WIAS Preprint No. 1688, (2012)

Homogenization of elastic waves in fluid-saturated porous media using the Biot model



Authors

  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Rohan, Eduard

2010 Mathematics Subject Classification

  • 35B27 74F10 76M50 76S05

Keywords

  • Two-scale homogenization, porous media, acoustic waves, elastodynamics, Darcy's law, seepage

Abstract

We consider periodically heterogeneous fluid-saturated poroelastic media described by the Biot model with inertia effects. The weak and semistrong formulations for displacement, seepage and pressure fields involve three equations expressing the momentum and mass balance and the Darcy law. Using the two-scale homogenization method we obtain the limit two-scale problem and prove the existence and uniqueness of its weak solutions. The Laplace transformation in time is used to decouple the macroscopic and microscopic scales. It is shown that the seepage velocity is eliminated form the macroscopic equations involving strain and pressure fields only. The plane harmonic wave propagation is studied using an example of layered medium. Illustrations show some influence of the orthotropy on the dispersion phenomena.

Appeared in

  • Math. Models Methods Appl. Sci., 23 (2013) pp. 873--916.

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