# A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis

## TL;DR

This paper develops a thermodynamically consistent model for magneto-elastic materials under large strains with diffusion, analyzing existence of solutions and suggesting numerical methods, applicable to various magnetic and phase transformation phenomena.

## Contribution

It introduces a novel, comprehensive model combining magneto-elasticity, diffusion, and large strains, with rigorous existence analysis and numerical strategy development.

## Key findings

- Established existence of weak solutions for the model
- Provided a Galerkin-based approximation and regularization approach
- Outlined potential applications in magnetic and phase transformation processes

## Abstract

The theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick's and Fourier's laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous Cahn-Hilliard equations are used. The formulation of the problem uses Lagrangian (reference) configuration while the transport processes are pulled back. Except the static problem, the demagnetizing energy is ignored and only local non-selfpenetration is considered. The analysis as far as existence of weak solutions of the (thermo)dynamical problem is performed by a careful regularization and approximation by a Galerkin method, suggesting also a numerical strategy. Either ignoring or combining particular aspects, the model has numerous applications as ferro-to-paramagnetic transformation in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied by magnetic effects (magnetic gels), or metal-hydride phase transformation in some intermetalics under diffusion of hydrogen accompanied possibly by magnetic effects (and in particular ferro-to-antiferromagnetic phase transformation), all in the full thermodynamical context under large strains.