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.     

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.     

Honeycomb cores with enhanced buckling strength

Honeycombs, as cores in sandwich panels, are in wider use in transport applications where density-specific performance is critical. The ability of honeycombs to withstand through-thickness compression, and in particular resist buckling, is a key performance factor in many applications. However reports of the systematic study of buckling limits in such materials are scant. Honeycomb unit cells with a range of geometries, including conventional hexagonal, re-entrant hexagonal geometries, and modifications of both thereof, were tested mechanically and simulated via finite element modelling. The primary figure of merit was the density-specific peak compressive stress immediately prior to onset of buckling collapse. The conventional hexagonal honeycomb unit cell, as examined here, is not well optimised for density-specific peak stress; in comparison the re-entrant unit cell examined here had approximately 13% higher density-specific peak stress. Modifications to these geometries, such as face stiffeners and fillets, increased absolute values of peak stress but in most cases were deleterious or at best neutral to density-specific peak stress due to the subsequent increase mass of the honeycombs.     

Manufacturing and testing of a sandwich panel honeycomb core reinforced with natural-fiber fabrics

A novel honeycomb core made of a natural-fiber reinforced composite consisting of a vinylester matrix reinforced with jute fabric is introduced. Six-mm- and 10-mm-cell honeycombs are manufactured using two compression-molding techniques. Best results are obtained for the mold with lateral compression. Experimental tests are conducted to characterize the elastic response of the composite and the core response under flatwise compression. The effective elastic properties of the core are computed via a homogenization analysis and finite element modeling. The results of the homogenization analysis are in very good agreement with estimations done using analytical formulas from the bibliography. The flatwise compression tests show that the core failure mechanisms are yarn pull-out and fiber breaking. The large wall thickness relative to the cell size of the jute–vinylester cores, which inhibits buckling, and the heterogeneities in the composite, which are preferential damage initiation sites, explain the observed behavior. When compared in terms of the specific strengths, the jute/vinylester cores introduced in this work show similar performances to those of their commercially available counterparts. The results from this study suggest that jute-reinforced cores have the potential to be an alternative to standard cores in applications that sustain compressive static loads.     

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.     

Flexible cellular solid spokes of a non-pneumatic tire

Non-pneumatic tires (NPTs) have been introduced with a compliant cellular solid spoke component which functions as the air of the pneumatic tire. In this paper, hexagonal honeycomb spokes for a high fatigue resistance design are investigated by seeking compliant hexagonal structures that have low local stresses under macroscopic uni-axial loading. Using the honeycomb mechanics, two cases of hexagonal honeycombs are designed: (i) the same cell wall thickness and (ii) the same load carrying capacity. The elastic limits of the hexagonal honeycombs are obtained from the ABAQUS finite element code considering the geometric nonlinearity of a cellular structure associated with the cell wall buckling and bending. The compliant cellular structures having low local stress values are applied to the honeycomb spokes of an NPT for the structural validation and the local stresses of the honeycomb spokes are investigated under the same vertical loading conditions. Hexagonal honeycombs with a highly positive cell angle have low local stresses and low mass under the same vertical load carrying capability; the Type C honeycomb spokes in this study.     

六边形蜂窝芯异面类静态压缩力学行为的仿真分析

目的研究六边形蜂窝芯材异面类静态压缩载荷的数值模拟方法及相关力学行为。方法基于蜂窝单元阵列的方法,构筑了单双壁厚六边形蜂窝芯材异面类静态压缩有限元数值计算模型和分析方法。结果借助于该模拟方法,分析计算了不同结构参数条件下单双壁厚六边形蜂窝芯材的异面变形模式、变形曲线和类静态峰应力值,并绘制了相应的图、压缩力位移曲线和数据表格。结论将计算结果与现有的实验和理论计算结果作对比分析可知,计算结果与已有结果吻合较好,证明了所提出的有限元分析方法的可靠性。     

Dynamic crushing strength of hexagonal honeycombs

Based on the repeatable collapsing mechanism of cells’ structure under dynamic crushing, an analytical formula of the dynamic crushing strength of regular hexagonal honeycombs is derived in terms of impact velocity and cell walls’ thickness ratio. It is consistent with the equation obtained from the shock wave theory that regards cellular material as continuum, in which the key parameter is approximately measured from the “stress–strain” curve of the cellular material. The effect of unequal thickness of cell walls on the honeycomb's dynamic crushing strength is discussed, and the result shows that the dynamic crushing strength of the hexagonal honeycomb with some double-thickness walls is about 1.3 times of that of the hexagonal honeycomb without double-thickness wall. All of the analytical predictions are compared with the numerical simulation results, showing good agreements.     

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.     

The out-of-plane compressive behavior of metallic honeycombs

Stainless steel square-honeycombs have been manufactured by slotting together steel sheets and then brazing the assembly. Their out-of-plane compressive response has been measured as a function of the relative density, the ratio of specimen height to cell size, and the degree of constraint associated with bonding of the honeycomb to face-sheets. It has been found that, for the practical range of relative densities (less than 20%), the peak strength is relatively insensitive to both the ratio of the specimen height to cell size and to the presence or absence of bonding to face-sheets. An analytical model, derived from existing models for the buckling of shells, for elastic and plastic buckling of the square-honeycombs is shown to be in good agreement with the experimental measurements.     

In-plane elastic constants and strengths of circular cell honeycombs

The in-plane elastic modulus, Poisson’s ratio, brittle crushing strength and plastic yielding strength of honeycombs with hexagonally packed circular cells are analyzed theoretically. The resulting theoretical expressions are compared with the numerical results obtained from a series of finite element analyses for circular cell honeycombs with various relative densities, leading to a good correlation. It is also found that the in-plane mechanical properties of circular cell honeycombs are significantly affected by the ratio of cell-wall thickness to cell radius. Though the elastic constants along the two principal directions of circular cell honeycombs are the same, the brittle crushing strength and plastic yielding strength along the two principal directions are not identical. Furthermore, the in-plane mechanical properties of circular cell honeycombs are compared to those of regular hexagonal honeycombs with straight and uniform-thickness cell walls to evaluate their microstructural efficiency.     

构型对正多边形蜂窝异面缓冲性能的影响

目的 利用有限元法研究应变率不敏感的双线性各向同性应变硬化正多边形（等边三角形、正方形、正六边形和正八边形）蜂窝的异面缓冲性能。方法 建立基于正多边形蜂窝特征单元的异面冲击分析有限元模型，提出最佳应变这一缓冲性能评价新指标，基于此重新定义各能量吸收评价指标，形成新缓冲性能评价方法。结果 以此获取不同相对密度的各正多边形蜂窝在不同冲击速度下的变形模式和应力-应变曲线，以及平均平台应力、比能量吸收和冲击力效率等评价指标值，并进行了分析。结论 给定相对密度下，正八边形蜂窝具有最大的异面平均平台应力；正多边形蜂窝的比能量吸收与冲击速度成二次关系；定密度的正六和八边形蜂窝的冲击力效率优于等边三角形和正方形蜂窝。     

基于多尺度方法的蜂窝夹层复合材料结构轴向压缩稳定性

为有效预测蜂窝夹层复合材料结构压缩失稳载荷和破坏模式,本文基于层压板宏细观多尺度数值分析模型,研究蜂窝夹层复合材料结构在轴向压缩载荷下的屈曲稳定性。基于改进的通用单胞理论模型,并结合ABAQUS用户自定义子程序接口,建立蜂窝夹层复合材料结构宏细观数值模型,预报蜂窝夹层复合材料结构失效载荷和破坏模式,并与试验结果对照,验证了模型的有效性。结果表明:通过本文建立的数值模型可以有效预测蜂窝夹层复合材料结构在压缩载荷下的失稳载荷和破坏模式,其一阶失稳载荷为128.12 kN,与试验结果误差为4.58%,蜂窝夹层复合材料结构破坏模式为先发生屈曲失稳,然后迅速破坏。      

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.     

芯子开槽对蜂窝纸板平压强度的影响

在试验的基础上,研究了芯子开槽后蜂窝纸板平压强度的变化情况,并得到了蜂窝纸板的压缩特性曲线。试验结果表明,芯子的一侧均匀开槽后的蜂窝纸板,其平压强度较未开槽的蜂窝纸板的平压强度高。     

Functional grading in hierarchical honeycombs: Density specific elastic performance

The introduction of hierarchy into structures has been credited with improving their elastic and other properties. Similarly, functional grading has been demonstrated to increase the damage tolerance of honeycomb structures, although with the penalty of reduced Young’s modulus or increased density. The combination of both hierarchy and functional grading has not been reported for honeycomb structures, although it is known in natural materials. A parametric numerical modelling study has been made of the in-plane elastic properties of honeycombs and how they are affected by functional grading and hierarchy, and importantly to establish whether it is possible to avoid reductions in Young’s modulus. A set of analytical models has been developed to describe functional grading and hierarchy in honeycombs, based upon beam mechanics and the transform section method. The conditions for transition of a hierarchical honeycomb in behaviour from that of a discrete structure to that of a continuum are established. Furthermore, conditions are established for which hierarchical honeycombs, uniform or functionally graded, can surpass in-plane Young’s moduli of conventional honeycombs a by factor of up to 2, on an equal density basis.     

Transverse shear stiffness of thickness gradient honeycombs

This paper describes the transverse shear stiffness of a novel topology of gradient honeycomb structures. Opposite to classical honeycomb configurations, gradient honeycombs feature elements of their unit cells with a regular geometry variation across the whole honeycomb panel. The tessellation of the cells is not periodic, but is dictated by geometric constraints between adjacent units. Gradient honeycombs with wall thickness linearly increasing along the panel are described using experimental data and Finite Element models. The gradient behaviour of the cellular structure provides additional complexity, and the possibility of tailoring design properties, such as the stiffness per unit of weight. We observe a good agreement between the Finite Element and the experimental results, with maximum percentage errors <7% for the shear moduli of the honeycombs.     

蜂窝结构对蜂窝纸板平压性能影响的研究

研究了蜂窝纸板结构对其平压性能的影响,分析了蜂窝纸板平压强度与蜂窝半径与孔径比的理论计算模型,将试验结果与理论模型进行了综合分析,得出了平压强度的预测计算公式,且预测结果与试验结果有较好的一致性。     

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。     

The inplane elastic properties of circular cell and elliptical cell honeycombs

Summary The inplane elastic properties of perfectly circular and elliptic cell honeycombs are derived through an analytical method and validated numerically. In the case of perfectly circular cell hexagonally packed honeycomb, the inplane elastic properties are shown to be isotropic. However, a departure from circularity of the cells leading to cell ellipticity results in the inplane properties becoming orthotropic. The orthotropic elastic constants are also derived analytically and validated numerically.