The transverse elastic properties of chiral honeycombs

This work describes the out-of-plane linear elastic mechanical properties of trichiral, tetrachiral and hexachiral honeycomb configurations. Analytical models are developed to calculate the transverse Young’s modulus and the Voigt and Reuss bounds for the transverse shear stiffness. Finite Element models are developed to validate the analytical results, and to identify the dependence of the transverse shear stiffness vs. the gauge thickness of the honeycombs. The models are then validated with experimental results from flatwise compressive and simple shear tests on samples produced with rapid prototype (RP)-based techniques.     

Transverse shear modulus of SILICOMB cellular structures

This work describes the transverse shear stiffness properties of a novel honeycomb with zero Poisson’s ratio. The cellular configuration is simulated using a series of finite element models representing full-scale and representative unit cells of the honeycomb topology. The models are benchmarked against experimental results from pure shear and 3-point bending ASTM tests. The benchmarked models are used to perform a parametric study of the shear moduli (G₁₃ and G₂₃) against the geometry of the unit cell and the gauge thickness of the honeycomb panels. The shear stiffness maps obtained allow comparison of the SILICOMB configuration against classical centresymmetric and rectangular honeycomb topologies.     

The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs

Four novel cylinder-ligament honeycombs are described, where each cylinder has 3 tangentially-attached ligaments to form either a hexagonal or re-entrant hexagonal cellular network. The re-entrant cylinder-ligament honeycombs are reported for the first time. The in-plane linear elastic constants and out-of-plane bending response of these honeycombs are predicted using finite element (FE) modelling and comparison made with hexagonal and re-entrant hexagonal honeycombs without cylinders. A laser-crafted re-entrant cylinder-ligament honeycomb is manufactured and characterized to verify the FE model. The re-entrant honeycombs display negative Poisson’s ratios and synclastic curvature upon out-of-plane bending. The hexagonal and ‘trichiral’ honeycombs possess positive Poisson’s ratios and anticlastic curvature. The ‘anti-trichiral’ honeycomb (short ligament limit) displays negative Poisson’s ratios when loaded in the plane of the honeycomb, but positive Poisson’s ratio behaviour (anticlastic curvature) under out-of-plane bending. These responses are understood qualitatively through considering deformation occurs via direct ligament flexure and cylinder rotation-induced ligament flexure.     

Mechanical behaviors of carbon fiber composite sandwich columns with three dimensional honeycomb cores under in-plane compression

Mechanical properties and failure modes of carbon fiber composite egg and pyramidal honeycombs cores under in plane compression were studied in the present paper. An interlocking method was developed for both kinds of three-dimensional honeycombs. Euler or core shear macro-buckling, face wrinkling, face inter-cell buckling, core member crushing and face sheet crushing were considered and theoretical relationships for predicting the failure load associated with each mode were presented. Failure mechanism maps were constructed to predict the failure of these composite sandwich panels subjected to in-plane compression. The response of the sandwich panels under axial compression was measured up to failure. The measured peak loads obtained in the experiments showed a good agreement with the analytical predictions. The finite element method was used to investigate the Euler buckling of sandwich beams made with two different honeycomb cores and the comparisons between two kinds of honeycomb cores were conducted.     

Graded conventional-auxetic Kirigami sandwich structures: Flatwise compression and edgewise loading

The work describes the manufacturing and testing of graded conventional/auxetic honeycomb cores. The graded honeycombs are manufactured using Kevlar woven fabric/914 epoxy prepreg using Kirigami techniques, which consist in a combination of Origami and ply-cut processes. The cores are used to manufacture sandwich panels for flatwise compression and edgewise loading. The compressive modulus and compressive strength of stabilized (sandwich) honeycombs are found to be higher than those of bare honeycombs, and with density-averaged properties enhanced compared to other sandwich panels offered in the market place. The modulus and strength of graded sandwich panel under quasi-static edgewise loading vary with different failure mode mechanisms, and offer also improvements towards available panels from open literature. Edgewise impact loading shows a strong directionality of the mechanical response. When the indenter impacts the auxetic portion of the graded core, the strong localization of the damage due to the negative Poisson’s ratio effect contains significantly the maximum dynamic displacement of the sandwich panel.     

Flatwise buckling optimization of hexachiral and tetrachiral honeycombs

The flatwise compressive behaviour of tetrachiral and hexachiral honeycombs is analysed, using analytical and Finite Element simulations, both with explicit and implicit formulations. The tetrachiral and hexachiral cells are composed by cylinders connected by four and six tangent ligaments respectively. The ligaments act as mixed stiffeners-elastic foundations during flatwise compressive loading, providing different buckling mode shapes during deformation. The models are compared with experimental results obtained using RP-based honeycombs tested according to ASTM C 393-00 and ASTM C365-00.     

Elastic buckling of hexagonal chiral cell honeycombs

The paper describes a combined analytical, numerical and experimental analysis on the compressive strength of hexagonal chiral honeycombs due to elastic buckling of the unit cells under flatwise compressive loading. Hexagonal chiral honeycombs are cellular structures composed noncentresymmetric unit cells, with an in-plane negative Poisson’s ratio (NPR) with a value of −1. Cylinders connected by tangent ligaments at 60° degrees compose the unit cells. Approximated analytical models are proposed for the purpose of initial design assuming the main contribution to the elastic collapse stress being given by the nodes, and considering also the superposition of the critical elastic loads of each component of the unit cell. The models are expressed in terms of nondimensional geometric unit cell parameters (ligament to cylinder radius aspect ratio and relative density), and core material properties. Finite element calculations using shell and brick elements are also performed on unit cell models with periodic boundary conditions using linear bifurcation buckling analysis. The analytical and numerical results are compared with the outcome of a series of experimental flatwise compressive tests carried out on chiral honeycomb samples manufactured using rapid prototyping technique in PA sintered powder and ABS plastics. The comparison shows good convergence between the sets of results, and highlights the specific deformation mechanisms of the hexagonal chiral honeycomb cell.     

倾斜胞壁Nomex蜂窝芯压剪复合力学响应

成形具有一定曲率的夹层结构时,需要将蜂窝芯铣削成曲面形状,造成蜂窝胞壁呈一定倾角,进而降低蜂窝夹芯结构面外承载能力。为了定量化分析面外载荷作用下倾斜胞壁蜂窝芯的力学性能,建立了倾斜胞壁蜂窝芯面外压剪复合有限元模型,并通过设计专用Arcan夹具实现蜂窝芯的面外压剪复合加载,用于验证模型的有效性。对比仿真与实验结果,发现蜂窝芯压剪响应及胞壁变形模式吻合较好。利用验证的有限元模型对胞壁倾角范围为0°～40°的蜂窝芯在面外压剪复合载荷下的力学响应进行了研究,结果表明随着蜂窝胞壁倾角的增大,蜂窝芯面外承载能力逐渐降低;当胞壁倾斜角由0°增加到40°,初始应力峰值下降最大幅度为47.7%,平原阶段强度下降幅度为29%;进一步分析了倾斜胞壁蜂窝芯截面芯格尺寸与胞壁倾角的几何关系,将倾斜胞壁蜂窝芯等效为具有相同截面尺寸的垂直胞壁蜂窝芯,推导了倾斜胞壁蜂窝芯在面外压缩及剪切载荷作用下的坍塌强度,揭示了胞壁倾角对蜂窝芯坍塌强度影响机制。     

复合材料蜂窝夹层结构T型接头拉伸性能研究

通过试验测量了复合材料蜂窝夹层结构T型整体接头的拉伸性能,得到其拉伸强度与破坏模式。建立了接头结构有限元模型,利用分类损伤判据、失效准则与刚度退化准则对结构的损伤情况进行模拟,研究了接头的拉伸破坏行为。有限元分析结果与试验结果吻合良好。研究结果表明,结构的薄弱点位于腹板内靠近蒙皮的位置。蜂窝在此处发生面外拉伸破坏,从而导致结构的最终破坏。腹板上的拉伸载荷主要通过过渡区填料传递给蒙皮,腹板与蒙皮间的搭接段对载荷传递的贡献较小。参数研究表明,对于复合材料蜂窝夹层结构T型接头,搭接段长度对结构的强度几乎没有影响,而增大蒙皮蜂窝的高度或采用低模量蜂窝可以提高结构强度。     

The effects of foam filling on compressive response of hexagonal cell aluminum honeycombs under axial loading-experimental study

In this paper the effects of foam filling of honeycomb panels on their plastic behavior and mechanical properties are studied experimentally. Five types of Al 5052-H39 honeycombs in bare and foam filled conditions are subjected to quasi-static axial compressive loading. The panels are selected so that the effects of parameters such as the cell size, the cell walls thickness and the panel thickness on the mean crushing strength, energy absorption capacity and the wavelength of the folds could be investigated. Tests show that foam filling of panels increases their mean crushing strength and energy absorption capacity up to 300% and the less the honeycomb density the greater the effect of foam filling. Furthermore, mean crushing strength of foam filled panels is larger than the sum of the mean crushing strengths of bare honeycomb and foam alone. The wavelength of folds and densification strain in foam filled panels are smaller than those of bare honeycombs. These tests also showed that unlike the theoretic formula the panel thickness influences the mean crushing strength of honeycomb.     

The effect of honeycomb relative density on its effective in-plane elastic moduli: An experimental study

Honeycombs are discrete materials at the macro-scale level but their mechanical properties need to be calculated as a continuum material in order to simplify their design in engineering applications. The effective mechanical behavior of hexagonal honeycombs was studied by analytical means and correlated with experimental results for aluminum honeycombs. In particular, the effective in-plane elastic moduli of the honeycombs were studied as a function of their relative density. The effect of the bending, shear and axial deformations on various existing beam models was analyzed for both in-plane honeycomb directions. An experimental program was performed with honeycombs of densities ranging from the commercial low-density ones to the solid construction material. It is shown experimentally that the beam models describe well the material response in the direction of the honeycomb double wall. However, it is concluded that the effective elastic moduli for honeycombs with low relative densities are not similar in the two in-plane directions as predicted by previous studies.     

Nomex蜂窝夹层结构弯曲刚度温度相关性的力学建模

胶黏剂粘接性能下降导致的面板与蜂窝芯分离是Nomex蜂窝夹层结构在高温下力学性能发生退化的主要原因。为此定义了胶黏剂的等效脱粘系数为温度升高引起蜂窝夹层结构弯曲刚度下降的损伤变量,并引入面板和蜂窝芯弹性模量的温度保持系数,建立了蜂窝夹层结构弯曲刚度温度相关性的力学模型。经外伸梁三点弯曲法试验校验,所建力学模型计算值与试验值的误差在15%内,可以较好地实现蜂窝夹层结构在高温下的弯曲刚度预报。研究成果可以用于软夹心蜂窝夹层结构在高温下弯曲刚度的估算。      

SPH evaluation of out-of-plane peak force transmitted during a hypervelocity impact

Smooth particle hydrodynamics (SPH) technique is applied to simulate a hypervelocity impact of an aluminum sphere on a simple aluminum target and on a honeycomb structure sandwich panel in order to provide a useful input to Finite Element Model or Statistical Energy Model on evaluating the vibration environment induced by the projectile on the target. The impact velocity range lays between 4 and 5 km/s. Different approaches have been analyzed. At first, the application of SPH technique for direct calculation of the vibration environment is described. Then the calculation of equivalent force impulse is evaluated. Two strategies have been applied: shear stress analysis and momentum calculation using drift velocity measurement. Momentum approach revealed to be the most convenient and reliable method. Results for an aluminum plate and a honeycomb sandwich panel are reported and compared to results of experiments and Finite Element Analysis.     

Dielectric properties of chiral honeycombs – Modelling and experiment

Electromagnetic properties of mechanically chiral honeycomb structures are investigated. In extension to previous works on the subject, rigorous analysis is performed above the quasi-static frequency range. Theoretical considerations and full wave 3D electromagnetic simulations are conducted to prove that, for the honeycombs of interest, higher order harmonics due to structure periodicity are attenuated away from the panel surface at frequencies up to several GHz, which covers a number of popular ISM bands. As a consequence, only individual plane TEM waves are observable at practical locations of transmitters and receivers away from the panel. Under the same conditions, it is demonstrated that the structural chirality does not translate into chiral electromagnetic behaviour. In other words, orthogonal modes of the honeycomb scenarios are linearly polarised, and transformation of the electromagnetic energy into heat occurs purely as a result of classical conductivity or loss tangent, which are low for the low-density panels made of low-loss dielectric cores. This indicates that EMC or shielding characteristics can only be designed either by utilizing the phenomenon of wave reflections, or by equipping the panels with additional foils on surfaces or absorbing foams in air volumes. While precise measurements of final-sized honeycomb panels remain as a challenging task for further work, preliminary experiments have been performed showing good agreement with theoretical and computed predictions.     

Compressive and flexural properties of biomimetic integrated honeycomb plates

The characteristics of honeycomb plates composed of an upper and lower lamination are employed to create a novel single-sided bonded honeycomb plate (SBHP) design, and the compressive and flexural properties of these biomimetic integrated honeycomb plates are investigated. The results demonstrate that even during the fracturing of the honeycomb plates (honeycomb core), no abrupt compression paralysis occurs (which would cause the load to decrease rapidly); furthermore, our honeycomb plates exhibit superior compressive properties compared to biomimetic sandwich plates manufactured using Zhang’s needle-injection method. The interfacial bonding surface and bonding quality have no significant effect on the flexural stiffness but do affect the failure modes and flexural failure strength of the honeycomb plates. The ultimate failure of the biomimetic integrated honeycomb without a bonding layer between the panel–core layers is determined by the material strength itself; therefore, the honeycomb possesses good mechanical properties. This experimental study confirms, for the first time, the effectiveness of the biomimetic integrated honeycomb structure manufacturing method.     

Mathematical modelling of energy absorption property for paper honeycomb in various ambient humidities

A mathematical model was developed to describe the relationship between the energy absorption properties of paper honeycombs and ambient humidity, as well as the structural parameters thereof. The model is a piecewise function modelling the energy absorption of four deformation stages of paper honeycomb (linear-elastic stage, yield stage, plateau stage and densification stage) separately. Function of each stage is a simple formula relating the energy absorption capacity to the thickness-to-length ratio of honeycomb cell, the mechanical property of a cell-wall material tested under a controlled atmosphere [23 °C and 50% relative humidity (RH)] and the RH. Energy absorption curves were thereby obtained for paper honeycombs with a wide range of thickness-to-length ratios in arbitrary humidity environments. The created model was then verified by comparing the predicted energy absorption curves with the experimental ones. A good accordance between the predictions and the observations was achieved, indicating that the energy absorption models developed here could be used to practical application for the designing optimisation and material selection of paper honeycombs.     

六角形纸蜂窝夹层板能量吸收研究进展

分析了纸蜂窝夹层板动静态压缩试验方法及不同结构参数的纸蜂窝夹层板动静态缓冲吸能特性。试验结果表明,平台应力是蜂窝胞壁厚跨比的幂指数函数。引入压缩密实化应变概念,构建了纸蜂窝材料压缩密实化应变评估方程。将纸蜂窝夹层板压缩应力应变曲线简化为线弹性区、平台区和密实化区,构建了纸蜂窝夹层板能量吸收曲线理论模型。基于纸蜂窝夹层板动静态压缩试验,可构建纸蜂窝夹层板二维能量吸收图,以便更好地袁征纸蜂窝夹层板的缓冲性能,并指出了该研究有待进一步完善之处。     

基于Ansys的新型双层蜂巢板抗压性能研究及优化设计

目的 利用Ansys研究一种新型双层蜂巢板的结构特征来优化该蜂巢板的结构参数,提高其抗压性能.方法 对蜂巢板进行压力试验和模型验证,利用响应面结果分析蜂巢单元的单元高度、厚度,以及中间面板厚度与蜂巢板平压最大等效应力的关系,最后利用响应面优化对蜂巢板进行多目标优化.结果 蜂巢板的平压最大等效应力与蜂巢单元高度、壁厚、中间面板厚度都有很大的关系,优化后的蜂巢的质量由8.9979 g降至7.8215 g,下降了13.07％,而蜂巢板的最大应力基本无变化.结论 通过Ansys Workbench的多目标优化,在保证蜂巢板抗压性能的情况下,有效地降低了蜂巢板的质量,同时也证明了此类方案的有效性.     

Macroscopic response of carbon-fiber pyramidal truss core panel taking account of local defect

In present paper, the macroscopic responses of carbon-fiber pyramidal truss core panel subject to uniaxial compressive loading are investigated through experimental, theoretical and finite element analysis (FEA) methods, taking account of local defect. The local defect is introduced in the form of missing strut for the unit cell. A theoretical model is proposed to predict the effect of defect on the compressive stiffness and ultimate strength of pyramidal truss core sandwich panel. To study the buckling and crushing behavior, a progressive damage model based on the Hashin failure criteria is implemented in ABAQUS software by means of a user subroutine VUMAT. The sensitivity of sandwich panel to the percentage of missing struts, defect type, and defect spatial configuration are respectively discussed. Comparing with the open-cell foam and honeycombs, the pyramidal truss has better defect tolerant than bending dominated construction. Moreover, the effects of defect type and defect spatial configuration on the strength of pyramidal truss panel are significant under the same percentage of missing struts. The numerical results reveal that the discrepancy can be up to 14% and 29%, respectively. The local defect should be considered in the design and application of pyramidal truss structure.     

On the Homogenization Analysis of Electromagnetic Properties for Irregular Honeycombs

Honeycombs are widely used in aerospace structures due to their low density and high specific strength. In this paper, effective electromagnetic properties of irregular honeycombs are investigated, by using the three dimensional homogenization theory and corresponding computational procedure. This homogenization method, being the extension of two-scale asymptotic approach, is employed to determine the expressions of the effective dielectric permittivity, magnetic permeability and electrical conductivity. To verify and validate the proposed model and procedure, effective permittivities of a typical irregular honeycomb are studied and compared with those of semi-empirical formulae. Moreover, the effect of geometry of honeycomb's unit cell on effective permittivities is also examined. Compared to semi-empirical estimations, the two-scale asymptotic homogenization method can be used to achieve more accurate results of effective electromagnetic properties for honeycombs in the scope of numerical modeling, and it can be also extended for estimation of effective electromagnetic tensors for various periodic composites.