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Wave propagation modeling in periodic elasto-thermo-diffusive materials via multifield asymptotic homogenization
arXiv - CS - Computational Engineering, Finance, and Science Pub Date : 2020-02-11 , DOI: arxiv-2002.11479
Francesca Fantoni and Andrea Bacigalupo

A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is provided in the present study. Field equations for the first-order equivalent medium are derived and overall constitutive tensors are obtained in closed form. These lasts depend upon the micro constitutive properties of the different phases composing the composite material and upon periodic perturbation functions, which allow taking into account the effects of microstructural heterogeneities. Perturbation functions are determined as solutions of recursive non homogeneous cell problems emanated from the substitution of asymptotic expansions of the micro fields in powers of the microstructural characteristic size into local balance equations. Average field equations of infinite order are also provided, whose formal solution can be obtained through asymptotic expansions of the macrofields. With the aim of investigating dispersion properties of waves propagating inside the medium, proper integral transforms are applied to governing field equations of the homogenized medium. A quadratic generalized eigenvalue problem is thus obtained, whose solution characterizes the complex valued frequency band structure of the first-order equivalent material. The validity of the proposed technique has been confirmed by the very good matching obtained between dispersion curves of the homogenized medium and the lowest frequency ones relative to the heterogeneous material. These lasts are computed from the resolution of a quadratic generalized eigenvalue problem over the periodic cell subjected to Floquet-Bloch boundary conditions. An illustrative benchmark is conducted referring to a Solid Oxide Fuel Cell (SOFC)-like material, whose microstructure can be modeled through the spatial tessellation of the domain with a periodic cell subjected to thermo-diffusive phenomena.

中文翻译:

通过多场渐近均匀化在周期性弹性热扩散材料中进行波传播建模

本研究提供了一种用于周期性热扩散弹性材料的多场渐近均匀化技术。推导出一阶等效介质的场方程,并以封闭形式获得整体本构张量。这些持续时间取决于组成复合材料的不同相的微观本构特性和周期性扰动函数,这允许考虑微观结构异质性的影响。微扰函数被确定为递归非齐次单元问题的解决方案,该问题源自将微观结构特征尺寸的幂的微场的渐近扩展代入局部平衡方程。还提供了无限阶的平均场方程,其形式解可以通过宏场的渐近展开来获得。为了研究在介质内传播的波的色散特性,将适当的积分变换应用于控制均质介质的场方程。从而得到一个二次广义特征值问题,其解表征一阶等效材料的复值频带结构。所提出的技术的有效性已被均质介质的色散曲线与相对于非均质材料的最低频率曲线之间获得的非常好的匹配所证实。这些尾数是根据 Floquet-Bloch 边界条件下周期性单元上的二次广义特征值问题的分辨率计算得出的。
更新日期:2020-02-27
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