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On multiscale aspects of fluid saturated porous media

S. S. Ahmed.

Master Thesis, Mechanical Engineering, Ruhr-University Bochum, Germany; Mechanics, Statistics, Dynamics, TU Dortmund, Germany (2013)

Abstract

The main goal of this contribution is to formulate appropiate lower level boundary condi- tions for a two-scale homogenization procedure for uid saturated porous media. In this approach we have considered a microscopic representative volume element to be attached at each material point on a overlaying macrostructure. It is assumed that the biphasic material can be modeled within the scope of Theory of Porous Media (TPM).

The boundary conditions to be applied on the representative volume element is de- scribed via quantities present in the macroscopic scale. This macro-to-micro transition is achieved by applying rst order computational homogeneization scheme. Both defor- mation gradient tensor and pressure gradient vector are used as transient variables, and various probable boundary conditions are explored.

The homogeneized representative volume elements are modied in order to allow them to capture biphasic ow in a weak sense. After solution of the microstructural problem, averaging techniques are used to project the problem specic microscopic quantities back to the macroscopic scale and the results are compared.


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