负泊松比蜂窝材料的动力学响应及能量吸收特性

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。

Dynamic responses and energy absorption properties of honeycombs with negative Poisson's ratio

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.