of bandgap is determined by only a few geometric parameters instead of topological structure under given assumptions. The customized bandgap ranges can be extended by introducing more resonators into the unit cell and combining different unit cells into an assembled structure. Numerical examples are provided to demonstrate the efficacy of the proposed method.

Analysis of effects of material anisotropy on ductile damage using microscopic unit‐cell model

AbstractIt is experimentally observed that the failure in ductile metals is mainly due to the nucleation, growth, and coalescence of micro‐voids as well as micro‐shear‐cracks. Furthermore, plastic anisotropy has significant role in damage and failure behavior of ductile metals. Finite element simulations of unit cell provide a basis to understand different mechanisms on micro‐scale, for example, changes in shape and size of single voids and defects as well as localization of plastic strains. This contribution deals with the numerical analysis of unit cell containing spherical void subjected to symmetrical boundary conditions taking material anisotropy into account. Elastic isotropic behavior is described by Hooke's law while Hoffman yield criterion considering the strength‐differential effect is used to model the anisotropic plastic behavior. Generalized anisotropic stress invariants, generalized stress triaxiality, and generalized Lode parameter are introduced to characterize the stress state in the anisotropic ductile metal. The effect of plastic anisotropy on the damage behavior of the aluminum alloy EN AW‐2017A is studied in detail by performing a series of numerical simulations covering a wide range of stress triaxialites and Lode parameters. Stress triaxility and Lode parameter are controlled and kept constant during the entire loading process. The numerical results are then used to discuss general mechanisms of damage and failure process in ductile metals.

Compression of filled, open-cell, 3D-printed Kelvin lattices

The sensitivity of compressive strength of a polymeric Kelvin lattice to the presence of an epoxy core has been investigated both experimentally and numerically. Crush bands develop in the empty lattice, with large oscillations in load due to geometric softening and the sequential fracture of successive layers of struts. In contrast, the epoxy core has a sufficiently high modulus and strength that outward lateral flow of the epoxy through the open-cell lattice is negligible: the boundary layer, wherein migration of epoxy occurs through the lattice, extends less than one cell size from the surface of the specimen. The epoxy core supports the struts and stabilises the bulk macroscopic response against crush band formation. Finite element analysis of periodic unit cells show that the presence of an almost incompressible epoxy core changes the deformation mode of the lattice from one that is close to uniaxial straining to an isochoric mode. However, both the compressible collapse mode of the empty lattice and the isochoric deformation mode of the filled lattice are bending-dominated. At finite strain, the observed macroscopic strength of the filled lattice is degraded by bending failure of the struts and by tensile cracking of the adjacent core; the failure location is at a particular subset of the nodes of the lattice. Microcrack coalescence leads to the formation of a series of vertical fissures in the specimen.

Synthesis of Polarization-Independent Perfect Anomalous Reflectors via Modulated Metasurfaces and an Analytical Design Model

A systematic approach to the synthesis of polarization-independent metasurfaces for anomalous reflection is presented. A fast analytical procedure is laid out to analyze the electromagnetic (EM) behavior of an impedance-modulated metasurface for arbitrary angles of incidence and reflection, subsequently serving as a means to provide the necessary impedance profile for reflection toward a specific direction, while capturing all propagation mechanisms, including surface waves (SWs) and nonlocal effects. We apply this procedure to design a metasurface for reflecting a normal incident wave to a different reflection angle, where the synthesized impedance is approximated by a discrete design, based on orthogonal metallic patches. This is done to provide control of both cases of incident wave polarization, while the unit cell analysis and extraction of equivalent impedance is easily performed by a full-wave computational eigenmode analysis of the unit cell. The unit cell design is performed by a simple fine-tuning process with minimal geometric modifications, and the actual discrete metasurface design is proven to agree well with the continuous model. The validity of the synthesis approach is perfectly demonstrated by the fabrication and experimental verification of a model design.

Elastic metamaterials with fractional-order resonators

Elastic metamaterials incorporating locally resonating unit cells can create bandgap regions with lower vibration transmissibility at longer wavelengths than the lattice size and offer a promising solution for vibration isolation and attenuation. However, when resonators are applied to a finite host structure, not only the bandgap but also additional resonance peaks in its close vicinity are created. Increasing the damping of the resonator, which is a conventional approach for removing the undesired resonance peaks, results in shallowing of the bandgap region. To alleviate this problem, we introduce an elastic metamaterial with resonators of fractional order. We study a one-dimensional structure with lumped elements, which allows us to isolate the underlying phenomena from irrelevant system complexities. Through analysis of a single unit cell, we present the working principle of the metamaterial and the benefits it provides. We then derive the dispersion characteristics of an infinite structure. For a finite metastructure, we demonstrate that the use of fractional-order elements reduces undesired resonances accompanying the bandgap, without sacrificing its depth.

Inverted fuel geometry implementation for a fast reactor: Potential improvements in neutronic and thermalhydraulic performance

This paper presents a detailed procedure for implementing the inverted fuel geometry to a fast reactor to improve its safety system and economy. The study is starting from the fuel unit cell, fuel assembly, reactor core, and burnup analysis. A proposed multivariable graph (v, ΔP, TFmax–Dco, VF) introduced at the fuel unit cell level provides comprehensive thermalhydraulic and neutronic parameters in a single graph, allowing for an efficient optimization process. The fuel unit cell study reveals that the inverted fuel design has a higher fuel volume fraction and lower core pressure drop than conventional pin-typed fuel. This is beneficial for the reactor economy and enhances the reliability of the safety system. With the inverted fuel design, the primary loop can save pumping power by up to 40 % and provides an excess driving force for natural circulation. The male–female axial grid structure separating the fuel assembly potentially eliminates coolant flow path restriction and fretting issues. The core is named the Inverted Core Fast Reactor (IC-FR), an LBE-cooled fast SMR designed to generate 60 MWth for at least 40 years of full-power operation without refueling and fuel shuffling. IC-FR is a transportable reactor and has load following capability that can be deployed for many applications, including marine and land-based applications, and stand alone or mixing power grid. The burnup study of IC-FR reveals that the balance of neutron leakage and fissile inventory yields a small reactivity swing (<1$) for 40 years. This study extensively utilizes Monte Carlo (MC) code MCS for neutronic calculation. Owing to the high computational expense of MC code, the approaches to optimize the MC usage are also presented.

Direct-Homogenization-Based Plate Models of Integrated Thermal Protection System for Reusable Launch Vehicles

Integrated thermal protection systems of reusable launch vehicles (RLVs) can have a corrugated core sandwich structure and experience location-dependent thickness-wise temperature gradient. The sandwich structure can be optimized depending on the location on RLV using finite element method simulations of RLV components. However, such analysis can be computationally challenging due to the disparate length scales between the RLV components and features of the sandwich structure. Two different equivalent plate models based on first-order shear and normal deformation theory, and first-order shear and second-order normal deformation theory (FSSNDT) have been utilized in this work to address this drawback. A direct homogenization technique involving unit cell and cantilever beam analysis has been developed to calibrate the equivalent plate properties for different thickness-wise temperature variations. The accuracy of the plate models has been evaluated by comparing their responses with a full-scale model for different thickness-wise temperature gradients and a uniform pressure. The comparisons clearly indicate that the FSSNDT-based plate model calibrated via direct homogenization captures both the displacements and strains in the in-plane and transverse directions accurately, and can be used to perform RLV component analysis efficiently to obtain location-specific optimal design of corrugated core sandwich structures.

An extended full field self-consistent cluster analysis framework for woven composite

In this work, the self-consistent clustering analysis (SCA) framework is extended to include homogenization and full field analysis of 3D anisotropic woven composite Representative Unit Cell (RUC). The developed extended framework has two new features, namely, (i), to reconstruct the local field variables, a strain refinement stage is presented by solving full field Lippmann–Schwinger equations within 3D anisotropic woven composite RUC following the online predictive stage in SCA, and (ii), discrete Green’s operator based on finite difference is adopted to improve the accuracy of refined point-wise physical field variables. To demonstrate the accuracy and efficiency of the proposed method, benchmark problems are analyzed, and results are compared to directly numerical simulation (DNS). For the reproducibility of presented results, the developed code can be freely downloaded from https://github.com/Tong-RuiLiu/Extended-SCA-and-FFT-based-strain-refinement-method-.

Reflection Phase Compensation for Finite Metasurface Using Notches and Slots on the Backing Conductor

This study described a technique to compensate for the difference in reflection phase characteristics yielded by a finite-size meta-surface (MS) to render them identical to the reflection characteristics analyzed using the unit cell model corresponding to the infinite MS structure. Thus, an MS with a backing conductor having notches and slots to compensate for the reflection phase affected by the complex diffraction at the edge, was proposed. The notches and slots’ mechanism inducing the inductive reactions was discussed based on the current distributions. The proposed and conventional MSs were fabricated to verify the deterioration and compensation effect; the former was consistent with the designed performance based on the unit cell analysis corresponding to the infinite structure.

Printed Metasurface Leaky Wave Antennas Based on Penetrable Aperture Field Synthesis

A design methodology for 1-D modulated printed metasurface leaky-wave antennas (LWAs) with a pattern synthesis capability in 2-D TE polarization is presented. For a desired radiation pattern, complete tangential fields on the surface of a grounded dielectric substrate are constructed and optimized to find a pointwise passive surface impedance distribution. Dielectric and conductor losses are taken into account in the field synthesis process via a design curve obtained using analysis of a physical unit cell with lossy constituents. It enables accurate prediction of the aperture field distribution when practical lossy materials are used. A spatially modulated impedance can be realized using an array of printed copper strips. Three 10-wavelength-long LWA designs are demonstrated numerically for broadside, two-beam, and sector patterns. The LWA for broadside radiation is fabricated and measured, showing a good agreement with the simulation results.

Analysis of a tuneable NZRI metamaterial unit cell for satellite applications

In this paper, a new single negative metamaterial (MTM) unit cell structure with low profile of 6.2 × 6.2 m2 is proposed. The unit cell shows near zero refractive index (NZRI) characteristics in C, X and Ku bands whereas epsilon negative index (ENG) in Ku-Band frequency. The properties of the proposed MTM unit cell are analysed with the Rogers 5880 substrate which displays low permittivity. To verify the effectiveness of the split ring resonators (SRR) as a metamaterial, a comparison of the unit cell properties in 2 × 3 array structures is created. Besides low profile, tunability performance is shown in the proposed design by adjust the central strip line width of the proposed metamaterial whereas the frequency resonance can be shifted and controlled accordingly. Using commercially available CST software, the reflection (S11) and transmission (S12) parameters of the unit cell are determined. The proposed MTM unit cell can be potentially used in many applications including satellite communication systems.

Mesoscopic unit cell analysis of ductile failure under plane stress conditions

Ductile failure under plane stress conditions is analyzed at the meso-scale using periodic unit cell model simulations of void growth in a plastically deforming matrix. Equivalent strains to failure by the onset of plastic instability at the macro-scale are estimated using the loss of ellipticity criterion for the equilibrium equations. Failure loci obtained from the cell model simulations are compared with the predictions of an instability-based ductile failure model and the Hosford–Coulomb damage indicator model, under both proportional and non-proportional loading conditions. The instability-based model is shown to quantitatively predict the shape of the failure locus under proportional loading, including the presence of a cusp at uniaxial tension and a ductility minimum under plane strain tension, in the absence of heuristic adjustable parameters in the failure criterion. It is shown that the characteristic shape of the plane stress failure locus is primarily due to the Lode dependence of the failure criterion, and not the damage growth law as assumed in the damage indicator models. Under non-proportional loading involving a step change in loading direction at an intermediate strain, the instability-based model correctly predicts the non-linear variation of the failure strain as a function of the intermediate strain; unlike a linear variation predicted by the damage indicator models, which is not in agreement with the cell model simulations. Forming limit curves showing the strains to the onset of localized necking in thin sheets are also obtained from the cell model simulations using an appropriate modification of the macroscopic instability criterion.

Geometric parameterization of unit cell configurations for reduced basis approximation

To facilitate rapid yet accurate multiscale homogenization, we formulate geometric mapping schemes that effectively handles the fiber radius changes of a unit cell to dispense with mesh regeneration. To further expedite unit cell analysis involving fiber radius variation, we integrate the formulated geometric transformations into reduced basis analysis using an empirical interpolation method. For demonstration, we examine the proposed geometric parameterization strategies with the linear elastic analyses of square and hexagonal unit cells under tension and shear loads, respectively. Overall, reduced basis analyses combined with the devised geometric mappings are found more efficient than the corresponding finite element analyses while producing insignificant errors.

Design and Analysis of S-shaped Broadside Coupled Metamaterial Unit Cell as a Sensor to Ease the Classification of Different Oil Samples

Design and Analysis of S-shaped Broadside Coupled Metamaterial Unit Cell as a Sensor to Ease the Classification of Different Oil Samples

Coupled flexural and torsional vibration attenuation with locally resonant metamaterials

A metamaterial beam with coupled bending and torsional resonators for broadband flexural–torsional vibration suppression is studied. The main objective is to design and analyse the metamaterial beam for simultaneous attenuation of flexural and torsional vibration waves using FEM and the Bloch-Floquet theorem. The bandgaps of the single unit cell with an infinite periodic structure assumption are studied using Bloch-Floquet reduction with a commercial multi-physics program. Initially, the beam with a bending resonator is examined, and a high-frequency broadband vibration frequency bandgap above 10 kHz is observed. With the addition of a torsional resonator, the existing bending bandgaps are widened, and further new bandgaps are formed. Transmissibility analysis of a metamaterial beam with the above unit cells is performed using the finite element method. The FRFs show similar bandgaps observed in the dispersion curves, thereby validating unit cell analysis. It is observed that coupled bending and torsional resonators create the opportunity to widen and introduce new bandgaps compared to uncoupled resonators. These metamaterial beams with bending and coupled resonators can aid in vibration isolation and frequency filtering of structures subjected to bending and torsional impact loads.

A novel monoclinic auxetic metamaterial with tunable mechanical properties

Missing rib auxetics with a reinforced central core may have tunable negative Poisson's ratios (NPRs) and other mechanical parameters. In analogy with the other enhanced missing rib configurations (e.g., enhanced hexa-, anti-tri- and anti-tetra-missing rib honeycombs), a novel enhanced tetra-missing rib honeycomb metamaterial is proposed in this work. Similar as the classical tetra-chiral honeycomb, the proposed enhanced tetra-missing rib honeycomb metamaterial also exhibits monoclinic property, i.e., undergoing coupled shearing and stretching/shrinking under monotonic tension/compression. To facilitate the understanding of the underlying microstructural mechanisms, a theoretical model under the infinitesimal deformation assumption is developed by a simple energy-based approach. The obtained analytical solutions are validated by systematic finite element (FE) analyses conducted for a unit-cell with periodic boundary conditions, and elucidate different roles of the microstructural geometry on the effective mechanical properties of the proposed metamaterial. It is shown that the proposed metamaterial exhibits tailorable Poisson's ratios (from -1 to 0) as well as elastic (over five orders of magnitude) and shear moduli (over four orders of magnitude) in wide ranges. Compared with the previously developed enhanced anti-tetra-missing rib honeycomb, which has the same building block as the proposed design in this paper, the stiffness of the present design is improved remarkably with the same geometrical parameters owing to its monoclinic property. The improvement can even reach two orders of magnitude in some cases. Uniaxial tensile experimental tests and finite-size FE simulations for the proposed metamaterial structures consisting of an array of unit-cells are also performed to validate the theoretical and FE results obtained from the unit-cell analyses.