Keywords: multiscale modelling, porous media, Biot model, homogenization, sensitivity analysis, nonlinear problems..

This paper is concerned with modeling nonlinear effects in deforming porous fluid saturated media. The proposed modelling approaches are based on the homogenization of quasistatic fluid-structure interaction whereby the material derivative is considered as a tool for linearisation. Assuming the linear kinematics framework for the first proposed model, the nonlinearity in the Biot continuum is introduced in terms of the material coefficients which are expressed as linear functions of the macroscopic response. These functions are obtained by the sensitivity analysis of the homogenized coefficients computed for a given geometry of the porous structure which transforms as a result of the local deformation. The second model is derived in the framework of the Eulerian formulation allowing for the large deformation kinematics. The proposed sensitivity analysis approach to handle deformation-dependent material coefficients avoids solving local microscopic problems for updated configurations. It appears that difference between the linear and nonlinear models depends also on the microstructure of the porous medium; this observation is supported by the numerical examples.

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