In-plane tensile elasticity of a novel anti-tetrachiral cellular structure
-
摘要:
手性蜂窝结构不仅具有蜂窝结构轻质高强、高柔韧性等优点，同时还拥有负泊松比蜂窝的拉胀特性，在新型柔性结构方面受到国内外众多学者的广泛研究。但传统手性蜂窝结构通常具有刚性中心节点，且以切向直梁进行连接，虽具有较高的刚度，但刚性节点的存在也削弱了结构的变形能力，限制了其在具有高柔性需求场合的应用。本文提出一种由半周期正弦梁组成的新型反四手性蜂窝结构，该结构舍弃了中心刚性节点，单纯以梁结构进行连接，同时将直梁替换为特殊曲梁，缓解了结构在节点处的应力集中问题，结构简单且性能可调。因此，新型反四手性蜂窝具有更加优越的变形能力，等效弹性模量比传统手性结构低2~3个数量级，等效负泊松比的变化范围也扩大了近2倍，在船舶、医疗、航空航天等领域前景广阔。 正弦半周期型反四手性结构与传统手性结构随相对密度 ${\rho _{\text{r}}}$ 变化的${E_{\text{x}}}/E$ (a)和${\nu _{{\text{xy}}}}$ (b)性能比较(传统手性结构：$r = 5{\text{mm}}$ ，${L_{\text{x}}} = {L_{\text{y}}} = 20{\text{mm}}$ ；正弦半周期型结构：$H = L = 20{\text{mm}}$ )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. -
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
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
${\sigma _x}$ is the equivalent stress along the x-direction.${P_x}$ and ${P_y}$ are the tensile loads along the x- and y-directions, respectively; ${S_x}$ and ${S_y}$ are the shear loads along the x- and the y-directions，respectively; ${M_1}$ and ${M_2}$ are the 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
${\nu _{{\text{xy}}}}$ 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
${\nu _{{\text{xy}}}}$ 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 9 3 D打印反四手性蜂窝结构试件
Figure 9. 3 D printed anti-tetrachiral cellular structure specimens
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 $L$ Spanwise length of the half-period sine beam along the horizontal direction $\alpha = L/H$ Aspect ratio ${V_{\text{L}}}$ Chordwise height of the half-period sine beam along the horizontal direction $\beta = L/H$ Thickness ratio $H$ Spanwise length of the half-period sine beam along the vertical direction $\gamma = b/H$ Gauge thickness ratio ${V_{\text{H}}}$ Chordwise height of the half-period sine beam along the vertical direction $ \xi = {V_{\text{L}}}/H $ Chord ratio of the horizontal beam $t$ Thickness of the beams $\varphi = {V_{\text{H}}}/H$ Chord ratio of the vertical beam $b$ Gauge thickness 
下载: 导出CSV
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 ${u_x}\left( {\text{A}} \right) = 0$
${u_x}\left( {\text{C}} \right) = 0$ ${u_y}\left( {\text{C}} \right) = 0$
${u_x}\left( {\text{B}} \right) = {\varepsilon _x} \times 4 L$
${u_x}\left( {\text{D}} \right) = {\varepsilon _x} \times 4 L$Notes: ${u_x}$ is the displacement along the x-direction; ${u_y}$ is the displacement along the y-direction; ${\theta _z}$ is the angle around of the z-axis; ${\varepsilon _x}$ is the strain along the x-direction.
下载: 导出CSV
表 3 实验与理论值的比较
Table 3. Comparison between the experimental and theoretical results
Number Parameters 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\% $
下载: 导出CSV
表 4 传统手性蜂窝几何参数
Table 4. Geometric parameters of conventional chiral structures
Geometric parameter Dimensionless parameter $r$ Radius of central rigid node ${\alpha _x} = {L_x}/r$ Transverse beam ratio ${L_x}$ Length of transverse tangential ligaments ${\alpha _y} = {L_y}/r$ Longitudinal beam ratio ${L_y}$ Length of longitudinal tangential ligaments $\beta = t/r$ Thickness ratio $t$ Thickness of the beams $\gamma = b/r$ Gauge thickness ratio $b$ Gauge thickness
下载: 导出CSV
-
[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 Composite in Ships A Brief Analysis on Application of Honeycomb Sandwich Structure Composite 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 laminated 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 Yunan, et al. Study on the influence of geometric parameters of cellulars structure with negative 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. 2 D 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, MA Y, WEN W, et al. In Plane Mechanical Properties of Tetrachiral and Antitetrachiral Hybrid Metastructures[J]. Journal of Applied Mechanics:Transactions of the ASME,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]. Composites 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, WANG Z, WANG 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, TIAN R, ZHANG X, et al. A novel butterfly-shaped auxetic structure with negative Poisson’s ratio and enhanced stiffness[J]. Journal of Materials Science,2021,56:14139-14156. 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, HAO Yongtao, YE Xuesong, et al. Optimization of geometric parametersof 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 3 D chiral metamaterials[J]. Scientific Reports,2018,8(1):12575. doi: 10.1038/s41598-018-30737-7 [22] QI D, LU Q, HE C, 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, SONG X, 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, JIANG S, LU F, 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, YANG K, TIAN Y, 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 -
下载:
点击查看大图
计量
- 文章访问数: 264
- HTML全文浏览量: 214
- PDF下载量: 7
- 被引次数: 0
