HOMOGENIZATION OF ELASTIC WAVES IN FLUID-SATURATED POROUS MEDIA USING THE BIOT MODEL

Author:

MIELKE ALEXANDER12,ROHAN EDUARD3

Affiliation:

1. Weierstraß Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany

2. Institut für Mathematik, Humboldt-Universität zu Berlin, 12489 Berlin, Germany

3. Department of Mechanics, Faculty of Applied Sciences, University of West Bohemia in Pilsen, Univerzitní 8, 30614 Plzeň, Czech Republic

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 from 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation

Reference35 articles.

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3. Homogenization and Two-Scale Convergence

4. G. Allaire, Progress in PDE: Calculus of Variation, Applications, Pitman Research Notes in Mathematics Series 267 (Longman, 1992) pp. 109–123.

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