The application of phase-field method in magnetoelastic functional materials

The phase-field method has become a powerful tool in materials science and engineering, providing a strong framework to understand phase transitions and microstructure evolution. By connecting atomic-scale phenomena to macroscopic behavior via mesoscale modeling, it has greatly enhanced our understanding of material processes. This paper presents micromagnetic microelastic phase-field modeling and explores recent applications of this approach in studying microstructural evolution and ultrasensitive magnetoelastic responses at phase boundaries in magnetoelastic functional materials, including magnetostrictive compounds and ferromagnetic shape memory alloys. The paper also discusses significant advances in phase-field modeling of magnetoelastic-electric coupling in multiferroic systems and magnetoelectric heterostructures. Finally, we identify key challenges and future directions for the phase-field method to advance the development of magnetoelastic functional materials.