Siegel der Universität Augsburg

Universität Augsburg
Institut für Mathematik

Siegel der Universität Augsburg


Analysis-Seminar Augsburg-München


Professor Dr. Rufat Badal
FAU Erlangen-Nürnberg

spricht am
Donnerstag, 29. Juni 2023
15:45 Uhr
TUM, Boltzmann-3, Garching, Raum 03.08.011, Etage 3
über das Thema:

»Nonlinear and linearized models in thermoviscoelasticity«

We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. The force balance is formulated in the reference configuration by resorting to the concept of nonsimple materials whereas the heat transfer equation is governed by the Fourier law in the deformed configurations. Weak solutions are obtained by means of a staggered in-time discretization where the deformation and the temperature are updated alternatingly. Our result refines a recent work by Mielke & Roubíček since our approximation does not require any regularization of the viscosity term. Afterwards, we focus on the case of deformations near the identity and small temperatures, and we show by a rigorous linearization procedure that weak solutions of the nonlinear system converge in a suitable sense to solutions of a system in linearized thermoviscoelasticity. The same property holds for time-discrete approximations and we provide a corresponding commutativity result. The talk will be supplemented by several numerical experiments.


Hierzu ergeht herzliche Einladung.

[Impressum]      [Datenschutz],     Di 27-Jun-2023 17:46:28 MESZ