Linearized von K\'arm\'an theory for incompressible magnetoelastic plates

TL;DR

This paper analyzes the asymptotic behavior of thin incompressible magnetoelastic plates in the linearized von Kármán regime using Γ-convergence, incorporating a mixed Eulerian-Lagrangian formulation for magnetizations.

Contribution

It introduces a novel Γ-convergence analysis for thin incompressible magnetoelastic plates in the linearized von Kármán regime with a mixed formulation for magnetizations.

Findings

Derived a limit model for magnetoelastic plates as thickness approaches zero.

Established Γ-convergence of the energy functionals in the specified regime.

Provided insights into the deformation and magnetization behavior in thin plates.

Abstract

We study the asymptotic behaviour, in the sense of $\Gamma$-convergence, of a thin incompressible magnetoelastic plate, as its thickness goes to zero. We focus on the linearized von K\'arm\'an regime. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed confguration.