Huang Ming, Rokhlin Stanislav I, Lowe Michael J S
Department of Mechanical Engineering, Imperial College London, Exhibition Road, London SW7 2AZ, UK.
Department of Materials Science and Engineering, Edison Joining Technology Center, The Ohio State University, 1248 Arthur E. Adams Drive, Columbus, OH 43221, USA.
Philos Trans A Math Phys Eng Sci. 2022 Sep 5;380(2231):20210382. doi: 10.1098/rsta.2021.0382. Epub 2022 Jul 18.
This paper uses three-dimensional grain-scale finite-element (FE) simulations to appraise the classical scattering theory of plane longitudinal wave propagation in untextured polycrystals with statistically equiaxed grains belonging to the seven crystal symmetries. As revealed from the results of 10 390 materials, the classical theory has a linear relationship with the elastic scattering factor at the quasi-static velocity limit, whereas the reference FE and self-consistent (SC) results generally exhibit a quadratic relationship. As supported by the results of 90 materials, such order difference also extends to the attenuation and phase velocity, leading to larger differences between the classical theory and the FE results for more strongly scattering materials. Alternatively, two approximate models are proposed to achieve more accurate calculations by including an additional quadratic term. One model uses quadratic coefficients from quasi-static SC velocity fits and is thus symmetry-specific, while the other uses theoretically determined coefficients and is valid for any individual material. These simple models generally deliver more accurate attenuation and phase velocity (particularly the second model) than the classical theory, especially for strongly scattering materials. However, the models are invalid for the attenuation of materials with negative quadratic coefficients. This article is part of the theme issue 'Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)'.
本文采用三维晶粒尺度有限元（FE）模拟，来评估平面纵波在具有属于七种晶体对称性的统计等轴晶粒的无织构多晶体中传播的经典散射理论。从10390种材料的结果来看，经典理论在准静态速度极限下与弹性散射因子呈线性关系，而参考有限元结果和自洽（SC）结果通常呈二次关系。由90种材料的结果可知，这种阶次差异也延伸到了衰减和相速度上，导致对于散射更强的材料，经典理论与有限元结果之间的差异更大。另外，提出了两种近似模型，通过纳入一个额外的二次项来实现更精确的计算。一种模型使用准静态自洽速度拟合的二次系数，因此具有对称性特异性，而另一种模型使用理论确定的系数，对任何单个材料都有效。这些简单模型通常比经典理论能给出更精确的衰减和相速度（特别是第二种模型），尤其是对于强散射材料。然而，这些模型对于具有负二次系数的材料的衰减是无效的。本文是主题为“多尺度复杂介质和结构化超材料中的波产生与传播（第1部分）”的一部分。
