On the passage from nonlinear to linearized viscoelasticity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F18%3A00493138" target="_blank" >RIV/67985556:_____/18:00493138 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/17M1131428" target="_blank" >http://dx.doi.org/10.1137/17M1131428</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/17M1131428" target="_blank" >10.1137/17M1131428</a>

Result language
angličtina
Original language name
On the passage from nonlinear to linearized viscoelasticity
Original language description
We formulate a quasistatic nonlinear model for nonsimple viscoelastic materials atna finite-strain setting in the Kelvin-Voigt rheology where the viscosity stress tensor complies with the principle of time-continuous frame indifference. We identify weak solutions in the nonlinear framework as limits of time-incremental problems for vanishing time increment. Moreover, we show that linearization around the identity leads to the standard system for linearized viscoelasticity and that solutions of the nonlinear system converge in a suitable sense to solutions of the linear one. The same property holds for time-discrete approximations, and we provide a corresponding commutativity result. Our main tools are the theory of gradient flows in metric spaces and Γ-convergence.
Czech name
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Czech description
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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
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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