A new form of rate independence for hysteresis systems

Abstract

In mathematical texts hysteresis is defined as a rate independent phenomenon, and many mathematical models of hysteresis exhibit this rate independence property. However, experiments suggest that this property is only an approximation of the hysteresis behaviour when the excitation is slow enough. Using a generalized form of the hysteretic Duhem model, we show that, although this model is not rate independent, it still satisfies a new form of rate independence. We also explore the relationship between this new form and the usual property of rate independence.