周期材料方向性的分析
Analysis of the directionality on periodic materials
AI总结：
本文针对周期材料的方向性描述问题，提出一种基于动态行为的各向异性度量方法，以 Bloch 频散曲面为输入输出编码体方向性的曲线或曲面，并在弹性动力学中验证其有效性。
摘要：
目前，跨学科领域对超材料与周期材料的研究兴趣日益增长。这些材料具有各向异性，其性质呈现方向性，例如波速依赖于传播方向。此外，它们具有非均匀性，其方向性取决于其频谱。描述各向异性的常用方法已在大波长近似下用于静态性质。本文提出一种基于动态行为的各向异性度量。该方法以 Bloch 分析得到的频散曲面作为输入，输出一个在其上编码了体方向性的曲线或曲面。我们展示了弹性动力学方面的结果，但该方法也适用于其他物理现象。
英文摘要：
There is an increasing interest in the study of metamaterials and periodic materials across disciplines. These are anisotropic and their properties present directionality. For example, the wave speed depends on the propagation direction. Furthermore, they are heterogeneous, and their directionality depends on their spectra. Common approaches to describe anisotropy have been used in the large-wavelength approximation corresponding to static properties. Here we present an anisotropy measure based on the dynamic behavior. It receives dispersion surfaces from Bloch analyses and outputs a curve/surface with bulk directionality encoded on it. We present results for elastodynamics, but it is applicable to other phenomena.
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