DIGITAL DESIGN AND MODEL VERIFICATION OF MIURA ORIGAMI METAMATERIAL STRUCTURES
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摘要: 折纸结构在航空航天、柔性电子、汽车船舶和建筑结构等领域具有较好的应用前景. 三浦折纸单元沿三向拓展可构建出三浦折纸超材料结构, 具有高孔隙、可自锁、平面折展、负泊松比、形态可控等特性. 为了便于生成折纸超材料结构的复杂三维模型、推广应用于缓冲吸能结构及可展结构, 本文利用Matlab和Grasshopper软件, 发展了三浦折纸超材料结构的数字化设计方法, 利用数字化建模及3D打印技术, 实现了零厚度及非零厚度三维折纸模型的统一建模, 并开展了物理模型验证分析, 探讨了3D打印制作折纸超材料结构模型的优缺点; 推导了三浦折纸超材料的折痕长度、相对密度、折叠率等特性与几何参数的关系, 利用Abaqus/Explicit软件开展了结构准静态压缩过程分析与验证, 揭示相对密度对结构吸能指标的影响规律. 研究结果表明, 折纸超材料结构数字化设计方法高效、准确, 便于结构选型及优化分析, 所得三维模型结果与理论值吻合较好. 当胞元面板构型、面板厚度及结构折痕总长不变时, 相对密度较小的三浦折纸超材料结构具备更为优异的吸能效率.Abstract: Origami-inspired structures have bright engineering applications in many fields, such as aerospace engineering, flexible electronics, automobile, ships, and building structures. Miura origami metamaterial structures can be constructed by expanding the classic Miura origami patterns along three directions. Such structures possess the characteristics of high porosity, self-locking, flat folding, negative Poisson's ratio and programmable morphology. In order to better apply these metamaterials into energy-absorbing structures and deployable structures, this study introduces Matlab and Grasshopper to further improve the digital design method of Miura-ori metamaterial structures. Notably, digital modeling technology and 3D printing technology have been adopted to achieve unified modeling for zero-thickness origami models and non-zero-thickness three-dimensional origami models. Furthermore, a series of physical models are constructed for verification. Then, the advantages and disadvantages of using 3D printing technology to make origami metamaterial structural models have been discussed. On the basis of geometric parameters, analytical expressions for the crease length, relative density, and folding ratio of a Miura-ori metamaterial have been established. Abaqus/Explicit was used to analyze and verify the quasi-static compression process of these origami structures, and the influence law of relative density on the energy absorption index was revealed. The results show that the digital design method of metamaterial structure is efficient and accurate, which is convenient for structural selection and further optimization analysis. The obtained results from 3D printed models are in good agreements with the theoretical values. When panel configuration, thickness and crease length remain unchanged, the Miura origami metamaterial structure with a relatively lower density tends to exhibit better energy absorption efficiency.
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Key words:
- Miura-ori /
- mechanical metamaterials /
- digital design /
- geometric analysis /
- energy absorption
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图 4 三浦折叠超材料结构模型验证
Figure 4. 3D printing and digital Miura-ori metamaterial structural models
图 5 不同γB情况下L1与γA的关系曲线 (M = N = 5)
Figure 5. Change curve of L1 with γA under different γB conditions (M = N = 5)
图 7 标准模型沿X方向完全展开构型
Figure 7. Fully deployed configuration of reference model along direction X
图 8 折叠率ζV与γA及γB的关系曲线
Figure 8. Relation curve of maximum folding ratio ζV with γA and γB
图 11 三浦折纸超材料结构压缩性能分析
Figure 11. FEM results for Miura-ori metamaterial structures under quasi-static compressions
表 1 3D打印实物模型参数
Table 1. Parameters for physical models by 3D printing
No. M × N × O aA/mm bA/mm θA/(°) Material 1 3 × 3 × 4 10 10 45 PLA 2 7 × 6 × 9 5 5 45 PLA 3 6 × 6 × 8 5 5 30 PLA 4 8 × 7 × 9 5 5 60 PLA 5 3 × 3 × 4 10 10 45 Agilus30 6 7 × 6 × 9 10 10 45 TPU 
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表 2 模型参数与模拟结果
Table 2. Parameters and FEM results for different models
Model θA/(°) ρ0* SEA Mi-1 15 0.0661 21.09 Mi-2 30 0.0811 15.67 Mi-3 45 0.1069 11.72 Mi-4 60 0.1590 9.81 Mi-5 75 0.3166 8.62
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