A Reduced Model for Plates Arising as Low-Energy Gamma-Limit in Nonlinear Magnetoelasticity

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F23%3A00576563" target="_blank" >RIV/67985556:_____/23:00576563 - isvavai.cz</a>
Result on the web
<a href="https://epubs.siam.org/doi/10.1137/21M1446836" target="_blank" >https://epubs.siam.org/doi/10.1137/21M1446836</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/21M1446836" target="_blank" >10.1137/21M1446836</a>

Result language
angličtina
Original language name
A Reduced Model for Plates Arising as Low-Energy Gamma-Limit in Nonlinear Magnetoelasticity
Original language description
We investigate the problem of dimension reduction for plates in nonlinear magnetoelasticity. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed set in the actual space. We consider low-energy configurations by rescaling the elastic energy according to the linearized von Kármán regime. First, we identify a reduced model by computing the Γ-limit of the magnetoelastic energy, as the thickness of the plate goes to zero. This extends a previous result obtained by the first author in the incompressible case to the compressible one. Then, we introduce applied loads given by mechanical forces and external magnetic fields and we prove that sequences of almost minimizers of the total energy converge to minimizers of the corresponding energy in the reduced model. Subsequently, we study quasistatic evolutions driven by time-dependent applied loads and a rateindependent dissipation. We prove that energetic solutions for the bulk model converge to energetic solutions for the reduced model and we establish a similar result for solutions of the approximate incremental minimization problem. Both these results provide a further justification of the reduced model in the spirit of the evolutionary 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
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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