Nonlinear and Linearized Models in Thermoviscoelasticity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F23%3A00573354" target="_blank" >RIV/67985556:_____/23:00573354 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/68407700:21110/23:00381422

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00205-022-01834-9" target="_blank" >https://link.springer.com/article/10.1007/s00205-022-01834-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00205-022-01834-9" target="_blank" >10.1007/s00205-022-01834-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Nonlinear and Linearized Models in Thermoviscoelasticity

Popis výsledku v původním jazyce

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 and Roubíček (Arch Ration Mech Anal 238:1–45, 2020) 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.

Název v anglickém jazyce

Nonlinear and Linearized Models in Thermoviscoelasticity

Popis výsledku anglicky

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 and Roubíček (Arch Ration Mech Anal 238:1–45, 2020) 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF21-06569K" target="_blank" >GF21-06569K: Škály a tvary v termomechanice continua</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

e-ISSN

1432-0673

Svazek periodika

247

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

73

Strana od-do

5

Kód UT WoS článku

000908896900001

EID výsledku v databázi Scopus

2-s2.0-85145591440