Date: 05 Nov 2013

Mathematical Models of Hysteresis

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This chapter offers an overview of the hysteresis models that will be used throughout the book. After a short general classification of hysteresis models and parameter identification methods, the rectangular hysteresis operator is introduced. Then, the chapter focuses on summarizing the main equations, properties, and characteristics of the Preisach, energetic, Jiles-Atherton, Coleman-Hodgdon, and Bouc-Wen models. Particular attention is given to the analytical description of the general properties of hysteresis curves such as differential susceptibilities, remanence, coercivity, saturation, anhysteretic curve, energy lost, stability, accommodation, and limit cycle for each model. The second part of the chapter presents two techniques for the modeling of rate-dependent hysteresis, one based on the feedback (effective field) theory and the other one on the relaxation time approximation. Finally, a unified theory of vector models is presented; this theory can be applied to generalize any scalar model of hysteresis to vector systems.