Theoretical formulation and computational aspects of a two-scale homogenization scheme combining the TPM and FE2 method for poro-elastic fluid-saturated porous media

The focus of this investigation lies on the development of a two-scale homogenization scheme for poro-elastic fluid-saturated porous media. For this purpose, the general concepts of the Theory of Porous Media (TPM) are combined with the FE2 method. After an introduction of the basics of TPM, the weak forms for the macroscopic and the microscopic scale will be formulated and the averaged macroscopic tangent moduli considering the microscale will be derived. Additionally, the formulation of lower level boundary conditions, which refer to the quantities that will be transmitted from the macro- to the microscale, in strict compliance with the Hill–Mandel homogeneity condition, is derived. Finally, a numerical example will be presented, pointing out the gained features of the methodology.