三维手性力学材料设计与弹性波调控研究

This project is devoted to investigate the design, mechanical characterization and wave controlling applications of three-dimensional chiral mechanical materials. A three-dimensional micropolar constitutive relation will be established in order to completely and correctly characterize the mechanical chirality, which is a fundamental problem unsolved for anisotropic chiral solids currently. The mechanical chiral coupling effect, physical mechanism and its scaling law will be revealed analytically. The mechanical activity corresponding to optical activity will be demonstrated by studying the impact of chiral parameters on the wave polarization and dispersion relation. Three-dimensional chiral materials with different symmetries groups will be designed and homogenization methods will be developed to predict the effective properties with accuracy and efficiency. Optimization procedure for designing three-dimensional chiral materials with required material parameters will be established. Finally, elastic wave controlling applications based on the mechanical activity will be explored. Typical devices including polarization conversion and unidirectional transmitting devices will be designed and numerical simulations will be carried out to verify the designed functions. This project will promote the characterization and design of three dimensional mechanical materials and lay a theoretical foundation for controlling elastic wave through chirality.

课题通过理论与数值相结合的途径，系统开展三维手性力学材料设计、手性表征与弹性波调控应用研究。主要内容包括：建立一般性的三维手性微极介质本构关系，解决现有本构不适用于各向异性手性介质这一理论问题；基于建立的手性微极本构关系，研究手性耦合效应、机理及其尺度缩放规律，分析手性特征对弹性波偏振与色散关系的影响，揭示三维手性力学材料对弹性波的类旋光性；拓展现有三维手性拓扑构型设计方法，设计不同空间对称性的三维手性材料，给出预测等效性质的均质化表征方法，形成系统的三维手性材料设计、表征与优化设计方法；开发基于类旋光性的弹性波调控功能应用，设计弹性波偏振转换与单向传输器件，并通过数值仿真验证设计方法有效性。通过本项目研究，将推动三维手性力学材料表征与设计方法的建立，为通过手性调控弹性波奠定理论基础。

三维手性力学超材料由于不满足镜像对称，在静力学方面可实现新奇的拉扭耦合效应，在波动方面可实现与手性电磁波介质类似的旋声性，为调控剪切弹性波的偏振方向提供了途径。经典柯西弹性力学理论天然满足镜像对称，无法在均匀化层面刻画上述手性效果，微极弹性力学理论可以刻画手性效应，但相应的数值计算方法还有待发展。此外，当前设计的手性超材料均具有强各向异性，其旋声性仅在特定传波方向存在，在偏离这些方向后圆偏振本征模态迅速退化为线偏振模态。这种各向异性制约了其可能的实际应用，有必要设计各向同性的三维手性力学超材料。.针对上述问题，项目开展了三维手性力学超材料设计与建模研究。主要研究内容包括：1）基于微极弹性理论的三维手性力学超材料理论建模与数值计算方法；2）三维立方对称手性超材料的数值均匀化方法，3）基于准晶的各向同性三维手性超材料设计；4）基于周期晶体的各向同性三维手性超材料设计。项目发展了基于商业有限元的微极弹性问题数值求解方法，基于微极弹性理论正确刻画了手性超材料拉扭耦合以及旋声性的尺度效应，成功设计出了一种各向同性的手性准晶超材料以及两种各向同性手性周期晶体超材料，均可在三维空间任意波传播方向获得旋声性。.成果在固体力学顶级期刊《Journal of the Mechanics and Physics of Solids》、物理顶级期刊《Physical Review Letters》、经典综合期刊《Proceedings of the Royal Society A》等期刊发表手性超材料SCI论文4篇，另发表弹性波及拓扑绝缘体论文4篇。