Magnetoelastic modeling of magnetization rotation and variant rearrangement in ferromagnetic shape memory alloys

A magnetoelastic model is developed to study the domain structure evolution of ferromagnetic shape memory alloys (FSMAs), where both variant rearrangement and magnetization rotation are considered. A multi-rank laminated domain configuration is constructed first under the constrained theory, which is then relaxed by allowing the magnetization to rotate away from its easy axis, resulting in incompatibility in both magnetization and magnetostrictive strain. The internal magnetoelastic field is then analyzed using a hierarchical lamination theory, where the stress and magnetic field in the multi-rank laminate induced by incompatibility at two distinct length scales are evaluated. Microscopic variation of magnetization is evaluated on a unit cell using periodic boundary condition, while mesoscopic variation is evaluated on the specimen using averaged magnetization and actual boundary condition, utilizing a recently developed nonlinear homogenization theory of ferroelectrics. The minimization of the energy functional is carried out using Matlab optimization toolbox, allowing us to study the process of variant rearrangement and magnetization rotation under the combined magnetomechanical loading. It is observed that microstructure evolution of FSMA is dominated by rearrangement of variants when the applied stress is small, but such rearrangement is prohibited when the applied stress is relatively large, under which magnetization rotation takes over as the dominant mechanism for microstructure evolution. When the energy dissipation is considered through twinning stress, excellent agreement between the model and experiments is observed. The critical stress beyond which variant rearrangement is disfavored is also estimated in good agreement with experiment.