Efficient magnetic hysteresis model for field and stress application in magnetostrictive Galfenol

We present a discrete energy-averaged model for the nonlinear and hysteretic relation of magnetization and strain to magnetic field and stress. Analytic expressions from energy minimization describe three-dimensional rotations of domains about easy crystal directions in regions where domain rotation is the dominant process and provide a means for direct calculation of magnetic anisotropy constants. The anhysteretic material behavior due to the combined effect of domain rotation and domain wall motion is described with an energy weighted average while the hysteretic material behavior is described with an evolution equation for the domain volume fractions. As a result of using a finite set of locally defined energy expressions rather than a single globally defined expression, the model is 100 times faster than previous energy weighting models and is accurate for materials with any magnetocrystalline anisotropy. The model is used to interpret magnetization and strain measurements of << 100 >> oriented Fe79.1Ga20.9 and Fe81.5Ga18.5 as well as << 110 >> oriented Fe81.6Ga18.4.