Research on explosion-proof characteristics and optimization design of negative Poisson’s ratio honeycomb material
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摘要: 为了深入研究车辆底部防护组件爆炸冲击下的结构响应，提高防护型车辆的抗爆炸冲击性能，建立了某车辆底部防护组件在爆炸冲击下的有限元模型，并进行爆炸冲击台架试验验证了有限元模拟的可靠性；将内凹六边形负泊松比蜂窝材料作为防护组件的夹芯部分，分析负泊松比蜂窝材料在爆炸冲击下的变形模式，并对比了同等质量的其他3种防护组件的抗爆炸冲击性能。结果表明，含有负泊松比蜂窝夹芯的防护组件具有更优的抗爆性能。建立了以内凹六边形负泊松比蜂窝胞元尺寸参数为设计变量的多目标优化问题的数学模型，采用多目标遗传算法获得胞元几何参数的最优方案，有效降低了防护组件基板的最大挠度和最大动能。Abstract: In order to study in depth the structural response of the bottom protective component of the vehicles under blast loading and improve the blast resistant performance of the protective vehicles, a finite element model of the bottom protective component of a vehicle under blast loading was established, and the reliability of the finite element simulation was verified by the explosion impact bench test; the concave hexagonal negative Poisson’s ratio honeycomb material was used as the core layer of the protective component, the deformation mode of the negative Poisson’s ratio honeycomb material under blast loading was analyzed, and the blast resistant performance was compared with the other three protective components of the same mass. The results show that the protective component containing negative Poisson’s ratio honeycomb core has better resistance to blast loading. A mathematical model was established for multi-objective optimization problems with the cell size parameters of the honeycomb material as design variables, and the multi-objective genetic algorithm was used to obtain the optimal solution of the cell geometric parameters, which effectively reduces the maximum deflection and maximum kinetic energy of the protective component substrate.
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图 1 负泊松比材料受载变形示意图
Figure 1. Schematic deformation of negative Poisson’s ratio material under load
图 8 负泊松比蜂窝夹芯防护组件
Figure 8. Negative Poisson’s ratio honeycomb sandwich protection component
图 9 负泊松比蜂窝夹芯材料局部结构
Figure 9. Local structure of honeycomb sandwich material with negative Poisson’s ratio
图 11 爆炸冲击下负泊松比蜂窝防护组件典型变形模式
Figure 11. Typical deformation mode of Poisson’s ratio honeycomb protection component under explosion impact
图 12 负泊松比蜂窝芯层中心变形图
Figure 12. Deformation diagram of negative Poisson’s ratio honeycomb core center
图 13 防护组件各部分结构动能时程曲线
Figure 13. Time history curve of the kinetic energy of each part of the protective component
图 14 防护组件各部分结构内能时程曲线
Figure 14. Time history curve of the internal energy of each part of the protective components
图 15 两种防护组件基板中心挠度时程曲线
Figure 15. Time history curve of the center deflection of the two kinds of protective component’s substrates
图 16 两种防护组件基板动能时程曲线
Figure 16. Time history curve of the kinetic energy of the two kinds of protective component’s substrates
图 17 正六边形蜂窝芯层部分结构
Figure 17. Partial structure of regular hexagonal honeycomb core layer
图 18 正六边形蜂窝胞元结构示意图
Figure 18. Schematic diagram of a regular hexagonal honeycomb cell structure
图 19 4种防护组件基板中心挠度时程曲线
Figure 19. Time history curves of center deflection of four kinds of protective component’s substrates
图 20 4种防护组件基板动能时程曲线
Figure 20. Time history curves of kinetic energy of four kinds of protective component’s substrates
图 22 优化前后基板挠度时程曲线
Figure 22. Time history curves of substrate deflection before and after optimization
图 23 优化前后基板动能时程曲线
Figure 23. Time history curves of substrate kinetic energy before and after optimization
表 1 防护组件各部分材料参数
Table 1. Material parameters for each part of the protective component
材料 密度ρ/(kg·m−3) 杨氏模量E/GPa 屈服强度σy/MPa 泊松比µ 抗拉强度σt/MPa np500钢 7.8 × 103 210 1382 0.3 1757 960E钢 7.8 × 103 210 986 0.3 1150 KS700钢 7.8 × 103 210 700 0.3 752 
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表 2 防护组件的结构响应与能量
Table 2. Structural response and energy of protective component
结构 最大挠度d/mm 最大加速度a/g 最大动能$ {E}_{\rm k} $/kJ 最大内能$ {E}_{\rm i} $/kJ 面板 132.82 1018.15 123.28 69.39 背板 89.38 470.87 16.35 31.72 基板 91.68 448.52 16.81 35.14
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表 3 H14铝材料参数
Table 3. H14 aluminum material parameters
材料 密度ρ/(kg·m−3) 杨氏模量E/GPa 屈服强度度σy/MPa 泊松比µ 抗拉强度σt/MPa H14铝 2.7×103 70 188 0.3 271
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表 4 防护组件的结构响应与能量
Table 4. Structural response and energy of protective components
结构 最大挠度d/mm 最大加速度a/g 最大动能Ek/kJ 最大内能Ei/kJ 比吸能η/(kJ·kg−1) 面板 130.4 1821.80 48.25 20.731 0.095 夹芯层 208.39 2.90 46.69 3.107 背板 78.35 350.67 7.98 10.99 0.063 基板 77.96 340.56 8.04 11.48 0.078
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表 5 基于D-optimal采样的试验设计及结果
Table 5. Experimental design and results based on D-optimal sampling
序号 $ {L}_{1} $/mm $ {L}_{2} $/mm $ {t}_{\rm c} $/mm $ \theta $/(°) M/kg d/mm $ {E}_{\rm k} $/kJ 1 21.15 16.97 0.34 55 18.61 77.66 8.10 2 22.95 16.28 0.31 60 13.00 76.76 7.78 $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ 27 21.33 16.56 0.30 50 16.81 78.83 8.59 28 23.13 15.87 0.34 55 14.75 77.76 8.16
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表 6 目标响应的决定系数
Table 6. Decision coefficients of target response
$ M $ $ {F}_{\rm d}\left(x\right) $ $ {F}_{\rm E}\left(x\right) $ $ {R}^{2} $ 0.963 0.987 0.959
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表 7 第50代Pareto解集（部分）及变量参数
Table 7. The 50th generation Pareto solution set (part) and variable parameters
解集序号 L1/mm L2/mm $ {t}_{\rm c} $/mm $ \theta $/(°) M/kg d/mm $ {E}_{\rm k} $/kJ 1 24.35 15.78 0.33 60 12.41 74.56 7.99 2 22.36 15.78 0.32 50 12.47 76.64 7.84 $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ 155 24.44 15.79 0.31 55 12.53 75.83 7.70 156 20.43 18.11 0.32 50 18.18 76.23 6.52 $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ $ \vdots $ 857 21.27 17.85 0.32 60 17.89 76.16 6.96 858 20.78 17.44 0.34 50 16.23 76.17 6.99
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