层状复合材料精确弹性动力均匀化方法再探讨
Exact Elastodynamic Homogenization of Laminated Composites Revisited
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- Shanghai Institute of Applied Mathematics（上海应用数学研究所）
- Shanghai University（上海大学）
- Columbia University（哥伦比亚大学）
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中文总结 AI 辅助
本文重新审视Willis弹性动力均匀化方法，修正公式差异，提出基于等效夹杂的特征场均匀化方案，并与精确方法取得一致，为多维扩展奠定基础。
中文摘要 AI 辅助
本文重新审视了Willis对周期层状复合材料的弹性动力均匀化方法（Mechanics of Materials, 41 (2009) 385-393），并采用基于等效夹杂的方法（EIM）利用特征场来评估独特的有效本构性质。在Willis的精确均匀化方法中，依赖于微结构的格林函数至关重要，该函数是从相应的周期层状材料中推导出来的。我们的重新检验发现，已发表的Floquet数及相关有效性质公式中存在若干代数差异。与此同时，本文采用包含两个特征场（即特征应变和特征动量）的比较介质来模拟不均匀性，分别对应刚度和质量密度的失配。因此，可以直接使用一般的格林函数。将采用更新后的特定格林函数的精确均匀化方法与所提出的基于特征场的EIM均匀化方案进行比较，两者获得了极好的一致性。本文为将均匀化框架扩展到多维Willis型均匀化提供了基础。
英文摘要
This paper revisits Willis' elastodynamic homogenization (Mechanics of Materials, 41 (2009) 385-393) of periodic laminate composites and uses the equivalent inclusion-based method (EIM) to evaluate the unique effective constitutive properties with eigen-fields. The microstructure-specific Green's function is essential in Willis's exact homogenization method, which was derived from the corresponding periodic laminates. Our re-examination identifies several algebraic differences in the published formulae for the Floquet number and the related effective properties. In parallel, this paper simulates inhomogeneities with a comparison medium containing two eigen-fields, namely eigenstrain and eigen-momentum, to simulate stiffness and mass density mismatch, respectively. Therefore, the general Green's function can be directly used. The exact homogenization method with the updated specific Green's function is compared to the proposed EIM with eigen-fields homogenization scheme, and excellent agreement is obtained. The present paper provides a base to extend the homogenization framework to multi-dimensional Willis-type homogenization.
