Homogenization Based Computational Two-Scale Modelling of Self-Contact in Collapsible Fluid Saturated Micropores

Modelling the unilateral contact due to collapsible pores in porous media presents a challenging nonlinear problem which requires convenient approximations allowing for a tractable numerical solutions.We have derived its two-scale formulation obtained by the homogenization of the fluid-structure interaction at the pore level.We focus on periodic structures with pores distributed as fluid-filled inclusions with narrow parts (fissures) in which the matching contact surfaces are specified.It is demonstrated how the fluid increases the structure stiffness.Two variational formulations of the macroscopic problem are considered; the first one is a nonlinear elastic problem coupled with the local contact problems introduced using a variational inequality, the second one is formulated as a two-scale contact problem with a two-scale contact constraint.To reduce the computational effort, we propose an approximation of the local contact problem solutions using master microproblems solved for selected macroscopic deformations.For this, the sensitivity analysis framework analogical to the one used in the shape optimization is employed.