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

A one-dimensional phenomenological model of hysteresis is presented. The model is suitable for application both to electrostrictive materials, such as lead magnesium niobate (PMN), and to magnetostrictive materials, such as Terfenol D. The concepts of ''inflation,'' ''field space,'' and the "reference 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 hysteretic model is deduced. Good agreement with the original (hysteretic) data-is seen. It is shown that, when a sample is driven by:a monofrequency electric field, the area of the polarization vs electric-field hysteresis loop is independent of-all harmonics in the polarization but. the first. A principle useful for understanding the shapes assumed by P-E and M-H hysteresis loops in general is described. [S0001-4966(99)03712-1].