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

0576563 - ÚTIA 2024 RIV US eng J - Článek v odborném periodiku
Bresciani, M. - Kružík, Martin
A Reduced Model for Plates Arising as Low-Energy Gamma-Limit in Nonlinear Magnetoelasticity.
SIAM Journal on Mathematical Analysis. Roč. 55, č. 4 (2023), s. 3108-3168. ISSN 0036-1410. E-ISSN 1095-7154
Grant CEP: GA MŠMT 8J19AT013; GA MŠMT 8J22AT017; GA ČR(CZ) GF19-29646L
Institucionální podpora: RVO:67985556
Klíčová slova: magnetoelasticity * Eulerian-Lagrangian energies * dimension reduction * Gamma-convergencerate-independent processes * evolutionary Gamma-convergence
Obor OECD: Pure mathematics
Impakt faktor: 2, rok: 2022
Způsob publikování: Omezený přístup
http://library.utia.cas.cz/separaty/2023/MTR/kruzik-0576563.pdf https://epubs.siam.org/doi/10.1137/21M1446836

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.
Trvalý link: https://hdl.handle.net/11104/0346493