Nonlinear and Linearized Models in Thermoviscoelasticity
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F23%3A00381422" target="_blank" >RIV/68407700:21110/23:00381422 - isvavai.cz</a>
Alternative codes found
RIV/67985556:_____/23:00573354
Result on the web
<a href="https://doi.org/10.1007/s00205-022-01834-9" target="_blank" >https://doi.org/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>
Alternative languages
Result language
angličtina
Original language name
Nonlinear and Linearized Models in Thermoviscoelasticity
Original language description
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 Roubicek (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.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Archive for Rational Mechanics and Analysis
ISSN
0003-9527
e-ISSN
1432-0673
Volume of the periodical
247
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
73
Pages from-to
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UT code for WoS article
000908896900001
EID of the result in the Scopus database
2-s2.0-85145591440