In-plane tensile elasticity of a novel anti-tetrachiral cellular structure
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摘要: 提出了由半周期正弦梁组成的新型反四手性蜂窝结构。基于能量法对蜂窝结构面内拉伸弹性进行了理论分析，通过有限元仿真和实验测试对理论模型进行了验证，并讨论了几何参数对结构拉伸性能的影响，最后将本文结构与传统手性结构进行性能比较，探讨了本文结构的变形机制。结果表明：该新型结构具有优秀的变形能力，其等效弹性模量可比原材料低5~6数量级，且具有低至−8.7的大等效负泊松比范围，接近传统手性结构等效泊松比范围的2倍。作为一种独特的新型拉胀结构，其高度可调的弹性模量和泊松比可用于开发缓冲装置、医用支架、变体机翼等，在船舶、医疗、航空航天等领域具有巨大的应用潜力。Abstract: A novel anti-tetrachiral cellular structure composed of half-periodic sine beams was proposed. The in-plane tensile elasticity of the cellular structure was theoretically analyzed based on the energy method, then the theoretical model was verified by finite element simulation and experimental test, and the influence of geometric parameters on the tensile properties of the structure was discussed. Finally, the properties of the proposed structure were compared with those of the conventional chiral structure, and deformation mechanism of the proposed structure was also discussed. The results show that the novel structure has excellent deformation capability. The in-plane equivalent elastic modulus can be 5-6 orders of magnitude lower than the raw material. The structure also has a range of large equivalent negative Poisson’s ratio with the lower bound of −8.7, which is nearly 2 times larger than that of conventional chiral structure. As a unique novel auxetic structure, its highly tunable elastic modulus and Poisson’s ratio can be used to develop buffer devices, medical stents, morphing wings, etc., which has great application potential in the field of shipbuilding, medical treatment, aerospace and so on.
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图 1 半周期正弦梁反四手性蜂窝结构
Figure 1. Anti-tetrachiral cellular structure of half-periodic sine beams
图 2 半周期正弦梁蜂窝单元结构参数
L—Spanwise length of the half-period sine beam along the horizontal direction; VL—Chordwise height of the half-period sine beam along the horizontal direction; H—Spanwise length of the half-period sine beam along the vertical direction; VH—Chordwise height of the half-period sine beam along the vertical direction; t—Thickness of the beams; b—Gauge thickness
Figure 2. Structural parameters of unit cell with half-periodic sine beams
图 3 反四手性蜂窝结构沿x方向单轴拉伸
Figure 3. Uniaxial stretching along the x-direction of the anti-tetrachiral cellular structure
${\sigma _x}$—Equivalent stress along the x-direction; Δ1, Δ2, Δ3 and Δ4—Virtual dividing lines; ${P_x}$ and ${P_y}$—Tensile loads along the x- and y-directions, respectively; ${S_x}$ and ${S_y}$—Shear loads along the x- and the y-directions, respectively; ${M_1}$ and ${M_2}$—Interacting bending moments of the cross sections
图 4 反四手性蜂窝结构有限元仿真模型
Figure 4. Finite element model of the anti-tetrachiral cellular structure
图 5 反四手性蜂窝结构等效弹性模量
${E_x}/E$ 随参数$\xi $ 和$\varphi $ 变化的理论预测和仿真结果FEM—Finite element method
Figure 5. Theoretical predictions and FE results for the equivalent elastic modulus
${E_x}/E$ of the anti-tetrachiral cellular structure varying with$\xi $ and$\varphi $ 
图 6 反四手性蜂窝结构等效泊松比
${\nu _{{{xy}}}}$ 随参数$\xi $ 和$\varphi $ 变化的仿真结果和理论值预测Figure 6. Theoretical predictions and FE results for the equivalent Poisson's ratio
${\nu _{{{xy}}}}$ of the anti-tetrachiral cellular structure varying with$\xi $ and$\varphi $ 
图 7 单轴载荷下变形前后反四手性蜂窝结构等效应力图
Figure 7. Equivalent stress diagram of the anti-tetrachiral cellular structure before and after deformation under uniaxial loads
图 8 单轴载荷下变形后反四手性蜂窝结构z向转角图
Figure 8. z-direction rotation angle diagram of the anti-tetrachiral cellular structure after deformation under uniaxial loads
图 11 反四手性蜂窝结构连接工艺示意图
Figure 11. Schematic diagram of the joining process of anti-tetrachiral cellular structure
图 13 正弦半周期型反四手性蜂窝结构与传统手性结构在不同壁厚下随相对密度
${\rho _{\text{r}}}$ 变化的性能比较(传统手性结构：$r = 5\;{\text{mm}}$ ，${L_x} = {L_y} = 20\;{\text{mm}}$ ；正弦半周期型结构：$H = L = 20\;{\text{mm}}$ )Figure 13. Comparison of the properties between the half-periodic sine anti-tetrachiral cellular structure and conventional chiral structures under different thickness varying with relative density
${\rho _{\text{r}}}$ (Conventional chiral structure:$r = 5\;{\text{mm}}$ ,$ {L_x} = {L_y} = 20\;{\text{mm}} $ ; Half-periodic sine anti-tetrachiral structure:$H = L = 20\;{\text{mm}}$ )表 1 几何参数及无量纲参数设定
Table 1. Geometric parameters and dimensionless parameters setting
Geometric parameter Dimensionless parameter L Aspect ratio $\alpha = L/H$ VL Thickness ratio $ \beta = t/H $ H Gauge thickness ratio $\gamma = b/H$ VH Chord ratio of the horizontal beam $ \xi = {V_{\text{L}}}/H $ t Chord ratio of the vertical beam $\varphi = {V_{\text{H}}}/H$ b — 
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表 2 有限元仿真周期条件和边界条件
Table 2. Periodic conditions and boundary conditions for finite element simulation
Condition Uniaxial loading along the x-direction Periodic
condition${u_x}\left( {\text{E}} \right) = {u_x}\left( {\text{F}} \right)$ ${u_x}\left( {\text{E}} \right) = {u_x}\left( {\text{F}} \right)$
${\theta _z}\left( {\text{A}} \right) = {\theta _z}\left( {\text{B}} \right)$ ${\theta _z}\left( {\text{C}} \right) = {\theta _z}\left( {\text{D}} \right)$
${\theta _z}\left( {\text{E}} \right) = {\theta _z}\left( {\text{F}} \right)$ ${\theta _z}\left( {\text{G}} \right) = {\theta _z}\left( {\text{H}} \right)$Boundary condition ${u_x}\left( {\text{A}} \right) = 0$
${u_x}\left( {\text{C}} \right) = 0$ ${u_y}\left( {\text{C}} \right) = 0$
${u_x}\left( {\text{B} } \right) = {\varepsilon _x} 4 L$
${u_x}\left( {\text{D} } \right) = {\varepsilon _x} 4 L$Notes: ${u_x}$—Displacement along the x-direction; ${u_y}$—Displacement along the y-direction; ${\theta _z}$—Rotation angle around the z-axis; ${\varepsilon _x}$—Strain along the x-direction.
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表 3 实验与理论值的比较
Table 3. Comparison between the experimental and theoretical results
Number Parameter of the unit
($H = L = 20\;{\text{mm}}$)$ {E_x}/E $
(Theoretical value)${E_x}/E$
(Experiment value)Error/% ① $\begin{gathered} \xi = \varphi = 0.5 \\ t = 1\;{\text{mm}} \\ \end{gathered} $ $4.13 \times {10^{ - 5}}$ $3.74 \times {10^{ - 5}}$ $9.4$ ② $\begin{gathered} \xi = \varphi = 0.5 \\ t = 2\;{\text{mm}} \\ \end{gathered} $ $3.29 \times {10^{ - 4}}$ $2.99 \times {10^{ - 4}}$ $9.1$ ③ $\begin{gathered} \xi = \varphi = 0.5 \\ t = 3\;{\text{mm}} \\ \end{gathered} $ $1.10 \times {10^{ - 3}}$ $9.98 \times {10^{ - 4}}$ $9.3$ ④ $\begin{gathered} \xi = 0.3,\varphi = 0.5 \\ t = 2\;{\text{mm}} \\ \end{gathered} $ $1.01 \times {10^{ - 4}}$ $9.21 \times {10^{ - 4}}$ $8.8$ ⑤ $\begin{gathered} \xi = 0.8,\varphi = 0.5 \\ t = 2\;{\text{mm}} \\ \end{gathered} $ $1.08 \times {10^{ - 4}}$ $1.00 \times {10^{ - 4}}$ $7.4$ ⑥ $\begin{gathered} \xi = 0.5,\varphi = 0.3 \\ t = 2\;{\text{mm}} \\ \end{gathered} $ $3.37 \times {10^{ - 4}}$ $3.07 \times {10^{ - 4}}$ $8.9$ ⑦ $\begin{gathered} \xi = 0.5,\varphi = 0.8 \\ t = 2\;{\text{mm}} \\ \end{gathered} $ $3.18 \times {10^{ - 4}}$ $2.92 \times {10^{ - 4}}$ $8.2$
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表 4 传统手性蜂窝几何参数
Table 4. Geometric parameters of conventional chiral structures
Geometric parameter Dimensionless parameter Radius of central rigid node $r$ Transverse beam ratio ${\alpha _x} = {L_x}/r$ Length of transverse tangential ligaments ${L_x}$ Longitudinal beam ratio ${\alpha _y} = {L_y}/r$ Length of longitudinal tangential ligaments ${L_y}$ Thickness ratio $\beta = t/r$ Thickness of the beams $t$ Gauge thickness ratio $\gamma = b/r$ Gauge thickness $b$ —
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[1] 郭哲璐, 陈倩清, 刘在良. 浅析蜂窝夹层结构复合材料在舰船中的应用[J]. 信息记录材料, 2018, 19(11): 14-16.GUO Zhelu, CHEN Qianqing, LIU Zailiang. A brief analysis on application of honeycomb sandwich structure compo-site in ships[J]. Information Recording Materials, 2018, 19(11): 14-16(in Chinese). [2] AJAJ R M, PARANCHEERIVILAKKATHIL M S, AMOOZGAR M, et al. Recent developments in the aeroelasticity of morphing aircraft[J]. Progress in Aerospace Sciences,2021,120:100682. doi: 10.1016/j.paerosci.2020.100682 [3] WU B, ZHANG X, YANG D. Real ship application analysis of vibration isolation base made by auxetic metamaterials[J]. Ship Engineering,2018,40(2):56-62. [4] 杨德庆, 马涛, 张梗林. 舰艇新型宏观负泊松比效应蜂窝舷侧防护结构[J]. 爆炸与冲击, 2015, 35(2):243-248. doi: 10.11883/1001-1455(2015)02-0243-06YANG Deqing, MA Tao, ZHANG Genglin. A novel auxetic broadside defensive structure for naval ships[J]. Explosion and Shock Waves,2015,35(2):243-248(in Chinese). doi: 10.11883/1001-1455(2015)02-0243-06 [5] 颜芳芳, 徐晓东. 负泊松比柔性蜂窝结构在变体机翼中的应用[J]. 中国机械工程, 2012, 23(5):542-546. doi: 10.3969/j.issn.1004-132X.2012.05.007YAN Fangfang, XU Xiaodong. Negative Poisson’s ratio honeycomb structure and its applications in structure design of morphing aircraft[J]. China Mechanical Engineering,2012,23(5):542-546(in Chinese). doi: 10.3969/j.issn.1004-132X.2012.05.007 [6] ALI A R, AKHTER M Z, OMAR F K. Performance enhancement of a small-scale wind turbine featuring morphed trailing edge[J]. Sustainable Energy Technologies and Assessments,2021,46:101229. doi: 10.1016/j.seta.2021.101229 [7] SHU Y, CHANG Q, DONG W, et al. A comparative study of ballistic resistance of sandwich panels with aluminum foam and auxetic honeycomb cores[J]. Advances in Mechanical Engineering,2013,2:496-500. [8] YANG S, CHALIVENDRA V B, KIM Y K. Fracture and impact characterization of novel auxetic Kevlar®/epoxy lami-nated composites[J]. Composite Structures,2017,168:120-129. doi: 10.1016/j.compstruct.2017.02.034 [9] 刘宇, 郝琪, 田钰楠, 等. 负泊松比蜂窝结构胞元几何参数影响研究[J]. 机械强度, 2021, 43(6):1409-1416. doi: 10.16579/j.issn.1001.9669.2021.06.019LIU Yu, HAO Qi, TIAN Yu'nan, et al. Study on the influence of geometric parameters of cellulars structure with nega-tive Poisson’s ratio[J]. Journal of Mechanical Strength,2021,43(6):1409-1416(in Chinese). doi: 10.16579/j.issn.1001.9669.2021.06.019 [10] HAMZEHEI R, REZAEI S, KADKHODAPOUR J, et al. 2D triangular anti-trichiral structures and auxetic stents with symmetric shrinkage behavior and high energy absorption[J]. Mechanics of Materials,2020,142:103291. doi: 10.1016/j.mechmat.2019.103291 [11] LI H M, MA Y B, WEN W B, et al. In plane mechanical pro-perties of tetrachiral and antitetrachiral hybrid metastructures[J]. Journal of Applied Mechanics,2017,84(8):081006. doi: 10.1115/1.4036937 [12] 卢子兴, 李康. 手性和反手性蜂窝材料的面内冲击性能研究[J]. 振动与冲击, 2017, 36(21):16-22, 39. doi: 10.13465/j.cnki.jvs.2017.21.003LU Zixing, LI Kang. In-plane dynamic crushing of chiral and anti-chiral honeycombs[J]. Journal of Vibration and Shock,2017,36(21):16-22, 39(in Chinese). doi: 10.13465/j.cnki.jvs.2017.21.003 [13] PRALL D, LAKES R S. Properties of a chiral honeycomb with a Poisson’s ratio of −1[J]. International Journal of Mechanical Sciences,1997,39(3):305-314. doi: 10.1016/S0020-7403(96)00025-2 [14] ALDERSON A, ALDERSON K L, ATTARD D, et al. Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading[J]. Composites Science and Technology,2010,70(7):1042-1048. doi: 10.1016/j.compscitech.2009.07.009 [15] MOUSANEZHAD D, HAGHPANAH B, GHOSH R, et al. Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach[J]. Theoretical and Applied Mechanics Letters,2016,6(2):81-96. doi: 10.1016/j.taml.2016.02.004 [16] LORATO A, INNOCENTI P, SCARPA F, et al. The transverse elastic properties of chiral honeycombs[J]. Compo-sites Science and Technology,2010,70(7):1057-1063. doi: 10.1016/j.compscitech.2009.07.008 [17] LU X, TAN V B C, TAY T E. Auxeticity of monoclinic tetrachiral honeycombs[J]. Composite Structures,2020,241:112067. doi: 10.1016/j.compstruct.2020.112067 [18] SHEN L M, WANG Z G, WANG X X, et al. Negative Poisson’s ratio and effective Young’s modulus of a vertex-based hierarchical re-entrant honeycomb structure[J]. International Journal of Mechanical Sciences,2021,206:106611. doi: 10.1016/j.ijmecsci.2021.106611 [19] ZHANG Z W, TIAN R L, ZHANG X L, et al. A novel butterfly-shaped auxetic structure with negative Poisson’s ratio and enhanced stiffness[J]. Journal of Materials Science,2021,56(25):14139-14156. doi: 10.1007/s10853-021-06141-4 [20] 刘国勇, 侯永涛, 叶雪松, 等. 基于正交试验六韧带手性结构展收几何参数优化[J]. 湖南大学学报:自然科学版, 2020, 47(2):35-44.LIU Guoyong, HOU Yongtao, YE Xuesong, et al. Optimization of geometric parameters of hexagonal chiral structure based on orthogonal experiment[J]. Journal of Hunan University (Natural Sciences),2020,47(2):35-44(in Chinese). [21] WU W, QI D, LIAO H, et al. Deformation mechanism of innovative 3D chiral metamaterials[J]. Scientific Reports,2018,8(1):12575. doi: 10.1038/s41598-018-30737-7 [22] QI D X, LU Q Y, HE C W, et al. Impact energy absorption of functionally graded chiral honeycomb structures[J]. Extreme Mechanics Letters,2019,32:100568. doi: 10.1016/j.eml.2019.100568 [23] WU W W, SONG X K, LIANG J, et al. Mechanical properties of anti-tetrachiral auxetic stents[J]. Composite Structures,2018,185:381-392. doi: 10.1016/j.compstruct.2017.11.048 [24] ZHU Y L, JIANG S H, LU F C, et al. A novel enhanced anti-tetra-missing rib auxetic structure with tailorable in-plane mechanical properties[J]. Engineering Structures,2022,262:114399. doi: 10.1016/j.engstruct.2022.114399 [25] YANG C Q, YANG K J, TIAN Y P, et al. Theoretical analysis on the stiffness of compression-torsion coupling metamaterials[J]. Extreme Mechanics Letters,2021,46:101336. doi: 10.1016/j.eml.2021.101336 [26] CHEN Y J, SCARPA F, LIU Y J, et al. Elasticity of anti-tetrachiral anisotropic lattices[J]. International Journal of Solids and Structures,2013,50(6):996-1004. doi: 10.1016/j.ijsolstr.2012.12.004 -
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