基于机构特征映射的拉胀超材料拓扑设计与刚度综合研究

拉胀超材料是一种具有非常规特性的人工材料，在减振、声学等方面有良好的应用前景。然而现有设计或模仿自然、或凭借直觉，缺少有效的系统化指导。已有研究表明这类材料晶格的变形与机构的运动存在共性。本项目以机构学理论为基本框架，从机构构型和功能两个层面开展拉胀超材料的研究。基于从柔体变形到连杆-铰链机构运动的映射关系，确定机构结构参数与材料力学参数之间的数学关系，构建基于机构特征的拉胀超材料描述体系。分析拉胀机构输入-输出自由度与构型、尺度三者的内在联系，探究单环拉胀机构的设计问题；分析单环拉胀机构之间的运动协调机理，将数学中的“几何镶嵌”概念引入，探索机构单元周期/非周期排列的多环耦合机构综合，建立面向拉胀行为性能调控的设计理论。根据刚度需求反演各构件及铰链的刚度，从而确定柔性单元的结构与尺寸，将柔性机构的构型与尺度综合统一在刚度综合的体系下。通过微米级3D打印技术制备样件，并进行超材料性能实验。

Compared with traditional materials, metamaterials have the property of unique performance. However, existing designs come from imitating nature or resorting intuition, lacking of the scientific and effective systematic guidance. According to studies until present time, it is found that there is some commonness between the deformation of this kind of materials with the motion of mechanisms. This project takes the theory of mechanisms as the basic framework, and intend to study auxetic metamaterials from levels of depth and breadth. Based on the mapping from the deformation of flexible bodies to the motion of bar-and-joint mechanisms, the mathematical relationship between structural parameters of mechanisms and mechanical parameters of materials is determined, and the description of auxetic metamaterials based on mechanism characteristics is proposed. The correlation between input-output degrees of freedom, types and dimensions of auxetic linkages is analyzed, and the design problem is investigated. The kinematic compatibility of single-loop auxetic linkages is analyzed, and the synthesis of multi-loop coupled mechanisms based on the periodic/aperiodic arrangement of mechanism units is explored with the introduction of the mathematical concept of geometric tessellation. Thereupon the design theory for the performance regulation of auxetic behavior is established. The stiffness of each member and hinge is solved according to the stiffness requirement, then the structure and size of the flexible element are obtained, so that type and dimensional synthesis of compliant mechanisms are unifies in the framework of stiffness synthesis. Samples are designed based on the proposed design methodology, and fabricated by 3D printing technology. Finally, the stretching test of materials is carried out.