Magnetoelastic thin films at large strains

Elisa Davoli,Martin Kružík,Paolo Piovano,Ulisse Stefanelli

doi:10.1007/s00161-020-00904-1

Abstract

Starting from the three-dimensional setting, we derive a limit model of a thin magnetoelastic film by means of varGamma -convergence techniques. As magnetization vectors are defined on the elastically deformed configuration, our model features both Lagrangian and Eulerian terms. This calls for qualifying admissible three-dimensional deformations of planar domains in terms of injectivity. In addition, a careful treatment of the Maxwell system in the deformed film is required.

Highlights

Magnetoelasticity describes the mechanical behavior of solids under magnetic effects
The magnetoelastic coupling is based on the presence of small magnetic domains in the material [13]
Mechanical deformations modify the magnetic response of a specimen by influencing the magnetic anisotropy of the domains, so that the magnetic

Summary

Introduction

Magnetoelasticity describes the mechanical behavior of solids under magnetic effects. One has to mention rare-earth alloys such as TerFeNOL and GalFeNOL, as well as ferromagnetic shape-memory alloys as Ni2MnGa, NiMnInCo, NiFeGaCo, FePt, FePd, among others [16] These materials exhibit a remarkable magnetostrictive behavior, for reversible strains as large as 10% can be activated by the imposition of relatively moderate magnetic fields. This strong magnetoelastic coupling makes them relevant in a wealth of innovative applications including sensors and actuators [2]. Magnetostriction in thin films has been considered, from the numerical viewpoint, in [24,25,26] With respect to these results, this paper presents a fundamental novelty as it represents the first rigorous analytical treatment including the large-strain magnetoelastic regime.

Setting of the problem

Change of variables

Main results

Findings

Proofs