Transformation front kinetics in deformable ferromagnets

TL;DR

This paper develops a thermodynamic framework and a computational method for modeling the propagation of phase boundaries in deformable ferromagnetic materials, specifically magnetic shape-memory alloys, capturing their coupled magnetic and mechanical behaviors.

Contribution

It derives the thermodynamic driving force for transformation fronts and adapts the cut-finite-element method for efficient simulation of phase boundary kinetics in magneto-mechanical systems.

Findings

Thermodynamic driving force for phase boundary propagation is formulated.

Cut-finite-element method is successfully adapted for magneto-mechanical interfaces.

Qualitative modeling of magnetic shape-memory alloys demonstrates the approach.

Abstract

Materials such as magnetic shape-memory alloys possess an intrinsic coupling between material's magnetisation and mechanical deformation. These materials also undergo structural phase transitions, with phase boundaries separating different phases and the kinetics of the phase boundaries governed by the magnetic field and the mechanical stresses. There is a multiplicity of other materials revealing similar phenomena, e.g. magnetic perovskites. To model the propagation of the phase boundaries in deformable magnetic materials at the continuum scale, three ingredients are required: a set of governing equations for the bulk behaviour with coupled magnetic and mechanical degrees of freedom, a dependency of the phase boundary velocity on the governing factors, and a reliable computational method. The expression for the phase boundary velocity is usually obtained within the continuum thermodynamics setting, where the entropy production due to phase boundary propagation is derived, which gives a thermodynamic driving force for the phase boundary kinetics. For deformable ferromagnets, all three elements (bulk behaviour, interface kinetics, and computational approaches) have been explored, but under a number of limitations. The present paper focuses on the derivation of the thermodynamic driving force for transformation fronts in a general magneto-mechanical setting, adapts the cut-finite-element method for transformation fronts in magneto-mechanics, which allows for an exceptionally efficient handling of the propagating interfaces, without modifying the finite-element mesh, and applies the developments to qualitative modelling of magneto-mechanics of magnetic shape-memory alloys.