On babuška's model for asymmetric hysteresis

Hysteresis is a complex phenomenon that occurs in many areas of science and engineering. To model hysteresis, scientists combine first laws of physics with fictitious equations to obtain phenomenological models that aim to match the macroscopic behavior of hysteresis processes. In this paper we focus on a model of hysteresis that was proposed by the physicist P. Duhem starting from thermodynamical considerations. On the one hand, we strengthen the results obtained by the mathematician I. Babuška in relation with the existence and uniqueness of a global solutions and of a periodic solution when the input is periodic. On the other hand, we specialize into a specific form of the Duhem model proposed by Babuška. For Babuška’s model we determine the explicit analytic expression of the hysteresis loop. We apply our findings to dry friction modeling and to asymmetric hysteresis loop matching.Peer ReviewedPostprint (author's final draft