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首页> 外文期刊>Applied Mathematical Modelling >Homogenization approach and Floquet-Bloch theory for wave analysis in fluid-saturated porous media with mesoscopic heterogeneities
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Homogenization approach and Floquet-Bloch theory for wave analysis in fluid-saturated porous media with mesoscopic heterogeneities

机译：介质异质介质流体饱和多孔介质波分析均质化方法与浮子 - 黑色理论

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摘要

We consider fluid-saturated poroelastic media whose the mechanical response is governed by the Biot model relevant to a mesoscopic scale. Assuming the material properties being described by periodic functions, to analyze wave propagation in such heterogeneous and anisotropic media, we derive a formulation based on the Floquet-Bloch (FB) wave decomposition which enables to analyze waves within the whole first Brillouin zone associated with the periodic structure. The wave dispersion results obtained by the FB approach are compared with those computed using a model derived by the homogenization based on the asymptotic analysis with respect to the scale parameter. As another new ingredient, the homogenized model is extended to describe media saturated simultaneously by multiple different fluids, so that the model involves new permeability tensors and differs in structure from the model derived earlier. The dispersion analysis by the FB approach leads to a cumbersome quadratic eigenvalue problem to be solved for complex wave numbers. We suggest an efficient filtration strategy to identify the principle propagating modes (the fast and slow compressional waves and the shear waves). For comparison with results of the FB transformation applied at the mesoscopic heterogeneity scale, the homogenized model responses are reconstructed using the corrector results of the homogenization with fixing a finite scale. Numerical examples illustrate very good correspondence of the dispersion results, as computed by both the approaches.
机译：我们考虑流体饱和的腹腔弹性介质，其机械响应由与介观标尺相关的BIOT模型控制。假设通过定期功能描述的材料特性，以分析这种异构和各向异性介质中的波传播，我们基于FLOQUET-BLOCH（FB）波分解来推导出配方，这使得能够分析与之相关的整个第一布里渊区内的波浪。定期结构。将通过FB方法获得的波形分散结果与使用由均质化的模型基于相对于刻度分析进行的模型进行比较。作为另一种新成分，均质模型扩展以描述通过多个不同流体同时饱和的介质，使得该模型涉及新的渗透性张量并且与前面衍生的模型的结构不同。 FB方法的分散分析导致繁琐的二次特征值问题，用于复杂波数。我们建议一种有效的过滤策略来识别原理传播模式（快速和慢速压缩波和剪切波）。为了比较施加在介术异质性规模的FB变换的结果，使用均质化的均匀化与固定有限规模的校正结果重建均质模型响应。数值示例说明了分散结果的非常良好的对应关系，通过这两种方法计算。

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  • 来源
    《Applied Mathematical Modelling》 |2021年第3期|1-23|共23页
  • 作者

    Eduard Rohan; Vu-Hieu Nguyen; Salah Naili;

  • 作者单位

    NTIS - New Technologies for The Information Society Faculty of Applied Sciences. University of West Bohemia Technicka 8 Pilsen 30100 Czech Republic;

    CNRS MSME University Paris Est Creteil Creteil F-94010 France MSME University Custave Eiffel Mame-la-Vallee F-77447 France;

    CNRS MSME University Paris Est Creteil Creteil F-94010 France MSME University Custave Eiffel Mame-la-Vallee F-77447 France;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Poroelasticity; Biot model; Floquet-Bloch waves; Wave dispersion; Periodic media; Homogenization;

    机译：孔弹性;BIOT模型;Floquet-Bloch波浪;波浪分散;定期媒体;均质化;

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