Out-of-Plane Mechanical Behaviors of Intorsion Hierarchical Honeycomb-Like Structures
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摘要: 结合几何学的胞元设计思路，提出了一种新型多胞结构—内旋层级类蜂窝（intorsion hierarchical honeycomb-like，IHH）结构，通过数值模拟方法对其面外力学性能和变形特征进行深入研究，并与普通蜂窝结构、填充圆管的蜂窝结构进行了比较。研究发现，采用内旋层级设计的多胞结构，其胞元内部产生了独特的约束效果，在多层级设计条件下，可以进一步加强这种约束效果，从而提高结构的力学性能。此外，通过开展参数化研究，以揭示相对密度变化对结构性能的影响；基于简化超级折叠单元理论，建立了内旋层级类蜂窝结构的理论模型。结果表明，内旋层级类蜂窝结构在渐进式折叠变形模式下表现出最佳的吸能效率，理论模型能够有效地预测内旋层级类蜂窝结构的平台应力。研究结果可为多胞结构性能优化设计提供指导。Abstract: In this study, a novel type of the intorsion hierarchical honeycomb-like (IHH) structures was proposed based on the cell geometrical design. The out-of-plane mechanical behaviors and deformation characteristics were studied by numerical simulation, and the results were compared with that of ordinary honeycomb (OH) structure as well as the honeycomb structure filled with circular tube (HFCT). It is found that the intorsion hierarchical design makes the constraint effect inside the cell. Through multi-order hierarchical design, the constraint effect can be further strengthened, so as to improve the mechanical behaviors. In addition, parametric studies were carried out to reveal the influence of the change of relative density on mechanical performance. Based on the simplified super folding element (SSFE) theory, a theoretical model of IHH was established. The results show that the proposed IHH exhibit the progressive folding deformation mode and attain the optimal energy absorption efficiency among all the competitors. The theoretical model can effectively predict the mean stress of IHH. The results in this study can provide guidance for the mechanical performance optimization of multi-cell structure.
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图 1 内旋层级类蜂窝结构的胞元设计思路
Figure 1. Design method of unit cell of intorsion hierarchical honeycomb-like structure
图 5 3种多胞结构的应力-应变曲线与能量吸收曲线数值模拟结果
Figure 5. Numerical results of stress-strain curves and total energy absorption curves of three multi-cell structures
图 6 3种多胞结构的变形过程比较
Figure 6. Deformation process comparison between three multi-cell structures
图 7 3种多胞结构的顶部变形视图
Figure 7. Top view of deformation patterns of three multi-cell structures
图 14 理论预测与数值模拟结果比较
Figure 14. Comparison between theoretical prediction and numerical simulation
表 1 3种多胞结构的相对密度
Table 1. Relative density of three multi-cell structures
Structures $ V $ ${V}{_{\mathrm{s} }}$ $ \Delta \rho $ OH $\dfrac{69\sqrt{3} }{2}{l}{^{2}}T$ $ 88ltT $ $\dfrac{176\,t}{69\sqrt{3}\,l}$ HFCT $\dfrac{69\sqrt{3} }{2}{l}{^{2}}T$ $(88+23\sqrt{3}\text{π})ltT$ $\left(\dfrac{176}{69\sqrt{3} }+\dfrac{2\text{π} }{3}\right)\dfrac{t}{l}$ IHH $\dfrac{69\sqrt{3} }{2}{l}{^{2}}T$ $\left(88+138\displaystyle\sum _{i=1}^{n}{\lambda }^{i}\right)ltT$ $\left(\dfrac{176}{69\sqrt{3} }+\dfrac{4}{\sqrt{3} }\displaystyle\sum _{i=1}^{n}{\lambda }^{i}\right)\dfrac{t}{l}$ 
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表 2 3种多胞结构的力学性能指标
Table 2. Mechanical properties of three multi-cell structures
Structures $ \mathrm{\Delta }\rho $ ${E}{_{\mathrm{A} } }$/J ${E}{_{\mathrm{S}\mathrm{A} } }$/(J·g−1) ${\sigma }{_{\mathrm{p} } }$/MPa ${\sigma }{_{\mathrm{m} } }$/MPa $ \eta $/% OH 0.018 4 52.59 13.95 4.27 1.00 23.39 HFCT 0.044 6 133.21 14.57 9.42 2.98 31.66 1st IHH 0.043 4 151.45 17.02 10.04 3.22 32.06
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表 3 角单元数量
Table 3. Number of various corner elements
Structure $ {N}_{1} $
(2-panel)$ {N}_{2} $
(3-panel)$ {N}_{3} $
(4-panel)$ {N}_{4} $
(6-panel)IHH 22 44 38+138(n–1) 50
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