Transformation front kinetics in deformable ferromagnets

TL;DR

This work develops a thermodynamically consistent framework for transformation-front kinetics in deformable ferromagnets, deriving the driving force for moving phase boundaries and their entropy production. It integrates Maxwell electromagnetism in a quasistatic setting with saturated magnetisation and magneto-mechanical coupling, then reduces to a coupled PDE system for displacement, magnetisation, and potential. A CutFEM-based computational approach enforces interface conditions weakly and robustly handles topology changes, enabling efficient resolution of moving transformation fronts via an interface-energy formulation. The framework is validated through 2D MSMAs simulations, demonstrating qualitative accuracy of twin-boundary kinetics under magnetic and mechanical loading, and the authors provide a public MATLAB implementation with topology-change capabilities.

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.

Figures (5)

• Figure 1: A schematic representation of coupled magneto-mechanics of MSMAs. Black arrows represent the orientation of magnetisation coinciding with the magnetic anisotropy axis.
• Figure 2: The numerical solution of the magnetic domain wall (left); dependence of the solution error (a) and the magnetisation length error (b) on the mesh size in the first example.
• Figure 3: The evolution of the phase boundaries in the stress-induced phase transition example.
• Figure 4: The phase boundary kinetics, the contour plot of the energy density, and the deformed shape of the free-standing sample consisting of domains with different orientation of the magnetocrystalline anisotropy (indicated by grey arrows).
• Figure 5: The phase boundary kinetics under application of tension, compression, vertical and horizontal magnetic fields.