Machine learning-driven low-velocity impact response prediction and multi-objective optimization of origami metamaterial sandwich
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摘要: 受三浦折纸和星形蜂窝的混杂拓扑设计启发，提出了一种新型折纸超材料夹芯复合结构，并融合机器学习实现了其低速冲击响应的预测和多目标优化。通过落锤冲击实验和有限元仿真，系统探究了该结构在低速冲击下的动态力学响应和变形失效模式。结果表明，折纸启发的拓扑结构有效地将传统蜂窝结构的瞬时完全断裂转化为了渐进压溃失效，从而显著提升了其抗冲击性能。随后提出了残差连接增强的深度学习模型，实现了对该结构完整低速冲击响应的快速精确端到端预测，计算效率较有限元仿真大幅提升。并基于此参数分析了关键角度对冲击响应和等效密度的调控机理，特别是角度变化诱导的壁板拉压变形与折痕弯曲变形间的载荷重新分布现象，使结构能在承载型与缓冲型功能间切换，提供了冲击响应与失效模式主动可调控的机理依据。最后，进一步结合强化学习和帕累托前沿分析，以训练完备的深度学习模型作为代理模型，针对承载防护和缓冲防护需求实现了结构的轻量化多目标优化。在等效密度相近时，折纸超材料能够实现峰值力的大范围调控，有益于针对不同防护场景按需定制化开发的防护结构。Abstract: Inspired by the hybrid topology design that integrates Miura origami and star-shaped honeycomb, this study proposes a novel origami metamaterial sandwich and employs machine learning to predict low-velocity impact response and perform multi-objective optimization. Through drop-weight impact experiments and finite element simulations, the dynamic mechanical response and deformation failure modes of the sandwich under low-velocity impact are systematically investigated. The results demonstrate that the origami-inspired topologies effectively transform the instantaneous complete fracture of traditional honeycombs into progressive crushing failure, thereby significantly enhancing impact resistance. Subsequently, a residual connection-enhanced deep learning model is developed, enabling rapid and precise end-to-end prediction of the complete low-velocity impact response, with computational efficiency substantially surpassing that of finite element simulations. Parameterized analysis based on this model reveals the regulatory mechanisms of key angle parameters on impact response and effective density. Particularly, angle variations induce a load redistribution phenomenon between panel tension-compression deformation and crease bending deformation, allowing the metamaterial to switch between bearing and buffering protective functions. This provides a mechanism basis for actively controlling impact response and failure modes. Furthermore, by integrating reinforcement learning and Pareto front analysis, the trained deep learning model served as a surrogate model to achieve lightweight multi-objective optimization tailored for load-bearing and impact-mitigation protection requirements. At similar effective densities, the metamaterial enables broad-range tuning of peak force, offering significant advantages for developing customized protective structures for diverse scenarios. This research not only establishes a solid foundation for creating customizable high-performance impact protection structures but also advances the field toward a new paradigm of intelligent, on-demand design.
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图 2 实验、有限元仿真及3D打印试件示意图
Figure 2. Schematic of the experiment, the finite element simulation, and the 3D printed specimens
图 3 超材料夹芯复合结构的低速冲击响应
Figure 3. Comparison of low-velocity impact response of metamaterial sandwiches
图 4 超材料夹芯复合结构的失效破坏模式对比
Figure 4. Comparison of failure modes of metamaterial sandwiches
图 8 使用ResANN对折纸超材料夹芯复合结构冲击响应预测的结果
Figure 8. Results of impact response prediction of origami metamaterial sandwiches using ResANN
图 9 关键角度对夹芯复合结构冲击响应和力学属性的影响
Figure 9. Effects of key angles on impact response and mechanical properties of sandwiches
图 10 结合Q-learning和帕累托前沿分析的多目标优化框架。
Figure 10. Multi-objective optimization framework combining Q-learning and Pareto front analysis.
图 11 结合帕累托前沿分析的多目标Q-learning训练过程伪代码。
Figure 11. Pseudocode of the multi-objective Q-learning training process combined with Pareto front analysis.
图 12 承载-轻量化多目标优化结果示意图。
Figure 12. Results of the multi-objective optimization of load-bearing and lightweight.
图 13 缓冲-轻量化多目标优化结果示意图。
Figure 13. Results of the multi-objective optimization of buffering and lightweight.
图 14 折纸超材料芯层变形模式示意图。
Figure 14. Schematic of the deformation mode of the origami metamaterial cores
参考点 x坐标 y坐标 z坐标 A a 0 0 B 0 a tan α 0 C 0 a tan α+a tan θ −a D a a tan θ −a E a−a tan β a 0 F a−(a−a tan θ) tan β a −a 
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表 2 折纸超材料夹芯复合结构低速冲击响应及破坏模式对比
Table 2. Comparison of low-velocity impact response and failure modes of origami metamaterial sandwiches
超材料夹芯复合结构 FP/kN tP/ms Ea/J ρeff 破坏模式 Θ1 α=20°, β=20°, θ=20° 16.97 2.70 10.04 0.2447 未破坏 Θ2 α=20°, β=30°, θ=20° 12.34 1.93 17.44 0.2549 折痕渐进压溃 Θ3 内凹蜂窝 8.43 2.05 17.43 0.2155 瞬时完全断裂 Θ4 星形蜂窝 8.32 1.93 17.87 0.2713 瞬时完全断裂
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表 3 多类神经网络模型的性能对比
Table 3. Performance comparison of various types of neural network models
神经网络模型 参数量 训练时间/s 预测时间/s Smooth L1 loss R2 ResANN 4103552 2146.46 2.14 393.052 0.9906 ANN 3972480 2004.74 2.47 463.131 0.9880 CNN 3973472 1961.79 3.32 1886.84 0.8850 LSTM 4245632 1609.75 2.73 1837.11 0.8894
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表 4 多目标Q-learning优化模型所使用的Q表
Table 4. The Q-table used in the multi-objective Q-learning optimization model
S=(α, β, θ) A1 A2 … A7 S1 Q(S1, A1) Q(S1, A2) … Q(S1, A7) S2 Q(S2, A1) Q(S2, A2) … Q(S2, A7) … … … … …
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