A variational approach to the emergence of domain structures in magnetostrictive solids

TL;DR

This paper develops a variational model for magnetostrictive solids that captures the formation of magnetic domain structures considering large strains, magnetostriction, and magnetic fields, using advanced mathematical techniques like $ extGamma$-convergence.

Contribution

It introduces a novel variational framework for magnetoelastic solids that accounts for large strains, domain formation, and magnetostriction effects through rigorous mathematical analysis.

Findings

Identification of a new variational model for domain structures

Incorporation of magnetic field effects into the model

Proof of regularity of minimizers for uniaxial materials

Abstract

We consider a variational model for magnetoelastic solids in the large-strain setting with the magnetization field defined on the unknown deformed configuration. Through a simultaneous linearization of the deformation and sharp-interface limit of the magnetization with respect to the easy axes, performed in terms of $\Gamma$-convergence, we identify a variational model describing the formation of domain structures and accounting for magnetostriction in the small-strain setting. Our analysis incorporates the effect of magnetic fields and, for uniaxial materials, ensures the regularity of minimizers of the effective energy.