Periodic Honeycomb Research Articles

Vibration and Wave Propagation Characteristic Analysis of Periodic Auxetic Star-Shaped Structure System

In this paper, vibration and wave propagation characteristics of auxetic metamaterial of the star-shaped structure system are studied. The plane wave expansion method is adopted to investigate and calculate the band structures of the auxetic star-shaped structure system. Besides, the frequency ranges of the complete bandgaps are also obtained and discussed. Then, the COMSOL® finite element software is utilized to solve wave propagation characteristics within the periodic auxetic star-shaped honeycomb structures. After that, the auxetic star-shaped structure devices made by 3D printed machine are used to measure the experimental results and also compared with numerical results. It can be seen that good agreements can be found in the discussions.

Localized strain fields in honeycomb materials with convex and concaved cells

Characterizing the local deformations and strain fields in ligaments of periodic honeycomb materials is instrumental to applications such as cores of sandwich structure as well as honeycomb shaped tunable phononic crystals, compliant metamaterials, and 4D printed shape memory materials. Such applications employ honeycomb shaped materials whose nonlinear behavior is controlled by localized deformations in their ligaments. These local deformations can exhibit values and complex non-uniform states that far exceed the overall macroscopic deformations and strains sustained by the honeycomb material in value and complexity. Each of the aforementioned applications can be better designed with an improved understanding of the evolution of local strain fields in honeycombs' ligaments during their deformation. This work aims to characterize the local strains and deformations developing in honeycomb ligaments near honeycombs’ macroscopic onset of yielding. Finite element computations and the full field strain measurement technique digital image correlation (DIC) are used to measure and characterize the local deformations in the ligaments of concaved and convex honeycombs. Results show nonlinear strain gradients and significant localization in deformed ligaments. Moreover, complex state of stress comprising biaxial normal stresses and shear stresses exists near plastic zones.

Collapse response of two-dimensional cellular solids by plasticity and cracking: application to wood

The competition between fracture and plasticity in periodic hexagonal honeycomb structures subjected to (i) intercell cracking, (ii) intrawall cracking and (iii) transwall cracking is examined, and their effect upon the macroscopic collapse response is explored using dedicated FEM analyses of unit cell configurations. These three cracking mechanisms are regularly observed in wood microstructures, and insight into their influence on the macroscopic collapse behavior is necessary for adequately designing timber structures against failure. The numerical results are presented by means of collapse contours in the hydrostatic-deviatoric stress space, illustrating the effects of wall slenderness, relative fracture (versus yield) strength, and the relative size of the plastic zone at the crack tip. Both the hydrostatic and deviatoric collapse strengths of the honeycomb strongly increase in the transition from brittle cell walls with low relative fracture strength to ductile cell walls with high relative fracture strength. This strength increase typically changes the shape of the collapse contour, and is the largest for transwall cracking, followed by intercell cracking and finally intrawall cracking. The ultimate collapse strength of the honeycomb is significantly more sensitive to the fracture strength than to the fracture toughness of the cell walls, and correctly approaches the plastic yield surface under increasing relative fracture strength. The numerical results may serve as a useful guideline in the experimental calibration of the local fracture and yield strengths of cell walls in wood.

Design of compact multi-layer microwave absorber for ultra-wide band applications thru shaping and RAM technologies

The present paper deals with improving the radar cross section reduction (RCSR) of a manufactured compact double-layer radar absorber material (RAM). The basic idea is to monitor the RCS performance of both operating frequency bands and electromagnetic wave (EMW) incidence angles by means of three altered structures. The interaction of EM fields with the three different structure geometries has been studied through the homogenization and/or forward-backward propagation approaches. Firstly, shaping a manufactured double-layer structure by way of uncoated periodic honeycomb is considered. Then, lonly a periodic coated honeycomb composite structure along with the expressions for its effective EM material properties are presented. Finally, multi-layered radar absorbing structure (RAS) has been studied through adding another planar thin RAM by using the extracted effective EM material properties of a periodic coated honeycomb composite structure. Genetic algorithm (GA) was applied in all RAS to optimize the thicknesses and/or material properties for better absorption of the incident EM wave. The effective material properties are measured through rectangular waveguide WR-90 and microstrip line fixtures. Comparing the results obtained from both measured and numerical solutions of the actual cross-sectional geometry, the engineered third planar layer is then manufactured to cover X, Ku and K bands up to 60̂ incident angles. The simulated results show that the designed structures an effective absorption values less than −10 dB on average in the desired bandwidths and angle of incidents for TE & TM modes. Bistatic experiment showed that the RCS values for the proposed RAS achieved more than −10 dB.

Acoustic characterization of additive manufactured perforated panel backed by honeycomb structure with circular and non-circular perforations

This paper studies the acoustic properties of an additive manufactured micro-perforated panel backed by a periodic honeycomb structure. Extrusion-based Fused Filament Fabrication (FFF) technique of Additive Manufacturing (AM) is used to fabricate the integrated honeycomb structures with a perforated face sheet. Normal absorption coefficient of the fabricated structure is measured in impedance tube using two microphone transfer function method. A generalized analytical formulation based on unit section analysis applicable to various cross sections of perforations has been proposed to predict the absorption coefficient, where shape dependent viscous effects in the perforation are incorporated by deriving effective complex density of the medium. To study the effect of perforation shape, three geometries viz., circular, triangular and square perforations are considered for analysis where triangular shape found to have more absorption coefficient and lower frequency of peak absorption. In addition, broadband absorption coefficient of proposed structure has been demonstrated by deploying hexagonal cells of different lengths in a unit section. The analytical results are compared with experimental results and a good agreement is observed between them. A parametric study is conducted to understand effect of perforated hole size and cell length on the absorption coefficient and peak frequency. Results show that the proposed structures can be tuned to desired frequency range by altering geometric parameters like cell length, shape and size of perforation hole. Technique and methodology presented in the current study gives an alternative way to design and fabricate honeycomb structures with perforations for acoustic applications such as aircraft cabins, ship structures and building acoustics.

In-plane homogenization of commercial hexagonal honeycombs considering the cell wall curvature and adhesive layer influence

In the present paper a general parameterization of a periodic hexagonal honeycomb with double vertical walls (commercial honeycomb) is proposed and a new analytic model is established. More attention is paid to account for the radius of curvature of the inclined walls, the adhesive layer thickness, and adhesive fillet at nodes. Then, neglecting the skin effect, in plane elastic constants is obtained analytically using the beam theory. The deformation mechanisms of the honeycomb cells include flexure, stretching, shearing and hinging. The mechanism of hinging is included through small fictitious beams in order to balance the local effects which cannot be captured using the beam theory. Hinging can be neglected when the thickness of these beams becomes infinite or optimally chosen by a proper thickness as to minimize the cumulative errors of the analytical assumptions. The new analytic model presented in this paper can be particularized to the extended Balawi and Abot model if some parameters are adequately modified. The finite element modeling of a representative volume element is used for model calibration and validation considering different relative densities of real honeycombs. The numerical results obtained as a reference for the effective elastic constants are discussed by comparing them to the ones given by the analytic model; its advantages and pitfalls are discussed and explained through a case study and some sensitivity analyses. Numerical simulations are also done in order to establish the distribution of the stresses in cell walls and nodes to confirm the hypotheses used for determining the analytical relations and to explain some limits of the analytic model. The results provide new insights into understanding the mechanics of honeycombs and facilitate the design of new types of cellular materials, including composite hexagonal cell cores.

Honeycomb micro-textures for light trapping in multi-crystalline silicon thin-film solar cells.

The liquid phase crystallization (LPC) of silicon is an emerging technology for fabricating 10 - 20 µm thin multi-crystalline silicon layers on glass. LPC silicon solar cells exhibit similar electronic performance to multi-crystalline wafer-based devices. Due to the reduced absorber thickness, however, effective measures for light trapping have to be taken. We present tailor-made micro-structures for light trapping at the LPC silicon back-side, whereby a nano-imprinted resist layer serves as a three-dimensional etching mask in subsequent reactive ion etching. Contrary to state-of-the-art random pyramid textures produced by wet-chemical etching, this method allows to produce tailor-made textures independent of grain orientation. Differently shaped micro-textures were replicated in LPC silicon. Absorptance and external quantum efficiency of periodic honeycomb patterns and random pyramids were found to be equivalent. Thus, the method enables the potential to further optimize light trapping in LPC silicon solar cells.

Yield surfaces of periodic honeycombs with tunable Poisson's ratio

The yield surfaces of several honeycombs with tunable Poisson's ratio, i. e. hexagonal honeycomb, augmented hexagonal honeycomb, re-entrant honeycomb, and augmented re-entrant honeycomb, are investigated by both theoretical analysis and numerical simulations. A theoretical model is developed to predict the mechanical response of these honeycombs considering the coupling effect of the shear stress and axial stress. Explicit expressions of the yield strength are derived for the four types of honeycombs. Good consistency is obtained between the analytical solutions and the numerical simulations. The results of the study provide a new idea for designing new honeycomb materials with tunable Poisson's ratio for engineering applications in the future.

Dynamic compressive response of additively manufactured AlSi10Mg alloy hierarchical honeycomb structures

Periodic honeycombs have been used for their high strength, low weight and multifunctionality. The quasi-static and dynamic compressive responses of three types of additively manufactured AlSi10Mg honeycomb structures, specifically a single-scale honeycomb and two hierarchical honeycombs with two and three levels of hierarchy, respectively, have been investigated using experimental measurement and finite element (FE) simulations. The validated FE simulation has been employed to investigate the effects of relative density of the honeycombs and the key experimental parameters. The following failure modes of the three types of honeycombs have been observed both under quasi-static and dynamic compression: (1) the single-scale honeycomb experienced a transition of failure mechanism from local plastic buckling of walls to local damage of the parent material without buckling with the increase of the relative density of the honeycomb; (2) the hierarchical honeycombs all failed with parent material damage without buckling at different relative densities. For both quasi-static and dynamic compression, the hierarchical honeycombs offer higher peak nominal wall stresses compared to the single-scale honeycomb at low relative density of ρ¯=0.19; the difference is diminished as relative density increases, i.e. the three types of honeycombs can achieve similar peak wall stresses when ρ¯⩾0.26. Numerical results have suggested the hierarchical honeycombs can offer better energy absorption capacity than the single-scale honeycomb. The two-scale and three-scale hierarchical honeycombs achieved similar peak nominal wall stresses for both quasi-static and dynamic compression, which may suggest that the structural performance under out-of-plane compression is not sensitive to the hierarchical architecture. This work indicates that the structural advantage of hierarchical honeycombs can be utilised to develop high performance lightweight structural components.

A design of elastic metamaterials with multi-negative pass bands

In this paper, an elastic metamaterial is proposed by integrating a two-dimensionally periodic honeycomb lattice and tetrachiral metamaterial inclusions for low-frequency wave applications. Plane wave propagation in infinite periodic cells is investigated through using Floquet–Bloch principles and the finite element method. Two separate negative pass bands induced by different mechanisms appear in the band structures of wave propagation in the proposed elastic metamaterial. The working mechanisms of those two negative pass bands are revealed though analyzing the eigenmodes of the unit cell and the dynamic effective material properties. Numerical examples validate the proposed model and show that negative refraction of elastic waves in the elastic metamaterial has been obtained. The design concept of this type of elastic may be of use for the design of broadband flat lenses for elastic wave focusing.

Rigorous derivation of nonlinear Dirac equations for wave propagation in honeycomb structures

We consider a nonlinear Schrödinger equation in two spatial dimensions subject to a periodic honeycomb lattice potential. Using a multi-scale expansion together with rigorous error estimates, we derive an effective model of nonlinear Dirac type. The latter describes the propagation of slowly modulated, weakly nonlinear waves spectrally localized near a Dirac point.

Germanene on Al(111) grown at nearly room temperature

A -R19.1° superstructure has been formed on Al(111) by Ge deposition at nearly room temperature, which is different from the previously reported germanene on Al(111) with 3×3 periodicity. By scanning tunneling microscopy, scanning tunneling spectroscopy, and density functional theory calculation, the atomic structure of this surface is predicted to be a periodic honeycomb lattice of Ge atoms formed on Al(111), in which one Ge atom per unit cell markedly protrudes into the vacuum side. The calculated band structure based on the predicted germanene/Al(111) structure indicates strong hybridization between the Ge layer and the Al(111) substrate.

Effective In-Plane Elastic Modulus of a Periodic Regular Hexagonal Honeycomb Core with Thick Walls

AbstractThe effective in-plane elastic moduli of different types of honeycomb cores with thick walls are studied using analytical and numerical approaches. Analytical equations derived in this pape...

Cell geometry effect on in-plane energy absorption of periodic honeycomb structures

With advances in 3D printing technology, now honeycomb structures can be made with virtually unlimited unit cell geometries and cell arrangements giving a wide range of possible mechanical properties. However, studies on such structures have been mainly limited to the hexagonal honeycombs with little work done on other cell geometries. This paper investigates the effect of unit cell geometry on the in-plane compressive response and energy absorption behaviour of honeycombs using full-scale non-linear numerical simulations. Nine types of honeycombs are designed from different unit cell shapes, but having the same relative density. Finite element analysis is used to simulate the honeycombs’ behaviour under uniaxial compression loading. The results showed that unit cell geometry and cell arrangement affect the honeycombs’ compressive response significantly and provide different energy absorption characteristics. This comparison study shows that the honeycombs in which the deformation mode is dominated by bending of cell edges present a lower stiffness (effective modulus) and compressive strength, but a smoother plateau stress. The honeycombs having their deformation mode dominated by plastic buckling present a higher stiffness with less stable and undulated plateau stress. The results of this study provide more understanding in predicting the global behaviour of honeycomb structures and their energy absorption characteristic through their micro-topology. The effect of cell shape and its arrangement on the selection of honeycombs for energy absorption application is discussed and a methodology is proposed to balance the energy absorption with maximum transmitted stress, which is crucial for energy-absorbing design of structures.

Theory versus experiment for a family of single-layer compounds with a similar atomic arrangement: (Tl,X)/Si(111)3×3(X=Pb,Sn,Bi,Sb,Te,Se)

Two-dimensional compounds made of one monolayer of Tl and one-third monolayer of Pb, Bi, Te, or Se (but not of Sn or Sb) on Si(111) have been found to have a similar atomic arrangement which can be visualized as a $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$-periodic honeycomb network of chained Tl trimers with atoms of the second adsorbate occupying the centers of the honeycomb units. Structural and electronic properties of the compounds have been examined in detail theoretically using density functional theory (DFT) calculations and experimentally using low-energy electron diffraction (LEED), scanning tunneling microscopy (STM), and angle-resolved photoelectron spectroscopy (ARPES) observations. It has been found that though structural parameters of the compounds are very similar for all species, the only common feature of their band structure is a considerable spin-splitting of the surface-state bands, while other basic electronic properties vary greatly with a change of species. The Tl-Pb compound is strongly metallic with two metallic surface-state bands; the Tl-Bi compound is also metallic but with a single metallic band; the Tl-Te and Tl-Se compounds appear to be insulators.

Nanostructured 2D cellular materials in silicon by sidewall transfer lithography NEMS

Sidewall transfer lithography (STL) is demonstrated as a method for parallel fabrication of 2D nanostructured cellular solids in single-crystal silicon. The linear mechanical properties of four lattices (perfect and defected diamond; singly and doubly periodic honeycomb) with low effective Young’s moduli and effective Poisson’s ratio ranging from positive to negative are modelled using analytic theory and the matrix stiffness method with an emphasis on boundary effects. The lattices are fabricated with a minimum feature size of 100 nm and an aspect ratio of 40:1 using single- and double-level STL and deep reactive ion etching of bonded silicon-on-insulator. Nanoelectromechanical systems (NEMS) containing cellular materials are used to demonstrate stretching, bending and brittle fracture. Predicted edge effects are observed, theoretical values of Poisson’s ratio are verified and failure patterns are described.

Investigation of 3-dimensional structural morphology for enhancing light trapping with control of surface haze

A comparative study of 3-dimensional textured glass morphologies with variable haze value and chemical texturing of the glass substrates was conducted to enhance light trapping in silicon (Si) thin film solar cells (TFSCs). The light trapping characteristics of periodic honeycomb structures show enhanced transmittance and haze ratio in numerical and experimental approaches. The periodic honeycomb structure of notched textures is better than a random or periodic carved structure. It has high transmittance of ∼95%, and haze ratio of ∼52.8%, and the haze property of the angular distribution function of transmittance shows wide scattering angles in the long wavelength region because of the wide spacing and aspect ratio of the texture. The numerical and experimental approaches of the 3-D texture structures in this work will be useful in developing high-performance Si TFSCs with light trapping.

Anisotropic failure and size effects in periodic honeycomb materials: A gradient-elasticity approach

This paper proposes a fracture mechanics model for the analysis of crack propagation in periodic honeycomb materials. The model is based on gradient-elasticity which enables us to account for the effect of the material structure at the macroscopic scale. For simulating the propagation of cracks along an arbitrary path, the numerical implementation is elaborated based on an extended finite element method with the required level of continuity. The two main features captured by the model are directionality and size effect. The numerical predictions are consistent with experimental results on honeycomb materials but also with results reported in the literature for microstructurally short cracks in metals.

Effects of size and surface on the auxetic behaviour of monolayer graphene kirigami.

Graphene is an active element used in the design of nano-electro-mechanical systems (NEMS) owing to its excellent in-plane physical properties on mechanical, electric and thermal aspects. Considering a component requiring negative Poisson’s ratio in NEMS, a graphene kirigami (GK) containing periodic re-entrant honeycombs is a natural option. This study demonstrates that a GK with specific auxetic property can be obtained by adjusting the sizes of its honeycombs. Using molecular dynamics experiments, the size effects on the auxetic behaviour of GK are investigated. In some cases, the auxetic difference between the hydrogenated GK and continuum kirigami (CK) is negligible, in which the results from macro CK can be used to predict auxetic behaviour of nano kirigami. Surface effect of GK is demonstrated from two aspects. One is to identify the difference of mechanical responses between the pure carbon GK and the hydrogenated GK at same geometry and loading condition. Another is from the difference of mechanical responses between the GK model and the CK model under same loading condition and geometric configuration. Generally, surface energy makes the GK possess higher variation of auxetic behaviour. It also results in higher modulus for the GK as comparing with that of the CK.

Mating of Polyhedrato Evince an Order ofthe All-Space-Filling Periodic Honeycombs

Earlier discovery and presentation of an inherent order of the regular and semiregular polyhedra that displays three interrelated classes, together with consideration of the honeycombs, has led me to posit the existence of a coherent and integral metapattern that should relate the various all-space-filling periodical honeycombs, which I advance in an earlier paper that should be read in conjunction with thispaper, as they form part of a series.Here, I approach the periodic polyhedral honeycombs byexploring how pairs of polyhedra regularly combine or mate, whether proximally or distally, along the √1, √2 and √3 axes of their reference cubic and tetrahedral lattices. This is first performed for pairs of what I elsewhere term the Great Enablers (GEs), the positive and negative tetrahedra and truncated tetrahedra; secondly, for pairs of GEs and the Primary Polytopes (PPs); and thirdly, for pairs of PPs. This reveals that these three forms of mating, GE:GE, GE:PP and PP:PP, correlate with the three symmetry groups {2,3,3|2,3,3}, {2,3,3|2,3,4} and {2,3,4|2,3,4}, respectively, of the periodical honeycombs.These matings typically occur in naturallyoccurring pairs along each axis, so in general, a PP mates with just two PPs, though in certain cases one of these is the same as the original. These pairsof matings display a one-to-one correspondence with the possible periodic honeycombs. Differentiating the PPs into two groups of four according to their formal behavior suggests a pathway towards a proposed new order of the honeycombs.