Computational homogenization and nonlinear effects in heterogeneous fluid saturated porous media

For the two-scale modelling of deforming fluid-saturated porous structure we apply the asymptotic homogenization approach to the fluid-structure interaction problem involving linear elastic porous skeleton and the Newtonian compressible fluid. The sensitivity analysis of effective coefficients depending on the geometrical configuration is used to introduce a weakly nonlinear formulation which enables to capture influences of the deformation on the material properties. The paper is devoted to the comparison of the linear and the weakly nonlinear models (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)