A consistent computational approach for general fluid-poroelasticity-structure-contact interaction problems

Abstract

The focus of this contribution is the numerical treatment of interface-coupled problems concerned with the interaction of impermeable or permeable elastic bodies1 and the surrounding fluid including the contact interaction of deformable bodies. The presented formulation is based on the approach for fluid-structural-contact interaction in [1], and consistently takes into account fluid-filled poroelastic bodies including the conditions of solid-poroelastic contact, poroelastic-poroelastic contact, and viscous flow poroelasticity interaction. The interface conditions in normal and tangential orientation to formulate this type of coupled problem, based on the fundamental balances of mass and linear momentum, the no-slip condition, the Beavers Joseph condition, and the conditions for frictionless contact on the respective interfaces, are discussed. A continuous transition of the different types of tangential conditions is enabled by application of the general Navier condition with varying slip length. The fluid stress in the zone of closed contact, which is essential for the lift-off behavior of contacting bodies, is obtained by an extension approach augmented by the porous fluid state to ensure continuity and physical accuracy. To account for topological changes of the fluid domain, the numerical approach utilizes non-interface fitted computational meshes for the fluid domain enabled by the Cut Finite Element Method. All interface conditions are incorporated in a weak sense by Nitsche-based approaches. Different numerical examples analyze the proper contacting and lift-off behavior for contact between the different pairs of impermeable and permeable bodies and demonstrate the robustness for more challenging configurations, which include topological changes of the fluid domain, large contacting areas, and 3D configurations.