Two dimensional hysteresis model

A model is presented that may be used to describe the magnetic behavior of biaxial material in the form of a polycrystalline sheet. Crystallite or grain easy directions are distributed within the plane either randomly, to model non-oriented material, or according to a Gaussian distribution of angles for a cube-oriented sheet. Switching energies of the grains are distributed in a way that reduces to the Preisach model in the one dimensional case. As the applied field H is changed, the magnetizations of representative grains are adjusted by switching to the neighborhood of easy axes close to the field direction and/or rotating to achieve torque balance. The total magnetization is then obtained by adding the contributions of these grains in appropriate proportions. Numerical calculations of B-H loops and both alternating and rotational hysteresis loss indicate that the method is able to replicate observed behavior.