A phenomenological mathematical model of hysteresis

Abstract

This paper starts with the description of a purely mathematical model of the saturation curve and the hysteresis loop based on the fundamental similarities between the Langevin function the specified T(x) function and the sigmoid shape. The T(x) function which is composed of tangent hyperbolic and linear functions with its free parameters can describe the regular anhysteretic magnetisation curve. Developed from this function the model describes not only the regular hysteresis loop but also the biased and other minor loops like the ones produced by the interrupted and reversed magnetisation process and the open “loops” created by a piecewise monotonic magnetising field input of diminishing amplitude. The remanent magnetism as the function of the interrupted field co‐ordinates is predicted by the model in this mathematical form for the first time. The model presented here is based on the principle that all processes follow the shape of the T(x) function describing the shape of the major hysteresis loop of the ferromagnetic specimen under investigation. The model is also applicable to hysteretic processes in other fields.