内向同构二次分层内凹六边形超材料力学特性建模与分析  

Modeling and Analysis of Mechanical Properties of Internal Isomorphic Secondary Hierarchical Re-entrant Hexagonal Metamaterials

作　　者：杨慧[1] 杨彦飞 王岩[1] 刘瀚孺 刘荣强[2] YANG Hui;YANG Yanfei;WANG Yan;LIU Hanru;LIU Rongqiang(Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System,Yanshan University,Qinhuangdao 066009,China;State Key Laboratory of Robotics and System,Harbin Institute of Technology,Harbin 150001,China)

机构地区：[1]燕山大学河北省机器人与机电系统实验室,秦皇岛066009 [2]哈尔滨工业大学机器人技术与系统国家实验室,哈尔滨150001

出　　处：《宇航学报》2025年第3期532-543,共12页Journal of Astronautics

基　　金：河北省自然科学基金(E2024203052,E2024203105);国家自然科学基金(52375028,52192631);河北省研究生创新资助项目(CXZZSS2024030)。

摘　　要：针对负泊松比超材料的刚度和强度低、胞元混合方式复杂等问题,提出了一种基于内凹六边形胞元的内向同构二次分层内凹六边形超材料胞元。首先基于铁木辛柯梁模型和卡式第二定理对超材料胞元的弹性参数进行理论建模,并采用Beam 188单元建立有限元模型进行静力学分析;同时采用3D打印技术研制胞元拉伸样件进行拉伸实验,验证了理论和仿真模型的准确性。最后对内向同构二次分层内凹六边形超材料胞元进行参数研究,并与内凹六边形超材料胞元进行性能对比。结果表明,通过调整胞元边长、胞壁厚度,可在保持泊松比不变的情况下显著提升胞元的刚度,为变形翼蒙皮和变形翼填充结构的设计提供了理论依据。Aiming at the problems such as low stiffness and strength and the complex mixing of unit cells in negative Poisson's ratio(NPR)metamaterials,a type of internal isomorphic secondary hierarchical re-entrant hexagonal(IISHRH)metamaterial cell based on re-entrant hexagonal cell is proposed.Firstly,the elastic property parameters of the IISHRH metamaterial are theoretically modeled based on the Timoshenko beam model and Castigliano's second theorem,and the finite element model is established by Beam 188 element for static analysis.Additionally,3D printing technology is used to fabricate tensile specimens of the unit cells,and tensile experiments are conducted to verify the accuracy of the theoretical and simulation models.Finally,a parameter study of the IISHRH metamaterial cell is conducted,and its performance is compared with that of the re-entrant hexagonal cell.The results show that by adjusting the dimensions of the cell edge length and wall thickness,it is possible to significantly enhance the stiffness and strength of the cell,while simultaneously maintaining a nearly constant Poisson's ratio,establishing a solid theoretical foundation for the design of morphing wing skins and filling structures for morphing wings.

关 键 词：变形翼 超材料 负泊松比 铁木辛柯梁模型 卡氏第二定理 

分 类 号：V250.1[一般工业技术—材料科学与工程]