Design and mechanical analysis of a novel chiral honeycomb structure
-
摘要: 当前手性蜂窝结构的研究除了关注结构本身所用材料以外，通过改变单元内部拓扑组合以提升力学性能成为绝大部分研究的重点，而大部分现有的手性蜂窝结构中都存在既会带来更大的结构刚度、同时也会增加整体结构重量的刚性大中心节点。针对现状，本文提出了一种易变形、延展性好的新型四手性细胞结构，通过能量法理论推导了梁结构力学性能的数值解，并用有限元方法进行了数值验证。通过参数分析，讨论了该结构的力学性能。结果表明：该负泊松比结构具有优异的力学表现，等效弹性模量低至10−6，且拥有最低为−5.5的大拉剪耦合系数范围。其等效弹性模量最低仅有V型梁结构的10%，等效剪切模量低于ATCS结构2个数量级；力学性能调节范围也接近于ATCS的1.5至2倍。作为一种新型手性结构，更低的等效弹性模量与范围更广的拉剪耦合系数在航空航天、船舶、医疗等领域有着巨大的应用潜力。Abstract: The current research on chiral honeycomb structures not only focuses on the materials used for the structure itself but also emphasizes improving mechanical performance by altering the internal topological arrangements of the units. Most existing chiral honeycomb structures feature rigid central nodes that increase both structural stiffness and overall weight. Addressing this situation, this paper proposed a novel tetra-chiral cell structure characterized by easy deformability and good extensibility. Theoretical deductions of beam structure mechanics using energy methods were presented, along with numerical validations using finite element analysis. Through parameter analysis, the mechanical performance of this structure was discussed. Results indicate that this structure, with a negative Poisson's ratio, demonstrates excellent mechanical properties. It exhibits an equivalent elastic modulus as low as 10−6 and a large range of shear coupling coefficients as low as −5.5. The equivalent elastic modulus is only 10% of that of a V-beam structure, and the equivalent shear modulus is lower by two orders of magnitude compared to an ATCS structure. The range of mechanical performance adjustment is also approximately 1.5 to 2 times that of the ATCS structure. As a new type of chiral structure, its lower equivalent elastic modulus and wider range of shear coupling coefficients present significant potential applications in aerospace, maritime, medical, and other fields.
-
图 2 新型手性结构整体构型及单元构型受拉伸载荷的受力分析
Figure 2. Force analysis of the overall configuration and the unit cell of the novel chiral structure under tensile load
图 5 新型手性结构整体构型以及单元构型受剪切载荷的受力分析
Figure 5. Force analysis of the overall configuration and the unit cell of the novel chiral structure under shear load
图 7 新型手性蜂窝结构变形图：(a)拉伸；(b)剪切
Figure 7. Deformation diagram of the novel chiral honeycomb structure:(a) Tension; (b) Shear
图 8 不同网格尺寸下新型手性蜂窝结构等效弹性模量的有限元仿真结果
Figure 8. Finite element simulation results of the effective elastic modulus of novel chiral honeycomb structures at different mesh sizes
图 9 传统四手性蜂窝结构anti-tetra-chiral structures (ATCS)有限元模型
Figure 9. Finite element model of anti-tetra-chiral structures (ATCS)
图 11 不同参数ζ、ξ下新型手性蜂窝结构等效弹性模量的理论预测、有限元仿真结果
Figure 11. Theoretical prediction and finite element simulation results of equivalent elastic modulus of novel chiral honeycomb structures under different parameters ζ and ξ
图 12 不同参数ζ、ξ下新型手性蜂窝结构拉剪耦合系数的理论预测、有限元仿真结果
Figure 12. Theoretical predictions and finite element simulation results of the tension-shear coupling coefficient of novel chiral honeycomb structures under different parameters ζ and ξ
图 13 不同参数ζ、ξ下新型手性蜂窝结构等效剪切模量的理论预测、有限元仿真结果
Figure 13. Theoretical predictions and finite element simulation results of the equivalent shear modulus of novel chiral honeycomb structures under different parameters ζ and ξ
图 14 不同参数ζ、ξ下新型手性蜂窝结构剪拉耦合系数的理论预测、有限元仿真结果
Figure 14. Theoretical prediction and finite element simulation results of shear-tension coupling coefficient of novel chiral honeycomb structures under different parameters ζ and ξ
图 15 V型蜂窝单元(VS)(a)和anti-tetra-chiral structures (ATCS)(b)单元
Figure 15. Unit cells of the V-shaped honeycomb (VS) (a) and anti-tetra-chiral structures (ATCS)(b)
图 16 三种结构等效弹性模量的理论预测结果
Figure 16. Theoretical prediction results of equivalent elastic moduli of three structures
图 17 三种结构拉剪耦合效应的理论预测结果
Figure 17. Theoretical prediction results of tension-shear coupling effects of three structures
图 18 三种结构等效剪切模量的理论预测结果
Figure 18. Theoretical prediction results of equivalent shear moduli of three structures
图 19 三种结构剪拉耦合效应的理论预测结果
Figure 19. Theoretical prediction of shear-tension coupling effects of three structures
表 1 有限元仿真载荷与边界条件
Table 1. Load and boundary conditions used in the finite element simulation
Conditions Tensile load in the X direction Shear load Load condition $ {U_x}(A) = \dfrac{{ - {\varepsilon _x}}}{2} \times H $
$ {U_x}(B) = \dfrac{{{\varepsilon _x}}}{2} \times H $
$ {U_y}(O) = 0 $$ {U_x}(C) = \dfrac{{ - {\varepsilon _x}}}{2} \times H $
$ {U_x}(D) = \dfrac{{{\varepsilon _x}}}{2} \times H $
$ {U_y}(O) = 0 $z-direction SYMM Periodic condition $ {U_x}(C) = {U_x}(D) $
$ {U_y}(C) = {U_y}(D) $
$ {\theta _{\textit{z}}}(A) = {\theta _{\textit{z}}}(B) $
$ {\theta _{\textit{z}}}(C) = {\theta _{\textit{z}}}(D) $$ {U_y}(A) = {U_y}(B) $
$ {\theta _{\textit{z}}}(A) = {\theta _{\textit{z}}}(B) $
$ {\theta _{\textit{z}}}(C) = {\theta _{\textit{z}}}(D) $
下载: 导出CSV
-
[1] Daynes S, Weaver P M. Review of shape-morphing automobile structures: concepts and outlook[J]. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2013, 227(11): 1603-1622. doi: 10.1177/0954407013496557 [2] Bubert E A, Woods B K S, Lee K, et al. Design and fabrication of a passive 1D morphing aircraft skin[J]. Journal of intelligent material systems and structures, 2010, 21(17): 1699-1717. doi: 10.1177/1045389X10378777 [3] Qiu K, Wang Z, Zhang W. The effective elastic properties of flexible hexagonal honeycomb cores with consideration for geometric nonlinearity[J]. Aerospace Science and Technology, 2016, 58: 258-266. doi: 10.1016/j.ast.2016.08.026 [4] 张大海. 冲击载荷下蜂窝及其夹芯结构力学行为研究[D]. 东南大学, 2018.Zhang Dahai. Study on the Mechanical Behavior of Honeycomb and Its Sandwich Structure under Impact Load[D]. Southeast University, 2018(in Chinese). [5] 吴鹤翔, 刘颖. 梯度变化对密度梯度蜂窝材料力学性能的影响[J]. 爆炸与冲击, 2013, 33(2): 163-168. doi: 10.3969/j.issn.1001-1455.2013.02.008Wu Hexiang, Liu Ying. The Influence of Gradient Variation on the Mechanical Properties of Density Gradient Honeycomb Materials[J]. Explosion and Impact, 2013, 33(2): 163-168(in Chinese). doi: 10.3969/j.issn.1001-1455.2013.02.008 [6] 赵畅, 周丽, 邱涛. 柔性铰可变形蜂窝结构的面内拉伸性能[J]. 复合材料学报, 2024, 42: 1-9.Zhao Chang, Zhou Li, Qiu Tao. In-plane tensile properties of flexible Hinge deformable honeycomb structures[J]. Journal of Composites, 2024, 42: 1-9(in Chinese). [7] 吴文旺, 肖登宝, 孟嘉旭, 等. 负泊松比结构力学设计、抗冲击性能及在车辆工程应用与展望[J]. 力学学报, 2021, 53(3): 611-638. doi: 10.6052/0459-1879-20-333Wu Wenwang, Xiao Dengbao, Meng Jiaxu, et al. Mechanical Design, Impact Resistance Performance, and Prospects for Application in Vehicle Engineering of Negative Poisson's Ratio Structures[J]. Acta Mechanica Sinica, 2021, 53(3): 611-638(in Chinese). doi: 10.6052/0459-1879-20-333 [8] 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 [9] Qiu K, Wang Z, Zhang W. The effective elastic properties of flexible hexagonal honeycomb cores with consideration for geometric nonlinearity[J]. Aerospace Science and Technology, 2016, 58: 258-266. doi: 10.1016/j.ast.2016.08.026 [10] 刘旭畅, 李爽, 杨金水. 一种新型手性负泊松比结构的减振性能[J]. 复合材料学报, 2024, 41(1): 477-484 doi: 10.13801/j.cnki.fhclxb.20230609.001Liu Xuchang, Li Shuang, Yang Jinshui. A new type of structure of chiral negative poisson's ratio of vibration reduction performance[J]. Journal of composite materials, 2024, 41(1): 477-484 doi: 10.13801/j.cnki.fhclxb.20230609.001 [11] Papka S D, Kyriakides S. In-plane crushing of a polycarbonate honeycomb[J]. International Journal of Solids and Structures, 1998, 35(3-4): 239-267. doi: 10.1016/S0020-7683(97)00062-0 [12] Ashby M F, Gibson L J. Cellular solids: structure and properties[J]. Press Syndicate of the University of Cambridge, Cambridge, UK, 1997: 175-231. [13] Masters I G, Evans K E. Models for the elastic deformation of honeycombs[J]. Composite structures, 1996, 35(4): 403-422. doi: 10.1016/S0263-8223(96)00054-2 [14] Xu M, Liu D, Wang P, et al. In-plane compression behavior of hybrid honeycomb metastructures: Theoretical and experimental studies[J]. Aerospace Science and Technology, 2020, 106: 106081. doi: 10.1016/j.ast.2020.106081 [15] M Wagner, T Chen, et al. Large Shape Transforming 4D Auxetic Structures[J]. 3D Printing and Additive Manufacturing, 2017, 4(3): 133-141. doi: 10.1089/3dp.2017.0027 [16] Gang X Z , Xin R , Wei J , et al. A novel auxetic chiral lattice composite: Experimental and numerical study[J]. Composite Structures, 2022, 282. [17] Yi Z , Xin R , Wei J , et al. In-plane compressive properties of assembled auxetic chiral honeycomb composed of slotted wave plate[J]. Materials & Design, 2022, 221. [18] Dirrenberger J, Forest S, Jeulin D. Effective elastic properties of auxetic microstructures: anisotropy and structural applications[J]. International Journal of Mechanics and Materials in Design, 2013, 9: 21-33. doi: 10.1007/s10999-012-9192-8 [19] Tabacu S, Negrea R F, Negrea D. Experimental, numerical and analytical investigation of 2D tetra-anti-chiral structure under compressive loads[J]. Thin-Walled Structures, 2020, 155: 106929. doi: 10.1016/j.tws.2020.106929 [20] 任鑫, 张相玉, 谢亿民. 负泊松比材料和结构的研究进展[J]. 力学学报, 2019, 51(3): 656-687. doi: 10.6052/0459-1879-18-381Ren Xin, ZHANG Xiangyu, Xie Yimin. Research progress of materials and structures with negative Poisson ratio[J]. Chinese Journal of Mechanical Mechanics, 2019, 51(3): 656-687(in Chinese). doi: 10.6052/0459-1879-18-381 [21] Ren X , Das R , Tran P , et al. Auxetic metamaterials and structures: a review[J]. Smart Materials and Structures, 2018, 27(2): [22] Sha Z D, She C M, Xu G K, et al. Metallic glass-based chiral nanolattice: Light weight, auxeticity, and superior mechanical properties[J]. Materials Today, 2017, 20(10): 569-576. doi: 10.1016/j.mattod.2017.10.001 [23] 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 [24] 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 [25] Yang P , Gang X Z , Dong H , et al. The out-of-plane compressive behavior of auxetic chiral lattice with circular nodes[J]. Thin-Walled Structures, 2023, 182(PA): [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 [27] Ma Q, Cheng H, Jang K I, et al. A nonlinear mechanics model of bio-inspired hierarchical lattice materials consisting of horseshoe microstructures[J]. Journal of the Mechanics and Physics of Solids, 2016, 90: 179-202. doi: 10.1016/j.jmps.2016.02.012 [28] Liu W, Li H, Yang Z, et al. In-plane elastic properties of a 2D chiral cellular structure with V-shaped wings[J]. Engineering Structures, 2020, 210: 110384. doi: 10.1016/j.engstruct.2020.110384 [29] Weidong L, Zhendong Y, Jiong Z. The in-plane tensile and shear properties of novel chiral cellular structures[J]. Mechanics of Advanced Materials and Structures, 2022, 29(27): 5933-5952. doi: 10.1080/15376494.2021.1969607 [30] 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 [31] 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 [32] 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 [33] 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 [34] 王雪松, 刘卫东, 刘典. 新型反四手性蜂窝结构的面内拉伸弹性[J]. 复合材料学报, 2023, 40(8): 4849-4861.Wang Xuesong, LIU Weidong, LIU Dian. New four chiral honeycomb structure of in-plane tensile elasticity[J]. Journal of composite materials, 2023, 40(8): 4849-4861 (in Chinese). -
下载:
点击查看大图
计量
- 文章访问数: 42
- HTML全文浏览量: 48
- 被引次数: 0
