新型星-菱形负泊松比蜂窝结构的动态力学特性

李娜; 刘述尊; 张新春; 张英杰; 齐文睿

doi:10.13801/j.cnki.fhclxb.20240308.001

新型星-菱形负泊松比蜂窝结构的动态力学特性

doi: 10.13801/j.cnki.fhclxb.20240308.001

李娜¹,
刘述尊¹,
张新春^{1, 2, ,},
张英杰^{1, 2},
齐文睿¹

1.
华北电力大学　机械工程系，保定 071003
2.
华北电力大学　河北省电力机械装备健康维护与失效预防重点实验室，保定 071003

基金项目: 河北省自然科学基金(A2020502005)

详细信息

通讯作者:
张新春，博士，副教授，硕士生导师，研究方向为新型功能/智能材料与结构　E-mail: xczhang@ncepu.edu.cn

中图分类号: O347；TB383；TB330.1
计量
- 文章访问数: 249
- HTML全文浏览量: 116
- PDF下载量: 16
- 被引次数: 0
出版历程
- 收稿日期: 2024-01-05
- 修回日期: 2024-02-05
- 录用日期: 2024-02-28
- 网络出版日期: 2024-03-11
- 刊出日期: 2024-09-15

Dynamic mechanical properties of novel star-rhombic negative Poisson's ratio honeycomb structure

LI Na¹,
LIU Shuzun¹,
ZHANG Xinchun^{1, 2
, ,},
ZHANG Yingjie^{1, 2},
QI Wenrui¹

1.
Department of Mechanical Engineering, North China Electric Power University, Baoding 071003, China
2.
Hebei Key Laboratory of Electric Machinery Health Maintenance & Failure Prevention, North China Electric Power University, Baoding 071003, China

Funds: Natural Science Foundation of Hebei Province (A2020502005)

摘要

摘要: 为进一步提高蜂窝结构的抗冲击性能和能量吸收能力，通过周期性阵列传统星形胞元和星-菱形胞元，本文构建了内凹星形蜂窝结构(Reentrant star-shaped honeycomb structures，RSH)和新型的面内增强星-菱形蜂窝结构(Enhanced star-rhombic honeycomb structures，ESH)。通过实验和有限元模拟，系统地研究了ESH在不同加载方向的面内力学响应和吸能特性。与RSH相比，准静态压缩下ESH的负泊松比特性减弱，但吸能能力显著提高。此外，结合微拓扑胞元的变形特征，揭示了低速冲击时ESH-y的应力-应变响应呈现双平台特征的变形机制，并讨论了结构参数α、t和b对平台应力的影响规律。基于高速冲击下ESH的周期性逐层坍塌变形特征和动量定理，给出了不同加载方向高速平台应力的理论解，理论结果与有限元结果吻合较好。该研究可为创新设计具有更优力学性能的新型负泊松比结构提供参考。
- 星-菱形负泊松比结构 /
- 平台应力 /
- 面内增强 /
- 冲击响应 /
- 能量吸收
Abstract: In order to further improve the crushing resistance and energy-absorbing capacity of the honeycomb structure, by periodically arraying typical star-shaped and star-rhombic cells, the reentrant star-shaped honeycomb structures (RSH) and the novel in-plane enhanced star-rhombic honeycomb structures (ESH) were constructed in this paper. The in-plane mechanical response and energy absorption characteristics of ESH under different loading directions were systematically investigated through experiments and finite element (FE) simulations. Compared with RSH, the negative Poisson's ratio characteristics of ESH under quasi-static compression are weakened, but the energy-absorbing capacities are significantly improved. In addition, by combining the deformation features of micro-topological cells, the deformation mechanism that the stress-strain response of ESH-y exhibits a double-plateau characteristic at low velocities of crushing is revealed, and the influence of the structural parameters α, t, and b on the plateau stresses is discussed. Based on the periodic layer-by-layer collapse deformation features of ESH under high-velocity crushing and the momentum theorem, the theoretical solutions of the high-velocity plateau stress in different loading directions are obtained, and theoretical results are in good agreement with FE results. This study can provide a reference for the innovative design of novel negative Poisson's ratio structures with better mechanical properties.
- star-rhombic honeycomb structures /
- plateau stresses /
- in-plane enhancement /
- crushing response /
- energy absorption

HTML全文

图 1 内凹星形和增强星-菱形蜂窝结构的设计策略

Figure 1. Design strategies for re-entrant star-shaped honeycomb structures (RSH) and enhanced star-rhombic honeycomb structures (ESH)

H—Height of specimen; W—Width of specimen; d—Out-of-plane depth; α—Reentrant angle; b—Cell length; t—Wall thickness; l₁, l₂—Length of cell wall; w—Width of unit cell; h—Height of unit cell

下载: 全尺寸图片幻灯片

图 2 (a)实验装置；(b)有限元模型

Figure 2. (a) Experimental setup; (b) Finite element model

v—Crushing velocity; ${x_{Li}}$, ${x_{Ri}}$—Displacement reference point

下载: 全尺寸图片幻灯片

图 3 网格收敛性验证

Figure 3. Validation of mesh convergence

下载: 全尺寸图片幻灯片

图 4 RSH的准静态力学响应与模拟结果比较：(a) y-方向变形历程；(b)应力-应变曲线；(c) x-方向变形历程；(d)泊松比

Figure 4. Comparison of quasi-static mechanical response and simulation results for RSH: (a) Deformation modes in y-direction; (b) Stress-strain curves; (c) Deformation modes in x-direction; (d) Poisson's ratio

S—Stress

下载: 全尺寸图片幻灯片

图 5 ESH的准静态力学响应与模拟结果比较：(a) y -方向变形历程；(b)应力-应变曲线；(c) x -方向变形历程；(d)泊松比

Figure 5. Comparison of quasi-static mechanical response and simulation results for ESH: (a) Deformation modes in y-direction; (b) Stress-strain curves; (c) Deformation modes in x-direction; (d) Poisson's ratio

下载: 全尺寸图片幻灯片

图 6 ESH和RSH的平台应力、吸收的总能量E_A与比能量吸收E_SEA

Figure 6. Plateau stress, energy absorption E_A and specific energy absorption E_SEA of ESH and RSH

下载: 全尺寸图片幻灯片

图 7 ESH的典型变形模式

Figure 7. Typical deformation modes of ESH

下载: 全尺寸图片幻灯片

图 8 ESH的应力-应变响应和定量评估

Figure 8. Stress-strain response and quantitative evaluation of ESH

Δσ—Stress fluctuation; ε_d—Densification strain

下载: 全尺寸图片幻灯片

图 9 低速冲击下ESH-y的变形机制

Figure 9. Deformation mechanism of ESH-y under low-velocity crushing

σ_p1—The first plateau stress; σ_p2—The second plateau stress; w₀—Initial width of representative cell; h₀—Initial height of representative cell

下载: 全尺寸图片幻灯片

图 10 内凹角度α、胞壁厚度t以及胞元长度b对ESH平台应力的影响

Figure 10. Effect of α, t and b on plateau stresses of ESH

下载: 全尺寸图片幻灯片

图 11 高速冲击下ESH-y的变形机制

Figure 11. Deformation mechanism of ESH-y under high-velocity crushing

σ₁—Top uniform stress; σ₂—Bottom uniform stress; h_f—Final height of representative cell

下载: 全尺寸图片幻灯片

图 12 ESH-y和ESH-x的平台应力比较

Figure 12. Comparison of plateau stresses for ESH-y and ESH-x

下载: 全尺寸图片幻灯片

表 1 实验试样的几何参数

Table 1. Geometric parameters of experimental specimens

	RSH-y	RSH-x	ESH-y	ESH-x
α/(°)	20	20	20	20
t/mm	1	1	1	1
b/mm	20	20	20	20
W/mm	85.89	80.53	85.58	80.34
H/mm	80.47	85.77	80.44	85.60
d/mm	15.19	15.31	15.48	15.47
m/g	21.75	22.05	31.65	31.70
$\bar \rho $	0.17	0.17	0.24	0.24
Notes: m—Mass of specimen; $\bar \rho $—Relative density.

下载: 导出CSV

表 2 基体材料属性

Table 2. Material properties of the matrix material

Matrix material	PLA	Aluminum alloy^[1]
Young's modulus E_s/GPa	2.04±0.04	68.2
Density ρ_s/(kg·m⁻³)	1240	2700
Yield stress σ_ys/MPa	30.42±2.21	80
Poisson's ratio ν	0.3	0.3
Note: PLA—Polylactic acid.

下载: 导出CSV

参考文献(29)

[1]	WANG H, LU Z, YANG Z, et al. A novel re-entrant auxetic honeycomb with enhanced in-plane impact resistance[J]. Composite Structures, 2019, 208: 758-770. doi: 10.1016/j.compstruct.2018.10.024
[2]	ZHOU S, LIU H, MA J, et al. Deformation behaviors and energy absorption characteristics of a hollow re-entrant auxetic lattice metamaterial[J]. Aerospace Science and Technology, 2023, 142: 108583. doi: 10.1016/j.ast.2023.108583
[3]	QI C, JIANG F, YANG S. Advanced honeycomb designs for improving mechanical properties: A review[J]. Composites Part B: Engineering, 2021, 227: 109393. doi: 10.1016/j.compositesb.2021.109393
[4]	GUO H, ZHANG J. Expansion of sandwich tubes with metal foam core under axial compression[J]. Journal of Applied Mechanics, 2023, 90(5): 051008. doi: 10.1115/1.4056686
[5]	刘浩, 周宏元, 王小娟, 等. 泡沫混凝土填充旋转薄壁多胞方管负泊松比结构面内压缩性能[J]. 复合材料学报, 2024, 41(2): 841-859. LIU Hao, ZHOU Hongyuan, WANG Xiaojuan, et al. In-plane compression properties of negative Poisson's ratio structure of rotating thin-walled multi-cell square tubes with foam concrete filler[J]. Acta Materiae Compositae Sinica, 2024, 41(2): 841-859(in Chinese).
[6]	MA L H, WEI T, RAO W, et al. 4D printed chiral metamaterials with negative swelling behavior[J]. Smart Materials and Structures, 2023, 32(1): 015014. doi: 10.1088/1361-665X/aca84d
[7]	ZHOU X, JING L. Large deflection response of sandwich beams with layered-gradient foam cores subjected to low-velocity impact[J]. International Journal of Impact Engineering, 2023, 172: 104429. doi: 10.1016/j.ijimpeng.2022.104429
[8]	ZHANG X C, LIU N N, AN C C, et al. Dynamic crushing behaviors and enhanced energy absorption of bio-inspired hierarchical honeycombs with different topologies[J]. Defence Technology, 2023, 22: 99-111. doi: 10.1016/j.dt.2021.11.013
[9]	ZHANG J, LU G, YOU Z. Large deformation and energy absorption of additively manufactured auxetic materials and structures: A review[J]. Composites Part B: Engineering, 2020, 201: 108340. doi: 10.1016/j.compositesb.2020.108340
[10]	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. REN Xin, ZHANG Xiangyu, XIE Yimin. Research progress in auxetic materials and structures[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(3): 656-687(in Chinese).
[11]	ZHANG X C, SHEN Z F, WU H X, et al. In-plane dynamic crushing behaviors of joint-based hierarchical honeycombs with different topologies[J]. Journal of Sandwich Structures & Materials, 2021, 23(8): 4218-4251.
[12]	ZHANG X, WANG J, SUN Q, et al. Mechanical design and analysis of bio-inspired re-entrant negative Poisson's ratio metamaterials with rigid-flexible distinction[J]. International Journal of Smart and Nano Materials, 2023, 15(1): 1-20.
[13]	QI C, JIANG F, REMENNIKOV A, et al. Quasi-static crushing behavior of novel re-entrant circular auxetic honeycombs[J]. Composites Part B: Engineering, 2020, 197: 108117. doi: 10.1016/j.compositesb.2020.108117
[14]	ZOU Z, XU F, NIU X, et al. In-plane crashing behavior and energy absorption of re-entrant honeycomb reinforced by arched ribs[J]. Composite Structures, 2023, 325: 117615. doi: 10.1016/j.compstruct.2023.117615
[15]	ZHANG X, HAO H, TIAN R, et al. Quasi-static compression and dynamic crushing behaviors of novel hybrid re-entrant auxetic metamaterials with enhanced energy-absorption[J]. Composite Structures, 2022, 288: 115399. doi: 10.1016/j.compstruct.2022.115399
[16]	ZHANG W, WANG H, LOU X, et al. On in-plane crushing behavior of a combined re-entrant double-arrow honeycomb[J]. Thin-Walled Structures, 2024, 194: 111303. doi: 10.1016/j.tws.2023.111303
[17]	冯学凯, 王宝珍, 巫绪涛, 等. 新型节圆正弦蜂窝面内压缩力学性能研究[J]. 力学学报, 2023, 55(9): 1910-1920. FENG Xuekai, WANG Baozhen, WU Xutao, et al. In-plane compression behavior of sinusoidal honeycomb with circular nodes[J]. Chinese Journal of Theoretical and Applied Mechanics, 2023, 55(9): 1910-1920(in Chinese).
[18]	韩会龙, 张新春, 王鹏. 负泊松比蜂窝材料的动力学响应及能量吸收特性[J]. 爆炸与冲击, 2019, 39(1): 47-57. HAN Huilong, ZHANG Xinchun, WANG Peng. Dynamic responses and energy absorption properties of honeycombs with negative Poisson's ratio[J]. Explosion and Shock Waves, 2019, 39(1): 47-57(in Chinese).
[19]	WEI L, ZHAO X, YU Q, et al. In-plane compression behaviors of the auxetic star honeycomb: Experimental and numerical simulation[J]. Aerospace Science and Technology, 2021, 115: 106797. doi: 10.1016/j.ast.2021.106797
[20]	LU H, WANG X, CHEN T. In-plane dynamics crushing of a combined auxetic honeycomb with negative Poisson's ratio and enhanced energy absorption[J]. Thin-Walled Structures, 2021, 160: 107366. doi: 10.1016/j.tws.2020.107366
[21]	LANG J P, HAN D, ZHANG X G, et al. A star-shaped tubular structure with multiple-directional auxetic effect[J]. Thin-Walled Structures, 2023, 193: 111247. doi: 10.1016/j.tws.2023.111247
[22]	DING H, GUO H, SUN P, et al. In-plane dynamic crushing of a novel hybrid auxetic honeycomb with enhanced energy absorption[J]. Mechanics of Advanced Materials and Structures, 2023, 31(19): 4635-4653.
[23]	LI N, LIU S Z, WU X N, et al. Mechanical characteristics of a novel rotating star-rhombic auxetic structure with multi-plateau stages[J]. Thin-Walled Structures, 2023, 191: 111081. doi: 10.1016/j.tws.2023.111081
[24]	LIU J Y, LIU H T. Energy absorption characteristics and stability of novel bionic negative Poisson’s ratio honeycomb under oblique compression[J]. Engineering Structures, 2022, 267: 114682. doi: 10.1016/j.engstruct.2022.114682
[25]	WU H X, ZHANG X C, LIU Y. In-plane crushing behavior of density graded cross-circular honeycombs with zero Poisson's ratio[J]. Thin-Walled Structures, 2020, 151: 106767. doi: 10.1016/j.tws.2020.106767
[26]	LIU K, CAO X F, ZHANG P, et al. Dynamic mechanical performances of enhanced anti-tetra-chiral structure with rolled cross-section ligaments under impact loading[J]. International Journal of Impact Engineering, 2022, 166: 104204. doi: 10.1016/j.ijimpeng.2022.104204
[27]	罗伟洪, 何婉青, 吴文军, 等. 不同速度下负泊松比弧形结构的变形行为[J]. 爆炸与冲击, 2023, 43(11): 75-87. LUO Weihong, HE Wanqing, WU Wenjun, et al. Deformation behavior of curved structures with negative Poisson's ratio under diverse loading velocities[J]. Explosion and Shock Waves, 2023, 43(11): 75-87(in Chinese).
[28]	WEI L, ZHAO X, YU Q, et al. A novel star auxetic honeycomb with enhanced in-plane crushing strength[J]. Thin-Walled Structures, 2020, 149: 106623. doi: 10.1016/j.tws.2020.106623
[29]	YANG X, XI X, PAN Q, et al. In-plane dynamic crushing of a novel circular-celled honeycomb nested with petal-shaped mesostructure[J]. Composite Structures, 2019, 226: 111219. doi: 10.1016/j.compstruct.2019.111219