To reflect the anisotropic degree of materials and to further reveal its relevance with the elastic wave propagation in materials, the Thomsen's parameters were proposed for transversely-isotropic materials with weakly anisotropy and were generalized to materials with lower symmetries. This paper derives the complete 21 anisotropic parameters of arbitrarily-anisotropic (triclinic) materials to reflect their anisotropic degree by virtue of the Christoffel equation, as the propagation of generally coupled bulk waves is considered. First, the derivation is conducted analytically on basis of the coordinate transformations to the propagation direction of general bulk waves and to the stiffness matrix of arbitrarily-anisotropic materials involved in the Christoffel equation, but does not require the concrete expanded expression of the Christoffel equation. Then, the influences of any anisotropic parameters on the anisotropy characteristics on arbitrary planes and on the dispersion characteristics along any directions of bulk waves are investigated in detail, which are reflected by the variations of the slowness/phase velocity curves and the comprehensive dispersion curves, respectively. Finally, the influential rules are illustrated and summarized with combination of numerical examples about two typical exemplified anisotropic materials. It is found that the 21 anisotropic parameters for triclinic materials, which can actually be utilized to describe the anisotropic degree for all materials, are divided into five groups according to their influential patterns on the anisotropy characteristics of bulk waves. Furthermore, the dispersion characteristics of each bulk wave mode along specific direction are affected by three anisotropic parameters.

中文翻译：

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任意各向异性材料中的各向异性参数和体波传播


为了反映材料的各向异性程度并进一步揭示其与材料中弹性波传播的相关性，针对弱各向异性的横各向同性材料提出了汤姆森参数，并将其推广到对称性较低的材料。本文在考虑一般耦合体波传播的情况下，利用Christoffel方程推导了任意各向异性（三斜）材料的完整21个各向异性参数来反映其各向异性程度。首先，根据Christoffel方程中涉及的一般体波传播方向和任意各向异性材料的刚度矩阵的坐标变换进行解析推导，但不需要Christoffel方程的具体展开表达式。然后，详细研究了任意各向异性参数对任意平面各向异性特性以及体波任意方向色散特性的影响，并通过慢度/相速度曲线和综合色散曲线的变化来反映，分别。最后，结合两种典型的各向异性材料的数值算例，说明和总结了其影响规律。结果发现，三斜材料的21个各向异性参数实际上可以用来描述所有材料的各向异性程度，根据它们对体波各向异性特性的影响模式分为五组。此外，每个体波模式沿特定方向的色散特性受到三个各向异性参数的影响。