Homogenization of magnetoelastic materials with rigid magnetic inclusions at small strains

TL;DR

This paper develops a homogenized model for magnetoelastic materials with rigid magnetic inclusions, capturing effective properties at small strains through periodic homogenization techniques.

Contribution

It introduces a homogenization framework for magnetoelastic composites with rigid inclusions, linking magnetic and elastic behaviors in a unified model.

Findings

Derived an effective magnetoelastic energy for periodic composites.

Established the connection between different magnetic models via Legendre-Fenchel transform.

Provided insights into the behavior of materials with rigid magnetic inclusions.

Abstract

We investigate a homogenization problem for a linearly elastic magnetic material that incorporates elastically rigid magnetic inclusions firmly bonded to the matrix. By considering a periodic arrangement of this material, we identify an effective magnetoelastic energy, obtained by homogenization when the period approaches zero. For comparison, we also briefly discuss alternative, essentially equivalent magnetic models naturally linked by a Legendre-Fenchel transform of magnetic energy density where the elastic deformation enters as a parameter.