Mechanically Consistent Modeling of Fluid-Structure-Contact Interaction without Collision Paradox
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The numerical simulation of systems involving fluid-structure-contact interaction raises many modeling, mathematical and numerical issues. It is also crucial for numerous biomedical applications (e.g., native or artificial cardiac valves). Modeling contact be- tween solids adds challenging difficulties to fluid-structure interaction (FSI). First, in some configurations, FSI models are unable to predict contact (see [1]); this is the so called no collision paradox. A second major issue is to obtain mechanically consistant models. Indeed, the simple addition of a contact constraint leads to mechanical inconsistencies like unphysical void creation at releases from contact or unbalanced stress at contact. A favored approach is to consider a poroelastic modeling of the fluid seepage induced by the roughness of the contacting solid (see [2, 3]). In this talk we will show that, in the case of a rigid disk moving over a fixed horizontal plane, the fluid-structure-contact model of [3] does encompass contact, and hence removes the above mentioned non collision paradox of traditional FSI models which rely on Dirichlet or Dirichlet/Navier boundary conditions. Numerical evidence on this result will also be provided. Finally, we will explore the extension of [3] to the case of moving elastic solids by replacing the surface Darcy model by a thin-walled poroelastic model reduced from [4].
