多胞材料可通过大变形大量地吸收冲击能量，引入密度梯度可进一步提高其耐撞性。梯度多胞材料的宏观力学响应对材料密度分布极为敏感，不同类型的细观构型的影响也极为不同。已有的研究工作主要局限在对给定的密度梯度分析其动态响应，较少对耐撞性设计方法进行研究。本文针对梯度闭孔泡沫金属材料，基于非线性塑性冲击波模型发展了耐撞性反向设计方法，以维持冲击物受载恒定为目标，运用级数法获得了简化模型和渐近解。利用变胞元尺寸法构建了连续梯度变化的三维Voronoi细观有限元模型，并利用ABAQUS/Explicit有限元软件对理论设计进行数值验证。结果表明，反向设计理论简化模型的渐近解对于梯度闭孔泡沫金属材料的耐撞性设计是有效的，所提出的耐撞性设计方法在控制冲击吸能过程和冲击物受载方面具有指导意义。%Cellular materials can absorb a large amount of impact energy with large deformation, and their crashworthiness may be improved by introducing density gradients. The macroscopic mechanical responses of graded cellular materials are very sensitive to their relative density distributions and the effects of meso-structures can be very different. Some of existing studies is mainly limited to the analysis on the dynamic mechanical response of graded cellular material with a given density gradient, and less on the crashworthiness design method is considered. Based on the nonlinear plastic shock wave model, a backward crashworthiness design method is developed for graded foams. A simplified model and an asymptotic solution are derived by applying the series method with the aim of maintaining a constant load on the impact object. The cell-based finite element models based on three-dimensional Voronoi structures with density continuously changing are constructed by applying the variable cell size method. The theoretical design is verified by using finite element software ABAQUS/Explicit. The numerical simulation results show that the asymptotic solution of the simplified model is effective for the crashworthiness design of graded foams, and the proposed crashworthiness design method is of instructive significance in controlling the energy absorption and impact process.
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