One-dimensional phenomenological model of hysteresis. I. Development of the model

A one-dimensional phenomenological model of hysteresis is presented. The mo del is suitable for application both to electrostrictive materials, such as lead magnesium niobate (PMN), and to magnetostrictive materials, such as T erfenol D. The concepts of ''inflation,'' ''field space,'' and the "referen ce ellipse" are introduced as suitable mechanisms for transforming measured hysteretic data into corresponding anhysteretic versions. An anhysteretic model is then fitted (in the least-squares sense) to the transformed data. By applying the inverse transforms to the fitted anhysteretic model, a hyst eretic model is deduced. Good agreement with the original (hysteretic) data -is seen. It is shown that, when a sample is driven by:a monofrequency elec tric field, the area of the polarization vs electric-field hysteresis loop is independent of-all harmonics in the polarization but. the first. A princ iple useful for understanding the shapes assumed by P-E and M-H hysteresis loops in general is described. [S0001-4966(99)03712-1].