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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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

SIAM Journal on Mathematical Analysis

ISSN

0036-1410

e-ISSN

1095-7154

Svazek periodika

55

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

50

Strana od-do

3108-3168

Kód UT WoS článku

001072914800005

EID výsledku v databázi Scopus

2-s2.0-85171594381