An auxetic tubular structure with tuneable stiffness
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摘要: 负泊松比材料具有优良的抗压痕性、抗剪切性、曲面同向性、断裂韧性和能量吸收性等特点，受到了国内外学者的广泛关注。负泊松比管状结构作为一个新兴的研究热点，在工程和医疗领域都有着广泛的应用前景。然而，在拉伸与压缩下同时具有负泊松比效应的管状结构仍鲜有报道。由于内部周期性孔洞的存在，大多数负泊松比材料和结构具有较低的比刚度。因此，本文提出了一种新型刚度可调控的负泊松比管状结构，并对不同旋转方式、密实点提前程度、变形区域高度h等参数进行了有限元分析与试验研究。研究结果表明：变刚度圆管的刚度大小可通过密实点比例因子进行调控，同时可以调整h值的大小来减小设计值与真实值之间的误差。新研制的负泊松比管状结构不仅大幅提升了负泊松比管状结构的刚度，且同时维持了理想的负泊松比效应。本文所研发的负泊松比管状结构在防护工程中具有较好的应用前景，且为负泊松比结构的设计提供了新思路。Abstract: Auxetic metamaterials have attracted great attention due to their indentation resistance, shear resistance, synclastic behaviour, fracture toughness and energy absorption properties. As one branch of auxetics, the tubular structure with negative Poisson’s ratio has potential to be used in engineering, medical treatment, vehicle and other fields. However, studies on mechanical properties of auxetic tubular structures are limited in both tension and compression in the current literature, and auxetic tubular structures tend to exhibit low stiffness ratio due to the existence of internal holes. In this paper, a novel type of auxetic tubular structure with tuneable stiffness was developed, and finite element analysis and experimental study were carried out on the parameters of different rotation modes, the degree of advanced compaction and the height of deformation zone. The results show that the stiffness of auxetic tubes with tuneable stiffness can be turned by adjusting different proportions of compaction point, and the h value can be used to reduce the error between the designed proportion and real proportion. Auxetic behaviour of the tubes with tuneable stiffness is not significantly weakened. The auxetic tubular structures with tuneable stiffness proposed in this paper bring about an innovative design concept and have good application prospects in protection engineering.
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图 1 模态比例因子为18%的负泊松比管状结构
Figure 1. Auxetic tubular structure with pattern scale factor of 18%
图 2 模态比例因子为18%的负泊松比管状结构对应的平面图
Figure 2. Corresponding planar sheet of auxetic tubular structure with pattern scale factor of 18%
2a—Long axis; 2b—Short axis; c—Separation distance
图 3 变刚度设计原理
Figure 3. Design concept of tuneable stiffness
θ—Maximum rotation angle; θ1—Angle between the cut line and the horizontal line; h—Height of deformation zone
图 4 变刚度负泊松比胞元旋转方式
Figure 4. Rotation modes of auxetic unit cell with tuneable stiffness
图 5 变刚度负泊松比代表性体积胞元(h=1 mm)
Figure 5. Representative volume element of auxetic unit cell with tuneable stiffness (h=1 mm)
η—Variable stiffness scale factor
图 6 负泊松比管状结构实验试件
Figure 6. Test specimens of auxetic tubular structures
H—Height; T—Thickness; D—External diameter; d—Internal diameter
图 7 3D打印热塑性聚氨酯弹性体橡胶(TPU)狗骨型样条的单轴拉伸实验
Figure 7. Uniaxial tensile test of 3D printed thermoplastic polyurethane elastomer rubber (TPU) dog-bone specimens
图 8 3D打印TPU狗骨型样条的名义应力-名义应变曲线
Figure 8. Nominal stress-nominal strain curve of 3D printed TPU dog-bone specimen
图 9 2种负泊松比管状结构的实验过程图像(标尺：10 mm)
Figure 9. Experimental images of two auxetic tubular structures (Scale bar: 10 mm)
图 11 2种负泊松比管状结构的名义应力-名义应变曲线
Figure 11. Nominal stress-nominal strain curves of two auxetic tubular structures
图 10 2种负泊松比管状结构的荷载-位移曲线
Figure 10. Load-displacement curves of two auxetic tubular structures
图 12 2种负泊松比管状结构有限元模型变形情况
Figure 12. Deformation of finite element models of two auxetic tubular structures
图 13 2种负泊松比管状结构的试验与有限元结果对比
Figure 13. Comparison of experimental and finite element results between two auxetic tubular structures
图 14 2种负泊松比管状结构的泊松比变化
Figure 14. Poisson’s ratio distribution of two auxetic tubular structures
图 15 变形区域高度h对变刚度负泊松比管状结构力学性能的影响
Figure 15. Effect of height of deformation zone
h on mechanical performances of auxetic tubular structures with tuneable stiffness -
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