Modeling active adjustment of negative Poisson’s ratio mechanical metamaterials
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摘要:
负泊松比材料作为一种新型的力学超材料，鉴于其优异的力学性能，在航天、航空、工业、医药科学等领域具有广泛的应用前景。科研人员针对有序的、变形行为单一的负泊松比结构已经做了大量的研究，但是面对更复杂的工作环境，这类结构仍然具有一定的局限性，因此开发新型性能宽范围可控超材料的研究尤为重要。本文基于旋转刚体原理的负泊松比结构，设计了一种二维的泊松比可调控的多孔结构，通过基本梁理论计算和有限元仿真，可以确定材料泊松比正负调节与结构单元排列之间的关系，从而实现二维多孔结构泊松比的调控。通过填充结构的结构设计，可实现该结构泊松比从正到负的自由转换，及其力学大范围可调，从而拓宽了该类材料的工程应用。例如本文设计的一种十字花套筒支撑结构如 图1 所示；具有十字花套筒支撑结构的超材料压缩曲线如图2 所示。在压缩过程中该结构的泊松比实现了从正到负的大范围转换，展现了该多孔材料良好的力学调节性能。十字花套筒支撑结构 Abstract: As a new type of metamaterials, negative Poisson’s ratio materials have great potential application prospects in aerospace, aviation, industry, medical science and other fields due to its excellent mechanical properties. In order to obtain metamaterials with actively adjustable performance and structure, a unit model of metamaterial structure was first designed based on the negative Poisson’s ratio structure. Then, through the calculation of basic beam theory, the critical parameters between the positive and negative transition of the Poisson’s ratio of the macrostructure and the rigid body structure were obtained. In addition, through finite element simulation, the relationship between positive and negative adjustment of Poisson’s ratio of materials and the proportion and arrangement of filling elements was determined. Finally, the vibration characteristics and mechanical properties of this two-dimensional structural material were analyzed in detail. The results show that this material shows excellent performance in regulating the structure and reducing vibration. Adjusting the filling form and arrangement of the internal unit, we can obtain different mechanical properties and energy absorption effects; At the same time, by introducing shape memory materials and microstructures, the materials show excellent macrostructure and intelligent adjustment of stiffness.-
Key words:
- mechanical metamaterials /
- Poisson's ratio /
- energy absorption /
- adjustable design
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图 1 (a)旋转型负泊松比结构；(b)轻量化设计结构
Figure 1. (a) Rotary type negative Poisson’s ratio; (b) Frame structure
图 2 结构单元尺寸参数
Figure 2. Size parameters of the unit structure
$ {L}_{x} $, $ {L}_{y} $- Length of the sides in the x and y directions; θ -Angle between the string and the sides; b-Chord length of the frame；$ {L}_{\mathrm{g}\mathrm{x}} $-Effective bending length of the ligament along the x direction
图 3 实心结构的压缩变形过程和曲线：((a)~(c))压缩前变形过程；((d)~(f))压缩曲线
Figure 3. Compressive deformation and curve process of solid structure: ((a)-(c)) Pre-compression deformation process; ((d)-(f)) Compression curve
图 4 几种不同排列的压缩变形和压缩过程的泊松比变化曲线
Figure 4. Poisson’s ratio curve of compressive deformation of several different arrangements
图 5 几种不同填充比例结构的压缩变形和压缩过程的泊松比变化曲线: (a) 36%; (b) 44%; (c) 52%; (d) 68%
Figure 5. Poisson’s ratio curve of compressive deformation of several different filling ratios: (a) 36%; (b) 44%; (c) 52%; (d) 68%
图 6 加热前后的压缩变形：(a)加热前；(b)加热后
Figure 6. Compressive deformation before (a) and after (b) heating
图 9 轮轴结构：(a)同向轮轴；(b)反向轮轴
Figure 9. Structure of the wheel shaft: (a) Co-directional wheel shaft; (b) Reverse wheel shaft
表 1 不同微结构泊松比拐点数值
Table 1. Poisson’s ratio inflection point values of different microstructures
Type Poisson’s ratio Equivalent strain Equivalent stress/Pa Cross bracing
structure0 0.053 2822 Co-directional
wheel shaft0 0.036 9616 Reverse wheel shaft 0 0.009 1992 
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