The engineering design of metamaterials with selected acoustic properties necessitates adequate prediction of the elastic wave propagation across various domains and specific frequency ranges. This study proposes a systematic approach centered on the finite element characterization of the three-dimensional Green’s function for a representative volume element. The inherent characteristics of broadband waves and singular impulses contribute to notable challenges related to accuracy and high-frequency oscillations, and thus the emphasis is set on providing an exhaustive analysis for this numerical characterization scheme. The study focuses on the broadband wave dispersion and requisite considerations for numerical damping, and evaluates the impact of dissipation and space–time discretization schemes for optimal performance. In contrast to conventional methods that employ a plane wave, the proposed approach does not need extra assumptions on the enforcement of boundary conditions and can effectively consider the influences of length scale from the material configurations. A quasi-equiaxed polycrystalline ice microstructure is utilized as an application example for homogenizing heterogeneous materials, in line with advancements in cryo-ultrasonic testing techniques.

中文翻译：

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多晶均匀化 3D 波传播中的数值色散和耗散


具有选定声学特性的超材料的工程设计需要对跨不同域和特定频率范围的弹性波传播进行充分预测。本研究提出了一种以代表性体积元素的三维格林函数的有限元表征为中心的系统方法。宽带波和奇异脉冲的固有特性导致了与精度和高频振荡相关的显着挑战，因此重点是为该数值表征方案提供详尽的分析。该研究重点关注宽带波色散和数值阻尼的必要考虑因素，并评估耗散和时空离散方案对最佳性能的影响。与采用平面波的传统方法相比，所提出的方法不需要对边界条件的执行进行额外的假设，并且可以有效地考虑材料配置的长度尺度的影响。准等轴多晶冰微结构被用作均质化异质材料的应用示例，与低温超声测试技术的进步保持一致。