Homogenization-based modelling of self-contact and fluid-structure interaction in the microstructure of poroelastic materials

Abstract

The paper presents two-scale homogenization-based models of fluid-saturated porous elastic materials with the self-contact interaction at the pore level. The periodic microstructures are constituted by a solid skeleton and fluid-filled pores. The unilateral frictionless contact interaction is considered on matching pore surfaces of the elastic skeleton, being coupled with the fluid-structure interaction. The periodic unfolding homogenization is employed to derive limit models for two types of periodic microstructures with disconnected and connected porosities. While in the first case the homogenized model is quite analogous with the one with void pores, in the latter case, the Stokes flow in deforming (possibly collapsible) porosity requires a special treatment by a regularization to retain the pore connectivity. The macroscopic model attains the form of a nonlinear Biot continuum, whereby the Darcy flow model governs the fluid redistribution. To respect the dependence of the permeability on the deformation, an approximation based on the shape sensitivity analysis is proposed which enables to avoid resolving the microflow problems in severely deformed pores. Numerical examples of 2D deforming structures are presented to illustrate the influence of the pore fluid on the unilateral contact in the two types of porous structures.