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arXiv · 2205.10814

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

Tomáš Roubíček
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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.

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Tomáš Roubíček. 2022-05-22. Interaction of finitely-strained viscoelastic multipolar solids and fluids by an Eulerian approach. https://arxiv.org/abs/2205.10814

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