Interaction of finitely-strained viscoelastic multipolar solids and fluids by an Eulerian approach

TL;DR

This paper develops an Eulerian approach to model the quasistatic interaction between finitely-strained viscoelastic fluids and solids using higher-order multipolar viscosity, establishing existence and regularity of solutions.

Contribution

It introduces a monolithic Eulerian framework for viscoelastic fluid-structure interaction with higher-order viscosity and proves existence and regularity of weak solutions.

Findings

Established a monolithic Eulerian formulation for viscoelastic FSI.

Proved existence and regularity of weak solutions using Schauder fixed-point.

Demonstrated the applicability of higher-order multipolar viscosity in FSI modeling.

Abstract

A mechanical interaction of compressible viscoelastic fluids with viscoelastic solids in Kelvin-Voigt rheology using the concept of higher-order (so-called 2nd-grade multipolar) viscosity is investigated in a quasistatic variant. The no-slip contact between fluid and solid is considered and the Eulerian-frame return-mapping technique is used for both the fluid and the solid models, which allows for a "monolithic" formulation of this fluid-structure interaction problem. Existence and a certain regularity of weak solutions is proved by a Schauder fixed-point argument combined with a suitable regularization.