Dynamic responses and energy absorption properties of honeycombs with negative Poisson's ratio
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摘要: 针对传统正方形蜂窝，通过用更小的双向内凹结构胞元替代原蜂窝材料的结构节点，得到了一种具有负泊松比特性的节点层级蜂窝材料模型。利用显式动力有限元方法，研究了冲击荷载作用下该负泊松比蜂窝结构的动力学响应及能量吸收特性。研究结果表明，除了冲击速度和相对密度，负泊松比蜂窝材料的动力学性能亦取决于胞元微结构。与正方形蜂窝相比，该负泊松比层级蜂窝材料的动态承载能力和能量吸收能力明显增强。在中低速冲击下，试件表现为拉胀材料明显的"颈缩"现象，并展示出负泊松比材料独特的平台应力增强效应。基于能量吸收效率方法和一维冲击波理论，给出了负泊松比蜂窝材料的密实应变和动态平台应力的经验公式，以预测该蜂窝材料的动态承载能力。本文的研究将为负泊松比多胞材料冲击动力学性能的多目标优化设计提供新的设计思路。Abstract: In this work, for the traditional square honeycombs, we obtained a joint-based hierarchical honeycomb model with the negative Poisson's ratio (NPR) by replacing the structural nodes of the original honeycombs having smaller inner concave structures. We numerically investigated the dynamic responses and energy absorption characteristics of these honeycombs with NPR under in-plane crushing using the explicit dynamic finite element analysis (DFEA), revealing that, apart from the impact velocity and the relative density, the in-plane dynamic properties of the honeycombs also depend upon the cell micro-structure. Compared with those of the square honeycombs, the dynamic strengths and energy absorption abilities of these honeycombs are obviously improved. Under low or moderate velocity crushing, the specimens exhibit the obvious "neck shrinkage" phenomenon of auxetic materials, and show the unique plateau stress enhancement effect. Based on the energy absorption efficiency method and the one-dimensional shockwave theory, the empirical formulae of densification strain and dynamic plateau stress were given to predict the dynamic load-bearing capacity of the honeycombs with NPR. Our study can serve as a guidance for the multi-objective optimal dynamic design of auxetic cellular materials.
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图 1 负泊松比蜂窝结构的构造过程及其代表性体积单元
Figure 1. The constructive process and representative volume element of honeycombs with negative Poisson's ratio (NPR)
图 3 面内冲击载荷作用下蜂窝材料的名义应力应变曲线
Figure 3. Nominal stress-strain curves of honeycombs under in-plane crushing
图 5 不同冲击速度下负泊松比蜂窝材料的宏观变形模式
Figure 5. Macroscopic deformation modes of honeycombs with NPR at different impact velocities
图 6 不同冲击速度下正方形蜂窝材料的宏观变形模式
Figure 6. Macroscopic deformation modes of square honeycombs at different impact velocities
图 7 负泊松比蜂窝名义应力应变曲线与能量吸收效率曲线
Figure 7. Nominal stress-strain curve and corresponding energy absorption efficiency curve of honeycomb with NPR
图 8 负泊松比蜂窝结构的密实应变与冲击速度间的关系
Figure 8. Variation of desification strain with impact velocity for honeycombs with NPR
图 9 负泊松比蜂窝结构的平台应力增强应变和密实应变关系曲线
Figure 9. Variation of plateau stress enhancement strain with densification strain for honeycombs with NPR
图 10 不同冲击速度下负泊松比蜂窝和正方形蜂窝的平台应力
Figure 10. Plateau stresses of honeycombs with NPR and square honeycombs at different impact velocities
图 11 不同微结构负泊松比蜂窝材料的平台应力与冲击速度间的关系
Figure 11. Variation of plateau stresses for honeycombs with NPR at different cellmicro-structures with respect to impact velocities
图 12 负泊松比蜂窝的名义应力应变关系
Figure 12. Relation between nominal stress and nominal strain of honeycombs with NPR
图 13 负泊松比蜂窝的能量吸收与名义应变关系
Figure 13. Relation between energy absorption and nominal strain of honeycombs with NPR
图 14 负泊松比蜂窝的内能分布系数与名义应变关系
Figure 14. Relation between internal energy distribution coefficient and nominal strain of honeycombs with NPR
表 1 基体材料与刚性板材料参数
Table 1. Parameters of matrix material and rigid plate material
材料 ρ/(kg·m-3) E/GPa ν σy/MPa 铝 2 700 69 0.3 76 刚性板 7 800 210 
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表 2 负泊松比蜂窝结构的密实应变
Table 2. Densification strains of honeycombs with NPR
v/(m·s-1) εD Δρ=0.13 Δρ=0.15 Δρ=0.19 Δρ=0.24 Δρ=0.32 3 0.666 1 0.642 0 0.617 5 0.550 7 0.515 1 20 0.739 0 0.714 7 0.689 1 0.649 5 0.558 4 70 0.786 7 0.759 7 0.729 6 0.683 9 0.583 8 120 0.808 0 0.780 4 0.744 5 0.702 5 0.645 4 200 0.814 9 0.793 0 0.755 6 0.719 3 0.651 3
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