Volume 44 Issue 1
Jan.  2023
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ZHOU Shiqi, HOU Xiuhui, DENG Zichen. Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States[J]. Applied Mathematics and Mechanics, 2023, 44(1): 12-24. doi: 10.21656/1000-0887.430202
Citation: ZHOU Shiqi, HOU Xiuhui, DENG Zichen. Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States[J]. Applied Mathematics and Mechanics, 2023, 44(1): 12-24. doi: 10.21656/1000-0887.430202

Buckling Analysis of Re-Entrant Honeycomb Structures Under General Macroscopic Stress States

doi: 10.21656/1000-0887.430202
  • Received Date: 2022-06-13
  • Rev Recd Date: 2022-07-08
  • Available Online: 2023-01-07
  • Publish Date: 2023-01-15
  • Based on the negative Poisson’s ratio effect of the re-entrant honeycomb, the finite element simulation of its buckling mechanical properties was carried out, and 2 buckling modes other than those of the traditional hexagonal honeycomb structures were obtained. The beam-column theory was applied to analyze the buckling strength and mechanism of the 2 buckling modes, where the equilibrium equations including the beam end bending moments and rotation angles were established. The stability equation was built through application of the buckling critical condition, and then the analytical expression of the buckling strength was obtained. The re-entrant honeycomb specimen was printed with the additive manufacturing technology, and its buckling performance was verified by experiments. The results show that, the buckling modes vary significantly under different biaxial loading conditions; the re-entrant honeycomb would buckle under biaxial tension due to the auxetic effect, being quite different from the traditional honeycomb structure; the typical buckling bifurcation phenomenon emerges in the analysis of the buckling failure surfaces under biaxial stress states. This research provides a significant guide for the study on the failure of re-entrant honeycomb structures due to instability, and the active application of this instability to achieve special mechanical properties.

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  • [1]
    QUAN C, HAN B, HOU Z, et al. 3D printed continuous fiber reinforced composite auxetic honeycomb structures[J]. Composites (Part B): Engineering, 2020, 187: 107858. doi: 10.1016/j.compositesb.2020.107858
    SON M A, CHAE K W, KIM J S, et al. Structural origin of negative thermal expansion of cordierite honeycomb ceramics and crystal phase evolution with sintering temperature[J]. Journal of the European Ceramic Society, 2019, 39(7): 2484-2492. doi: 10.1016/j.jeurceramsoc.2019.02.017
    TAO R, JI L, LI Y, et al. 4D printed origami metamaterials with tunable compression twist behavior and stress-strain curves[J]. Composites (Part B): Engineering, 2020, 201: 108344. doi: 10.1016/j.compositesb.2020.108344
    GAO Q, LIAO W H, WANG L. On the low-velocity impact responses of auxetic double arrowed honeycomb[J]. Aerospace Science and Technology, 2020, 98: 105698. doi: 10.1016/j.ast.2020.105698
    QI C, JIANG F, YU C, et al. In-plane crushing response of tetra-chiral honeycombs[J]. International Journal of Impact Engineering, 2019, 130: 247-265. doi: 10.1016/j.ijimpeng.2019.04.019
    CHEN Z, LIU L, GAO S, et al. Dynamic response of sandwich beam with star-shaped reentrant honeycomb core subjected to local impulsive loading[J]. Thin-Walled Structures, 2021, 161: 107420. doi: 10.1016/j.tws.2020.107420
    贠昊, 邓子辰, 朱志韦. 弹性波在星形节点周期结构蜂窝材料中的传播特性研究[J]. 应用数学和力学, 2015, 36(8): 814-820 doi: 10.3879/j.issn.1000-0887.2015.08.003

    YUN Hao, DENG Zichen, ZHU Zhiwei. Bandgap properties of periodic 4-point star-shaped honeycomb materials with negative Poisson’s ratios[J]. Applied Mathematics and Mechanics, 2015, 36(8): 814-820.(in Chinese) doi: 10.3879/j.issn.1000-0887.2015.08.003
    PAPKA S D, KYRIAKIDES S. In-plane compressive response and crushing of honeycomb[J]. Journal of the Mechanics and Physics of Solids, 1994, 42(10): 1499-1532. doi: 10.1016/0022-5096(94)90085-X
    AJDARI A, NAYEB-HASHEMI H, VAZIRI A. Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures[J]. International Journal of Solids and Structures, 2011, 48(3/4): 506-516. doi: 10.1016/j.ijsolstr.2010.10.018
    LIU Y, ZHANG X C. The influence of cell micro-topology on the in-plane dynamic crushing of honeycombs[J]. International Journal of Impact Engineering, 2009, 36(1): 98-109. doi: 10.1016/j.ijimpeng.2008.03.001
    YUAN C, MU X, DUNN C K, et al. Thermomechanically triggered two-stage pattern switching of 2D lattices for adaptive structures[J]. Advanced Functional Materials, 2018, 28(18): 1705727. doi: 10.1002/adfm.201705727
    PAPAKOSTAS A, POTTS A, BAGNALL D M, et al. Optical manifestations of planar chirality[J]. Physical Review Letters, 2003, 90(10): 107404. doi: 10.1103/PhysRevLett.90.107404
    SPADONI A, RUZZENE M, GONELLA S, et al. Phononic properties of hexagonal chiral lattices[J]. Wave Motion, 2009, 46(7): 435-450. doi: 10.1016/j.wavemoti.2009.04.002
    HOU X H, DENG Z C, ZHANG K, et al. Dynamic crushing strength analysis of auxetic honeycombs[J]. Acta Mechanica Solida Sinica, 2016, 29: 490-501. doi: 10.1016/S0894-9166(16)30267-1
    BERTOLDI K, REIS P M, WILLSHAW S, et al. Negative Poisson’s ratio behavior induced by an elastic instability[J]. Advanced Materials, 2010, 22(3): 361-366. doi: 10.1002/adma.200901956
    YANG D, MOSADEGH B, AINLA A, et al. Buckling of elastomeric beams enables actuation of soft machines[J]. Advanced Materials, 2015, 27(41): 6323-6327. doi: 10.1002/adma.201503188
    JIMÉNEZ F L, TRIANTAFYLLIDIS N. Buckling of rectangular and hexagonal honeycomb under combined axial compression and transverse shear[J]. International Journal of Solids and Structures, 2013, 50(24): 3934-3946. doi: 10.1016/j.ijsolstr.2013.08.001
    COMBESCURE C, ELLIOTT R, TRIANTAFYLLIDIS N. Deformation patterns and their stability in finitely strained circular cell honeycombs[J]. Journal of the Mechanics and Physics of Solids, 2020, 142: 103976. doi: 10.1016/j.jmps.2020.103976
    梁观坡, 傅禹鑫, 娄本亮, 等. 负压激励下含椭圆孔高弹体的屈曲分析[J]. 应用数学和力学, 2021, 42(12): 1221-1228

    LIANG Guanpo, FU Yuxin, LOU Benliang, et al. Buckling behaviors of elastomers with periodic elliptical holes under negative pressure activation[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1221-1228.(in Chinese)
    PENG X, ZHONG Y, SHI J, et al. Global buckling analysis of composite honeycomb sandwich plate with negative Poisson’s ratio using variational asymptotic equivalent model[J]. Composite Structures, 2021, 264(5): 113721.
    GAVAZZONI M, FOLETTI S, PASINI D. Cyclic response of 3D printed metamaterials with soft cellular architecture: the interplay between as-built defects, material and geometric non-linearity[J]. Journal of the Mechanics and Physics of Solids, 2022, 158: 104688. doi: 10.1016/j.jmps.2021.104688
    赵艳萍, 李琳, 金明. 柔性约束下压杆的一些稳定和不稳定的临界状态[J]. 应用数学和力学, 2017, 38(8): 877-887

    ZHAO Yanping, LI Lin, JIN Ming. Some stable and unstable critical states of a compression rod with a flexible support[J]. Applied Mathematics and Mechanics, 2017, 38(8): 877-887.(in Chinese)
    TIMOSHENKO S P, GERE J M. Theory of Elastic Stability[M]. 2nd ed. Dover Publications, 2009.
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