A reduced model for plates arising as low-energy gamma-limit in nonlinear magnetoelasticity

Bresciani M, Kru M (2023)

Publication Type: Journal article

Publication year: 2023

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Book Volume: 55

Pages Range: 3108-3168

Journal Issue: 4

DOI: 10.1137/21M1446836

Abstract

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 K'arm'an regime. First, we identify a reduced model by computing the Gamma-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 rate-independent 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 Gamma-convergence.

Authors with CRIS profile

Marco Bresciani Professur für Angewandte Mathematik (Angewandte Analysis)

Involved external institutions

Institute of Information Theory and Automation (UTIA) CZ Czech Republic (CZ)

How to cite

APA:

Bresciani, M., & Kru, M. (2023). A reduced model for plates arising as low-energy gamma-limit in nonlinear magnetoelasticity. SIAM Journal on Mathematical Analysis, 55(4), 3108-3168. https://dx.doi.org/10.1137/21M1446836

MLA:

Bresciani, Marco, and Martin Kru. "A reduced model for plates arising as low-energy gamma-limit in nonlinear magnetoelasticity." SIAM Journal on Mathematical Analysis 55.4 (2023): 3108-3168.

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