## What is/are Hexagonal Honeycomb?

Hexagonal Honeycomb - Its main structure is a hexagonal honeycomb, and the substructure is composed of an augmented double arrow honeycomb (ADAH) negative Poisson’s ratio unit.^{[1]}This study aims to analyze the deformation behavior of hexagonal honeycomb and classify the collapse modes during constrained bending for forming curved sandwich structures.

^{[2]}In this paper, using first-principles calculations, we have investigated the oxidized form of the hexagonal honeycomb (ODB-h) and zigzag dumbbell silicene (ODB-z).

^{[3]}The resulting deformation patterns are in good agreement with experiments and, surprisingly, are analogous to the in-plane buckling behavior of hexagonal honeycombs.

^{[4]}Compared with conventional honeycombs, the specific energy absorption (SEA) of the proposed honeycombs can be improved by 85%, 110% and 95% for triangular, square and hexagonal honeycombs, respectively.

^{[5]}Segments of ribbon-like molecular columns with left- or right-handed 180° twist lie on the bonds of a honeycomb lattice so that three ribbons meet in a vertex of the hexagonal honeycomb.

^{[6]}The hexagonal honeycomb is widely known for its space-filling capacity, structural stability, and high EA potential.

^{[7]}com By applying dual anodization procedures of aluminum (Al) thin film over silicon substrate under controlled anodizing process conditions, a thin anodic alumina (AAO) pattern with hexagonal honeycomb-like arrangement nanopores and highly-regular aligned arrays was created.

^{[8]}In order to enhance the energy absorption capacity of the honeycomb structure, a novel self-similar hierarchical honeycomb is proposed by adding smaller hexagons in the center and the vertex position of the hexagonal honeycomb (HH), and therefore named as center-vertex honeycomb (CVH).

^{[9]}We find that the number of enteric ganglia is fixed early in development and that subsequent ENS morphogenesis consists in the anisotropic expansion of a hexagonal honeycomb (chicken) or a square (mouse) lattice, without de-novo ganglion formation.

^{[10]}This study is a continuation of the computational analysis of the reactor equipped with hexagonal honeycomb based heat transfer enhancements, performed in Part A of the study.

^{[11]}The mechanical properties and energy absorption performance for equivalent honeycombs were investigated and compared with hexagonal honeycombs under dynamic impact.

^{[12]}Semi Reentrant structures, which exhibit zero Poisson’s ratio and monoclastic curvature, are combinations of hexagonal Honeycomb and auxetic Reentrant structures.

^{[13]}The simulation method is validated based on the experimental results of hexagonal honeycombs.

^{[14]}It is revealed that the hexagonal honeycombs exhibit comparative energy absorption capacity with re-entrant ones.

^{[15]}In addition, comparing with the hexagonal honeycomb, reentrant honeycomb with slightly thicker cell walls expressed weaker ability in specific energy dissipation.

^{[16]}In this study, we come up with an index to quantitatively depict the indentation resistance of the hexagonal honeycombs under large deformation.

^{[17]}In previous research projects, a software tool has been developed that achieves the placement of hexagonal honeycombs on free formed surfaces in a load-oriented manner and thus offers new possibilities for designing lightweight components (e.

^{[18]}The first natural frequency of sandwich beams with corrugated channel cores having an inclination angle θ > 45° is higher than those of sandwich beams constructed with competing core topologies, including tetrahedral, Kagome and pyramidal trusses and hexagonal honeycombs.

^{[19]}In the present paper the hexagonal honeycombs with double vertical walls (commercial), which usually are used as cores in sandwich plates, and the rigid skin effect are considered.

^{[20]}Thus an investigation was conducted to evaluate the mechanical behavior of three core geometries, specifically, regular honeycombs, lotus and hexagonal honeycombs with Plateau borders.

^{[21]}A variety of topological structures, including hollow warren structure (cross warren, diamond warren, triangular warren, four layer warren), 2D lattice structure (hexagonal honeycomb, tetragonal honeycomb), closed-cell foam structure (hexagonal foam, tetragonal foam), open-cell foam structure (multi-layer egg box), and three-dimensional lattice structure (pyramid, tetrahedron, X), were fabricated using the Superplastic Forming/Diffusion Bonding (SPF/DB) process.

^{[22]}

## Entrant Hexagonal Honeycomb

Furthermore, compared with the traditional re-entrant hexagonal honeycomb structure and the star-shaped honeycomb structure, the relative elastic modulus and auxetic effect of the BSH structure were greatly improved, and the stiffness of the novel structure was improved while maintaining a high auxetic effect.^{[1]}First, structural noise and vibration responses of the auxetic panel with the re-entrant hexagonal honeycomb core are studied.

^{[2]}In this paper, we experimentally study the use of corrugated SECs, in particular with grid, diagrid, reinforced diagrid, and re-entrant hexagonal honeycomb-type (auxetic) patterns as a significant improvement to the untextured SEC in monitoring fatigue cracks in steel specimens.

^{[3]}In particular, an SEC corrugated with a re-entrant hexagonal honeycomb pattern is studied to monitor strain and stresses for three specific suture patterns: simple interrupted, cruciate, and intradermal patterns.

^{[4]}Small variations in the geometry of the re-entrant hexagonal honeycomb unit cell and its relative density resulted in twelve different designs (relative density: ∼5-45%, re-entrant angle = 10-25°, Poisson's ratio = -0.

^{[5]}Four specific corrugation patterns are investigated: a symmetric grid, a diagonal diagrid, a reinforced diagrid, and a non-symmetric re-entrant hexagonal honeycomb (auxetic) pattern.

^{[6]}A lightweight auxetic cellular vibration isolation base and a novel floating raft structures constituted by re-entrant hexagonal honeycombs showed the effect of vibration reduction in a geophysical vessel.

^{[7]}

## Regular Hexagonal Honeycomb

Structures with configurations such as regular hexagonal honeycomb (Hr), lotus (Lt), and hexagonal honeycomb with Plateau borders (Pt), with 0°, 45°, and 90° orientations were analyzed.^{[1]}Graphene is a two-dimensional sheet of regular hexagonal honeycomb lattice formed by sp2 hybrid orbital bonding, with only one layer thickness of a single atom, which is known as the “super king” of the 21st century.

^{[2]}The tubes are made of AL6063 aluminum alloy and a regular hexagonal honeycomb filler of ABSplus plastics.

^{[3]}For multifunctional optimization design of honeycomb structures, the high stiffness hierarchical honeycombs with stochastic Voronoi substructures (HHSVS) are proposed by substituting cell walls of the regular hexagonal honeycombs (ORHH) with Voronoi honeycomb lattices of equal mass.

^{[4]}Theoretical analysis of regular hexagonal honeycomb with parallel gradient configuration (HPGC) demonstrates that it can achieve a maximum of more than 70% enhancement of static strength in the x direction compared with uniform honeycomb (UH) of the same relative density.

^{[5]}Result in form of cycles to failure contour plot was compared with corresponding contour plot obtained for regular hexagonal honeycomb lattice unit cell.

^{[6]}

## Periodic Hexagonal Honeycomb

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.^{[1]}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.

^{[2]}

## Reentrant Hexagonal Honeycomb

A series of experimental tests is conducted on two corrugated patterns, namely a reentrant hexagonal honeycomb pattern (auxetic pattern) and a symmetric diagonal grid pattern, to further characterize the signal of the corrugated sensor under various levels of localized strain resembling an opening wound.^{[1]}Firstly, two types of typical reentrant hexagonal honeycombs with thin-walled and thick-walled cells were manufactured and compressive tests were carried out to characterize the deformation modes, negative Poisson's ratio distribution and crushing stress.

^{[2]}

## Metallic Hexagonal Honeycomb

The metamaterial is constructed by introducing a rubber coating and an embedded metallic neck into a metallic hexagonal honeycomb Helmholtz resonator.^{[1]}, relatively short peak stress plateaus, followed by prolonged crushing stress plateaus) in metallic hexagonal honeycombs subjected to out-of-plane impact loading are characterized using a combined numerical and analytical study, with the influence of the strain-rate sensitivity of the honeycomb parent material accounted for.

^{[2]}

## Classical Hexagonal Honeycomb

The classical hexagonal honeycomb is analyzed numerically.^{[1]}75C6H5Br (1), (NBu4)[MnCr(C6O4Br2)3]·C6H5X with X = Cl (2), I (3) and CH3 (4) and (NBu4)[MnCr(C6O4Br2)3]·2C6H5X with X = CN (5) and NO2 (6), present the classical hexagonal honeycomb-(6,3) lattice with alternating Mn(ii) and Cr(iii) ions.

^{[2]}

## Traditional Hexagonal Honeycomb

The results show that under the same relative density, compared with the traditional hexagonal honeycombs, the three new configurations can reduce the difference of load-carrying capacity in in-plane and out of plane directions.^{[1]}It was found that the specific energy absorption (SEA) of the hierarchical honeycomb was much higher than the traditional hexagonal honeycomb under the same volume.

^{[2]}

## Hierarchical Hexagonal Honeycomb

Three kinds of bi-directional hierarchical honeycombs (BDHH), including hierarchical triangular honeycomb, hierarchical quadrangular honeycomb and hierarchical hexagonal honeycomb, are developed to investigate their out-of-plane crashworthiness.^{[1]}Nevertheless, these existing studies largely focused on hierarchical hexagonal honeycombs, and the bio-inspired hierarchical circular thin-walled structures under the out-of-plane crushing loads had not been well studied experimentally, numerically and analytically for energy absorption to date.

^{[2]}

## Metal Hexagonal Honeycomb

Energy absorption capacity of metal hexagonal honeycomb under out of plane local quasi-static loading is investigated, experimentally.^{[1]}The energy absorption characteristics of sandwich panels with aluminum plate as facesheet and metal hexagonal honeycomb as the core are investigated under quasi-static punch loading using two flat nose and spherical projectiles, experimentally.

^{[2]}

## Plane Hexagonal Honeycomb

This study shows an experimental analysis of the mechanical behavior of three types of core, including (i) out-of-plane and (ii) in-plane hexagonal honeycomb, and (iii) S-shape corrugated core.^{[1]}The plane hexagonal honeycomb structure determines the strong lubrication stability and abrasive resistance of the GR nanoparticles.

^{[2]}

## Aluminium Hexagonal Honeycomb

The system is equipped with distinctive aluminium hexagonal honeycomb based heat transfer enhancements (HTE) having higher surface area to volume ratio for effective heat transfer combined with low system weight addition.^{[1]}Three aluminium hexagonal honeycomb structures: standard honeycomb (HC), sheet reinforced honeycomb (RHC), and Kirigami modified honeycomb (KHC) structures are prepared and tested under quasi-static compression in three axial directions.

^{[2]}

## hexagonal honeycomb structure

BCMs with a hexagonal honeycomb structure and a pore size of 20–35 μm were prepared by carbonizing cypress in an Ar atmosphere.^{[1]}Silicon films of monatomic thickness with a predominantly hexagonal honeycomb structure were obtained on each substrate.

^{[2]}Furthermore, compared with the traditional re-entrant hexagonal honeycomb structure and the star-shaped honeycomb structure, the relative elastic modulus and auxetic effect of the BSH structure were greatly improved, and the stiffness of the novel structure was improved while maintaining a high auxetic effect.

^{[3]}Three aluminium hexagonal honeycomb structures: standard honeycomb (HC), sheet reinforced honeycomb (RHC), and Kirigami modified honeycomb (KHC) structures are prepared and tested under quasi-static compression in three axial directions.

^{[4]}Whereas, the lightweight core is considered as hexagonal honeycomb structure or functionally graded porous structure.

^{[5]}The lattice is built based on a hexagonal honeycomb structure.

^{[6]}First, we use observed grating lobes to measure the amplitude of mechanical dimpling of the reflectors, which is caused by the hexagonal honeycomb structure of the carbon fibre reflectors.

^{[7]}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.

^{[8]}The paper is limited to the study of strain the rate dependence of hexagonal honeycomb structures manufactured with four different additive manufacturing processes: one polymer (fused deposition modeling, or material extrusion with ABS), one composite (nylon and continuous carbon fiber extrusion) and two metallic (laser powder bed fusion of Inconel 718 and electron beam melting of Ti6Al4V).

^{[9]}Kim and Kim [10] analysed the load-carrying properties and ground pressure of a nonpneumatic tire with a hexagonal honeycomb structure.

^{[10]}1D Ni-MOFs with a hexagonal honeycomb structure, good electronic conductivity and fast Li+ kinetic diffusion were hydrothermally prepared, and they exhibited excellent lithium storage performance in terms of high-rate reversible capacity and long-duration cycling behavior as the anode material in lithium ion batteries.

^{[11]}This technique can be used to generate nanoparticle arrays with various nanoparticle arrangements, including hexagonal honeycomb structures, periodic nanoring structures, and their combinations.

^{[12]}Here, the phonon transports of monolayer GeC with a perfect planar hexagonal honeycomb structure are investigated by solving the linearized phonon Boltzmann equation within the single-mode relaxation time approximation (RTA).

^{[13]}The plane hexagonal honeycomb structure determines the strong lubrication stability and abrasive resistance of the GR nanoparticles.

^{[14]}

## hexagonal honeycomb core

Based on Gibson technique, the hexagonal honeycomb core is equalized with a solid core.^{[1]}Three kinds of honeycomb core crash boxes were obtained by filling the inside of the traditional crash box with the quasi-honeycomb core, the quasi-square honeycomb core and hexagonal honeycomb core.

^{[2]}In the present work, experimental shear tests using a custom-built picture-frame shear fixture have been conducted to investigate the in-plane pure-shear response of an HRP-C fiberglass/phenolic hexagonal honeycomb core under large deformation.

^{[3]}Present study addresses the ballistic performance and energy absorption behaviour of the hemispherical sandwich shell structure having hexagonal honeycomb core against conical and hemispherical nosed projectile.

^{[4]}The dynamic behavior of sandwich columns with aluminum face-sheets and hexagonal honeycomb core under axial low-velocity impact is investigated experimentally and theoretically.

^{[5]}First, structural noise and vibration responses of the auxetic panel with the re-entrant hexagonal honeycomb core are studied.

^{[6]}Non-probabilistic models for the in-plane elastic properties of hexagonal honeycomb cores are developed in which the imprecisely defined input and response parameters are represented by only their mean values and variations without the requirement of knowing the probability density distributions of the imprecise parameters as is required for probabilistic methods.

^{[7]}This paper presents an experimental study of the compressive response of hexagonal honeycomb core from the initial elastic regime to a fully crushed state.

^{[8]}Impact behavior of sandwich panels with auxetic and hexagonal honeycomb cores are investigated experimentally and numerically.

^{[9]}The dynamic response of cylindrical sandwich panels with aluminum foam core, hexagonal honeycomb core, and auxetic honeycomb core are compared numerically.

^{[10]}In this article, an analytical model is derived to investigate the in-plane homogenized stress-strain relationship of an adhesively bonded commercial hexagonal honeycomb core under large deformation.

^{[11]}In view of cushioning energy absorption of paper composite sandwich structures with sinusoidal corrugation and hexagonal honeycomb cores, the static yield strength and compression deformation were.

^{[12]}In this research, a hexagonal honeycomb core under a compressional load is studied numerically from the initial elastic regime to the fully crushed state using the Abaqus finite-element modelling.

^{[13]}

## hexagonal honeycomb lattice

These support cells - comprised of pigment and cone cells - generate the hexagonal honeycomb lattice on top of which lenses are secreted.^{[1]}The study from hexagonal honeycomb lattice monolayer MoS2 to square lattice monolayer so-MoS2, which broadens the promising topological material systems.

^{[2]}The two low-lying B2Se monolayers (α-B2Se and β-B2Se) possess a hexagonal honeycomb lattice, showing a natural Dirac cone and their Fermi velocities are in the same order of that of graphene.

^{[3]}Graphene nanoribbons (GNRs) are lengthened one-dimensional monolayer strips of graphene and have a hexagonal honeycomb lattice structure.

^{[4]}Graphene is a two-dimensional sheet of regular hexagonal honeycomb lattice formed by sp2 hybrid orbital bonding, with only one layer thickness of a single atom, which is known as the “super king” of the 21st century.

^{[5]}Here, on the basis of the time-spatial reversal symmetry and topological defect theory, we demonstrate broadening of the edge state bandwidth in spin TPCs made of regular metallic cross structures by simultaneously deforming the hexagonal honeycomb lattice and adjusting the rotation angle.

^{[6]}Graphene is a two-dimensional structured material with a hexagonal honeycomb lattice composed of carbon atoms.

^{[7]}Graphene is just single layer of carbon atom compactly bound in hexagonal honeycomb lattice.

^{[8]}This project will focus on different carbon nanostructures, including the hexagonal honeycomb lattices of a single graphene sheet.

^{[9]}Graphene with hexagonal honeycomb lattice arrangement is suitable for adsorption of individual uranium atoms, with a high binding energy (−1.

^{[10]}Graphene is a two dimensional carbon sheet which is bonded in the hexagonal honeycomb lattice form.

^{[11]}Result in form of cycles to failure contour plot was compared with corresponding contour plot obtained for regular hexagonal honeycomb lattice unit cell.

^{[12]}Graphene, a monolayer carbon atoms arranged in hexagonal honeycomb lattice possesses impressive electronic properties.

^{[13]}

## hexagonal honeycomb unit

Small variations in the geometry of the re-entrant hexagonal honeycomb unit cell and its relative density resulted in twelve different designs (relative density: ∼5-45%, re-entrant angle = 10-25°, Poisson's ratio = -0.^{[1]}Furthermore, the effectiveness of the guidelines is demonstrated by conducting comparative simulation studies on the hexagonal honeycomb unit-cell and top modified unit-cells for each guideline.

^{[2]}

## hexagonal honeycomb layer

The two compounds prepared, formulated as: [Dy2(C6O4H2)3(dmso)2(H2O)2]·2dmso·18H2O (1) and [Dy2(C6O4Cl2)3(dmso)4]·2dmso·2H2O (2) show distorted hexagonal honeycomb layers with the solvent molecules (dmso and H2O) located in the interlayer space and in the hexagonal channels that run perpendicular to the layers.^{[1]}The six compounds are isostructural and show hexagonal honeycomb layers of the type [MnCr(C6O4Cl2)3]− alternating with layers containing the NBu4+ cations.

^{[2]}

## hexagonal honeycomb sandwich

02g/cm3, square/hexagonal honeycomb sandwich structures with structural density of 42.^{[1]}In addition, the sound insulation performance of the considered DAH sandwich models was investigated regarding the sound transmission loss (STL) from 1 Hz to 1500 Hz under a normal incident planar wave, and this performance was compared with that for hexagonal honeycomb sandwich panels.

^{[2]}

## hexagonal honeycomb cell

The core layer composed of hexagonal honeycomb cells with negative Poisson’s ratio was made of a metallic material.^{[1]}Herein, the in-plane uniaxial compressive response and energy absorption capacity of a novel hybrid configuration, AuxHex structure, which consists of auxetic and hexagonal honeycomb cells, are systematically investigated through theoretical, finite element simulation and experimental methods.

^{[2]}

## hexagonal honeycomb pattern

A series of experimental tests is conducted on two corrugated patterns, namely a reentrant hexagonal honeycomb pattern (auxetic pattern) and a symmetric diagonal grid pattern, to further characterize the signal of the corrugated sensor under various levels of localized strain resembling an opening wound.^{[1]}In particular, an SEC corrugated with a re-entrant hexagonal honeycomb pattern is studied to monitor strain and stresses for three specific suture patterns: simple interrupted, cruciate, and intradermal patterns.

^{[2]}