Mechanical properties of arc concave honeycomb structure with negative Poisson’s ratio
-
摘要: 提出一种可变弧边内凹多胞蜂窝负泊松比结构。利用能量法得到了二维结构的等效泊松比和等效弹性模量的解析公式，讨论了弧角对等效泊松比和等效弹性模量的影响，解析解与有限元结果吻合较好，说明了该方法的有效性。利用ABAQUS研究了三维结构的冲击动力学特性，分析了蜂窝结构受冲击时的变形失效模式，讨论了冲击速度、结构应变和曲边弧角对动应力-应变曲线、能量吸收率和平台应力的影响规律。所得结果为该类机械超材料的冲击变形失效和吸能效果研究提供了力学依据。Abstract: In this paper, a variable arc concave honeycomb structure with negative Poisson’s ratio was proposed. The analytical formulas of the equivalent Poisson’s ratio and the equivalent elastic modulus of the two-dimensional structures were given by energy method. The influences of the arc angle on the equivalent Poisson’s ratio and the equivalent elastic modulus were discussed. The present analytical solution is in agreement with the finite element results, which shows validity of the present method. The three-dimensional structures’ characteristics of the dynamic were studied by ABAQUS, and the deformation failure mode of the whole honeycomb structures under impact was analyzed. The influences of the impact velocity, structural strain and arc angle on the dynamic stress-strain curve, the energy absorption rate and the platform stress were discussed. The results provide a mechanical basis for the analysis of impact deformation failure and energy absorption effect of such mechanical metamaterials.
-
图 1 可变弧角弧形内凹负泊松比蜂窝材料胞元
Figure 1. Variable arc angle arc concave negative Poisson's ratio cellular material
θ—Internal angle of arc edge; r—Arc radius; h—Half chord length; m—Length of connecting rod
图 2 弧边内凹蜂窝负泊松比二维结构静力分析图
Figure 2. Static analysis diagram of concave honeycomb 2D structure with negative Poisson's ratio
A-L—Structure of the node; F—Axial force; M0—Bending moment; 1—Unit load
图 3 弧边内凹蜂窝负泊松比二维结构模型结构图
Figure 3. Model structure diagram of arc concave honeycomb 2D structure with negative Poisson's ratio
图 4 弧边内凹蜂窝负泊松比二维结构等效泊松比与弧角的关系
Figure 4. Relationship between equivalent Poisson's ratio and arc angle of arc concave honeycomb 2D structure with negative Poisson's ratio
FEA—Finite element analysis
图 5 弧边内凹蜂窝负泊松比二维结构等效弹性模量与弧角的关系
Figure 5. Relationship between equivalent elastic modulus and arc angle of arc concave honeycomb 2D structure with negative Poisson's ratio
图 6 弧边内凹蜂窝负泊松比三维结构模型
Figure 6. Model diagram of arc concave honeycomb 3D structure with negative Poisson's ratio
图 7 不同冲击速度时弧边内凹蜂窝负泊松比三维结构的变形模式(应变为0.4)
Figure 7. Deformation modes of arc concave honeycomb 3D structure with negative Poisson's ratio at different impact velocities (Strain=0.4)
图 8 胞元弧角30°应变为0.4时弧边内凹蜂窝负泊松比三维结构变形图
Figure 8. Deformation diagram of cell with 30° arc angle and 0.4 strain for arc concave honeycomb 3D structure with negative Poisson's ratio
图 9 弧边内凹蜂窝负泊松比三维胞元变形模式
Figure 9. Three-dimensional cell deformation model of arc concave honeycomb 3D structure with negative Poisson's ratio
图 10 不同冲击速度时弧边内凹蜂窝负泊松比三维结构应力-应变曲线
Figure 10. Stress-strain curves of arc concave honeycomb 3D structure with negative Poisson's ratio at different impact velocities
图 11 不同冲击速度下的弧边内凹蜂窝负泊松比三维结构能量吸收曲线
Figure 11. Energy absorption curves of arc concave honeycomb 3D structure with negative Poisson's ratio at different impact velocities
图 12 弧边内凹蜂窝负泊松比三维结构平台应力随冲击速度的变化
Figure 12. Variation of platform stress with impact velocities of arc concave honeycomb 3D structure with negative Poisson's ratio
图 13 弧边内凹蜂窝负泊松比三维结构平台应力随弧角的变化
Figure 13. Variation of platform stress with arc angles of arc concave honeycomb 3D structure with negative Poisson's ratio
Young's modulus E/GPa Density ρ/(kg·m−3) Poisson's ratio ν 71 2770 0.33 
下载: 导出CSV
-
[1] KSHETRIMAYUM R S. A brief intro to metamaterials[J]. IEEE Potentials,2005,23(5):44-46. doi: 10.1109/MP.2005.1368916 [2] 于靖军, 谢岩, 裴旭. 负泊松比超材料研究进展[J]. 机械工程学报, 2018, 54(13):1-14. doi: 10.3901/JME.2018.13.001YU Jingjun, XIE Yan, PEI Xu. State-of-art of metamaterials with negative Poisson’s ratio[J]. Journal of Mechanical Engineering,2018,54(13):1-14(in Chinese). doi: 10.3901/JME.2018.13.001 [3] 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):656-689. doi: 10.6052/0459-1879-18-381REN Xin, ZHANG Xiangyu, XIE Yimin. Research progress in auxetic materials and structures[J]. Chinese Journal of Theoretical and Applied Mechanics,2019,51(3):656-689(in Chinese). doi: 10.6052/0459-1879-18-381 [4] 史炜, 杨伟, 李忠明, 等. 负泊松比材料研究进展[J]. 高分子通报, 2003(6):48-57. doi: 10.3969/j.issn.1003-3726.2003.06.008SHI Wei, YANG Wei, LI Zhongming, et al. Advances in negative Poisson’s ratio materials[J]. Polymer Bulletin,2003(6):48-57(in Chinese). doi: 10.3969/j.issn.1003-3726.2003.06.008 [5] JANUS-MICHALSKA M, JASIŃSKA D, SMARDZEWSKI J. Comparison of contact stress distribution for foam seat and seat of auxetic spring skeleton[J]. International Journal of Applied Mechanics and Engineering,2013,18(1):55-72. doi: 10.2478/ijame-2013-0004 [6] SAXENA K K, DAS R, CALIUS E P. Three decades of auxetics research-materials with negative Poisson’s ratio: A review[J]. Advanced Engineering Materials,2016,18(11):1847-1870. doi: 10.1002/adem.201600053 [7] NAKAMURA M. Fundamental properties of intermetallic compounds[J]. MRS Bulletin,1995,20(8):33-39. doi: 10.1557/S0883769400045085 [8] ALDERSON A. A triumph of lateral thought[J]. Chemistry & Industry,1999,10:384-387. [9] EVANS K E, CADDOCK B D. Microporous materials with negative Poisson’s ratios: microstructure and mechanical properties[J]. Journal of Physics D: Applied Physics,1989,22(12):1877-1882. doi: 10.1088/0022-3727/22/12/012 [10] LAKES R S. Advances in negative Poisson’s ratio materials[J]. Advanced Materials,1993,5(4):293-296. doi: 10.1002/adma.19930050416 [11] CHAN N, EVANS K E. Fabrication methods for auxetic foams[J]. Journal of Materials Science,1997,32:5725. doi: 10.1023/A:1018665617008 [12] LAKES R S. Foam structures with a negative Poisson’s ratio[J]. Science,1987,235:1038-1040. doi: 10.1126/science.235.4792.1038 [13] GIBSON L J, ASHBY M F. 多孔固体结构与性能[M]. 刘培生, 译. 北京: 清华大学出版社, 2003.GIBSON L J, ASHBY M F. Cellular solids: Structure and properties[M]. Translated by LIU Peisheng. Beijing: Tsinghua University Press, 2003 (in Chinese). [14] QIAO P, WANG J. Mechanics of composites sinusoidal honeycomb cores[J]. Jouranl of Aerospace Engineering,2005,18(1):42-50. doi: 10.1061/(ASCE)0893-1321(2005)18:1(42) [15] 卢子兴, 赵亚斌. 一种有负泊松比效应的二维多胞材料力学模型[J]. 北京航空航天大学学报, 2006, 32(5):594-597. doi: 10.3969/j.issn.1001-5965.2006.05.022LU Zixing, ZHAO Yabin. Mechanical model of two-dimensional cellular materials with negative Poisson's ratio[J]. Journal of Beijing University of Aeronautics and Astronautics,2006,32(5):594-597(in Chinese). doi: 10.3969/j.issn.1001-5965.2006.05.022 [16] 张伟, 侯文彬, 胡平. 新型负泊松比多孔吸能盒平台区力学性能[J]. 复合材料学报, 2015, 32(2):534-541.ZHANG Wei, HOU Wenbin, HU Ping. Mechanical properties of new negative Poission’s ratio crush box with cellular structure in plateau stage[J]. Acta Materiae Compositae Sinica,2015,32(2):534-541(in Chinese). [17] 蒋伟, 马华, 王军, 等. 基于环形蜂窝芯结构的负泊松比机械超材料[J]. 科学通报, 2016, 61(13):1421-1427. doi: 10.1360/N972015-01314JIANG Wei, MA Hua, WANG Jun, et al. Mechanical metamaterial with negative Poisson’s ratio based on circular honeycomb core[J]. Chinese Science Bulletin,2016,61(13):1421-1427(in Chinese). doi: 10.1360/N972015-01314 [18] 沈建邦, 肖俊华. 负泊松比可变弧角曲边内凹蜂窝结构的力学性能[J]. 中国机械工程, 2019, 30(17):2134-2141.SHEN Jianbang, XIAO Junhua. Mechanics properties of negative Poisson’s ratio honeycomb structures with variable arc angle curved concave sides[J]. China Mechanical Engineering,2019,30(17):2134-2141(in Chinese). [19] 王彦斌, 刘海涛. 负泊松比圆弧曲线蜂窝芯结构的力学分析[J]. 云南大学学报(自然科学版), 2020, 42(6):1159-1165.WANG Yanbin, LIU Haitao. Mechanical analysis of circular curve honeycomb core with negative Poisson’s ratio[J]. Journal of Yunnan University: Natural Sciences Edition,2020,42(6):1159-1165(in Chinese). [20] 卢子兴, 武文博. 基于旋转三角形模型的负泊松比蜂窝材料面内动态压溃行为数值模拟[J]. 兵工学报, 2018, 39(1):153-160.LU Zixing, WU Wenbo. Numerical simulations for the in-plane dynamic crushing of honeycomb material with negative Poisson’s ratio based on rotating triangle model[J]. Acta Armamentarii,2018,39(1):153-160(in Chinese). [21] 任毅如, 蒋宏勇, 金其多, 等. 仿生负泊松比拉胀内凹蜂窝结构耐撞性[J]. 航空学报, 2020, 42(3):223978.REN Yiru, JIANG Hongyong, JIN Qiduo, et al. Crashworthiness of bio-inspired auxetic reentrant honeycomb with negative Poisson’s ratio[J]. Acta Aeronautica et Astronautica Sinica,2020,42(3):223978(in Chinese). [22] 赵昌方, 朱宏伟, 仲健林, 等. 复合材料负泊松比结构力学性能数值研究[J]. 江苏师范大学学报(自然科学版), 2020, 38(4):61-64.ZHAO Changfang, ZHU Hongwei, ZHONG Jianlin, et al. Numerical study on the negative Poisson’s ratio structure with composite materials: tension and compression mechanics[J]. Journal of Jiangsu Normal University (Natural Science Edition),2020,38(4):61-64(in Chinese). [23] 刘宇, 郝琪, 田钰楠, 等. 不同泊松比填充结构在汽车前端的应用[J]. 湖北汽车工业学院学报, 2020, 34(2):50-54.LIU Yu, HAO Qi, TIAN Yunan, et al. Application on different negative Poisson’s ratio filling structures in automobile front end[J]. Journal of Hubei University of Automotive Technology,2020,34(2):50-54(in Chinese). [24] 魏路路, 余强, 赵轩, 等. 内凹-反手性蜂窝结构的面内动态压溃性能研究[J]. 振动与冲击, 2021, 40(4):261-269.WEI Lulu, YU Qiang, ZHAO Xuan, et al. In-plane dynamic crushing characteristics of en-entrant anti-trichiral honeycomb[J]. Journal of Vibration and Shock,2021,40(4):261-269(in Chinese). [25] 姚永永, 苏步云, 肖革胜, 等. 内凹负泊松比蜂窝结构的面内双轴冲击响应[J]. 高压物理学报, 2021, 35(2):72-79.YAO Yongyong, SU Buyun, XIAO Gesheng, et al. In-plane biaxial impact response of re-entrant auxetic honeycomb[J]. Chinese Journal of High Pressure Physics,2021,35(2):72-79(in Chinese). [26] 王博, 张雄, 徐胜利. 2D周期蜂窝结构面内静动态压缩力学行为研究[J]. 力学学报, 2009, 41(2):274-281.WANG Bo, ZHANG Xiong, XU Shengli. Mechanical behavior of 2D periodic honeycombs under in-plane uniaxial compression[J]. Chinese Journal of Theoretical and Applied Mechanics,2009,41(2):274-281(in Chinese). [27] 牛斌, 王博, 徐胜利. 正交各向异性Kagome蜂窝材料宏观等效力学性能[J]. 固体力学学报, 2009, 30(6):600-608.NIU Bin, WANG Bo, XU Shengli. Effective mechanical properties of orthotropic Kagome honeycomb materials[J]. Chinese Journal of Solid Mechanics,2009,30(6):600-608(in Chinese). [28] ZHANG W, MA Z D, HU P. Mechanical properties of cellular vehicle body structure with negative Poisson’s ratio and enhanced strength[J]. Journal of Reinforced Plastics and Composites,2014,33(4):342-349. doi: 10.1177/0731684413510752 [29] 邓小林. 分层梯变负泊松比蜂窝结构的面内冲击动力学分析[J]. 机械设计与制造, 2016, 57(4):219-223.DENG Xiaolin. In-plane impact dynamics analysis of honeycomb structure with layer gradient negative Poisson’s ratio[J]. Machinery Design & Manufacture,2016,57(4):219-223(in Chinese). [30] 高强, 王良模, 钟弘, 等. 负泊松比结构的三点弯曲性能研究[J]. 南京理工大学学报, 2019, 43(2):141-146.GAO Qiang, WANG Liangmo, ZHONG Hong, et al. Research of structure with negative Poisson’s ratio under three-point bending[J]. Journal of Nanjing University of Science and Technology,2019,43(2):141-146(in Chinese). [31] 周震, 叶茂. 新型三维负泊松比多胞结构的分析及相关问题的研究[D]. 广州: 广州大学, 2020.ZHOU Zhen, YE Mao. Analysis and experimental study of new three-dimensional negative Poisson’s ratio cellular structure[D]. Guangzhou: Guangzhou University, 2020 (in Chinese). [32] 沈建邦, 肖俊华, 梁希, 等. 负泊松比曲边内凹蜂窝结构的面内冲击动力学数值研究[J]. 中国机械工程, 2020, 31(16):1998-2004.SHEN Jianbang, XIAO Junhua, LIANG Xi, et al. Numerical study on in-plane dynamics of negative Poisson’s ratio honeycomb structures with curved concave sides[J]. China Mechanical Engineering,2020,31(16):1998-2004(in Chinese). [33] 白临奇, 史小全, 刘宏瑞, 等. 冲击载荷下箭头型负泊松比蜂窝结构动态吸能性能研究[J]. 振动与冲击, 2021, 40(11):70-77.BAI Linqi, SHI Xiaoquan, LIU Hongrui, et al. Dynamic energy absorption performance of arrow type honeycomb structure with negative Poisson’s ratio under impact load[J]. Journal of Vibration and Shock,2021,40(11):70-77(in Chinese). -
下载:
点击查看大图
计量
- 文章访问数: 1802
- HTML全文浏览量: 721
- PDF下载量: 180
- 被引次数: 0
