Three-dimensional finite element (FE) modelling, with representation of materials at grain scale in realistic sample volumes, is capable of accurately describing elastic wave propagation and scattering within polycrystals. A broader and better future use of this FE method requires several important topics to be fully understood, and this work presents studies addressing this aim. The first topic concerns the determination of effective media parameters, namely, scattering induced attenuation and phase velocity, from measured coherent waves. This work evaluates two determination approaches, through-transmission and fitting, and it is found that these approaches are practically equivalent and can thus be used interchangeably. For the second topic of estimating modelling errors and uncertainties, this work performs thorough analytical and numerical studies to estimate those caused by both FE approximations and statistical considerations. It is demonstrated that the errors and uncertainties can be well suppressed by using a proper combination of modelling parameters. For the last topic of incorporating FE model information into theoretical models, this work presents elaborated investigations and shows that to improve agreement between the FE and theoretical models, the symmetry boundary conditions used in FE models need to be considered in the two-point correlation function, which is required by theoretical models.

中文翻译：

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最大化多晶体中弹性波传播的有限元模拟的准确性

三维有限元（FE）建模，可以在真实的样品体积中以晶粒度表示材料，能够准确地描述弹性波在多晶内的传播和散射。此有限元方法的更广泛和更好的未来使用需要充分理解几个重要的主题，并且这项工作提出了解决该目标的研究。第一个主题涉及从测量的相干波确定有效的介质参数，即散射引起的衰减和相速度。这项工作评估了两种确定方法，即透射法和拟合法，发现这些方法实际上是等效的，因此可以互换使用。对于估算建模误差和不确定性的第二个主题，这项工作进行了彻底的分析和数值研究，以估计由有限元逼近和统计考虑引起的那些。结果表明，通过适当组合建模参数可以很好地抑制误差和不确定性。对于将有限元模型信息纳入理论模型的最后一个主题，这项工作进行了详尽的研究，并表明，为了提高有限元模型与理论模型之间的一致性，需要在两点相关函数中考虑有限元模型中使用的对称边界条件，这是理论模型所必需的。