Impact Resistance of Semi Re-Entrant Honeycombs under in-Plane Dynamic Crushing
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摘要: 半凹角蜂窝结构因其零泊松比特征，具有独特的变形方式。将其与传统正泊松比（正六边形）蜂窝以及负泊松比（凹角）蜂窝在面内冲击荷载作用下的抗冲击性能进行对比分析，揭示出零泊松比效应对动力学性能的影响。在给定胞元几何参数（长细比）的情况下，分析了3种蜂窝构型在不同冲击速度下的变形特征，得出半凹角蜂窝的零泊松比特性使结构的局部变形带以“I”型为主。根据一维冲击波理论，推导出半凹角蜂窝的平均抗压强度理论公式，与有限元结果进行对比，验证了该方法的有效性。数值结果表明，半凹角蜂窝的抗冲击性能介于正六边形蜂窝和凹角蜂窝之间。通过在半凹角蜂窝内部增加直杆，设计出一种新型零泊松比蜂窝，进一步提高了蜂窝结构的抗冲击性能，可为其他结构优化设计提供一定的理论参考。Abstract: The semi re-entrant honeycombs presented unique deformation modes due to its characteristic of zero Poisson’s ratio. The impact resistance of the semi re-entrant honeycombs under in-plane impact load was compared with that of the traditional positive Poisson’s ratio (regular hexagon) honeycombs and negative Poisson’s ratio (re-entrant) honeycombs, and the effects of zero Poisson’s ratio on its dynamic performance were revealed. Given cellular geometric parameters (cell wall’s aspect ratio), the deformation behaviors of three honeycomb configurations under different impact velocities were analyzed. It is concluded that dominant local deformation band of the semi re-entrant honeycomb is " I” type because of the zero Poisson ratio. According to the one-dimensional shock wave theory, a theoretical formula of the average dynamic crushing strength of semi re-entrant honeycombs was derived and compared with the finite element results to verify its effectiveness. Simultaneously, it was found that the impact resistance of semi re-entrant honeycombs was between regular hexagon honeycombs and re-entrant honeycombs. Therefore, a novel zero Poisson’s ratio honeycomb was designed by adding a rib into every cell of the semi re-entrant honeycomb, and its impact resistance was improved. These results provide certain theoretical references for other structural optimization designs.
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图 1 正六边形蜂窝、凹角蜂窝和半凹角蜂窝结构模型及代表性胞元
Figure 1. Structural models and representative basic cells for regular hexagon honeycombs, re-entrant honeycombs and semi re-entrant honeycombs
图 2 半凹角蜂窝代表性胞元受力分析
Figure 2. Force analysis of representative cell of semi re-entrant honeycombs
图 3 不同冲击速度下正六边形蜂窝的变形模式
Figure 3. Deformation modes of regular hexagon honeycombs under different impact velocities
图 4 不同冲击速度下凹角蜂窝的变形模式
Figure 4. Deformation modes of re-entrant honeycombs under different impact velocities
图 5 不同冲击速度下半凹角蜂窝结构的变形模式
Figure 5. Deformation modes of semi re-entrant honeycombs under different impact velocities
图 6 不同冲击速度下半凹角蜂窝的名义应力-应变曲线（h=0.5 mm）
Figure 6. Nominal stress-strain curves of semi re-entrant honeycombs under different impact velocities (h=0.5 mm)
图 7 不同胞壁厚度下半凹角蜂窝的名义应力-应变曲线（v=140 m/s）
Figure 7. Nominal stress-strain curves of semi re-entrant honeycombs under different cell wall thicknesses (v=140 m/s)
图 9 压溃初始时刻（t0）和结束时刻（tf）蜂窝变形模式
Figure 9. Deformation modes at the initial (t0) and final moments (tf) of crushing
图 10 3种蜂窝结构的冲击速度-平台应力曲线
Figure 10. Impact velocity versus plateau stress curves of three types of honeycombs
图 11 半凹角蜂窝的应力云图（h=0.5 mm，v=70 m/s）
Figure 11. Stress contours of semi re-entrant honeycombs (h=0.5 mm, v=70 m/s)
图 12 新型半凹角蜂窝的变形模式（h=0.5 mm，v=35 m/s）
Figure 12. Deformation modes of novel semi re-entrant honeycombs (h=0.5 mm, v=35 m/s)
图 13 半凹角蜂窝与新型半凹角蜂窝的名义应力-应变曲线
Figure 13. Nominal stress-strain curves of semi re-entrant honeycombs and novel semi re-entrant honeycombs
图 14 新型半凹角蜂窝与凹角蜂窝的名义应力-应变曲线
Figure 14. Nominal stress-strain curves of novel semi re-entrant honeycombs and re-entrant honeycombs
图 15 3种蜂窝结构的 (a)冲击速度-平台应力曲线（h=0.4 mm）和(b)胞壁厚度-平台应力曲线（v=100 m/s）
Figure 15. Impact velocity (a) and cell wall thickness (b) versus plateau stress curves of three types of honeycombs (v=100 m/s)
表 1 正六边形蜂窝的平均抗压强度
Table 1. Average crushing strength of regular hexagon honeycombs
h/mm v/(m∙s−1) Average crushing strength/MPa Deviation/% Ref.[9] Numerical 0.3 70 2.491 2.287 8.19 0.3 100 4.677 4.893 4.62 0.4 70 3.777 3.952 4.63 0.4 100 6.802 7.384 8.56 
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表 2 半凹角蜂窝结构的平台应力
Table 2. Plateau stress of the semi re-entrant honeycombs
h/mm v/(m∙s−1) Average crushing strength/MPa Deviation/% Theoretical Numerical 0.2 70 1.643 1.555 5.36 100 2.788 2.850 2.22 140 5.738 5.967 3.99 200 11.421 11.551 1.14 0.3 70 2.910 3.180 9.28 100 5.287 5.340 0.99 140 9.761 9.012 7.67 200 19.268 20.181 4.74 0.4 70 4.553 4.810 5.64 100 8.134 8.222 1.08 140 14.875 13.608 8.52 200 29.200 28.769 1.48 0.5 70 6.682 7.170 7.30 100 11.828 12.991 9.83 140 21.514 21.545 0.14 200 42.097 40.774 3.14
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