An Inverted Preisach Model With Analytical Weight Function and Its Numerical Discrete Formulation

This paper proposes a numerical discrete formulation for an inverted hysteresis model, which is based on the classic Preisach model, but applies an inverted switch operator. The inverted switch operator is modified from the switch operator of the classic Preisach model. By applying this inverted switch operator, the inverted model retains the wiping-out and congruency properties. The distribution of the weight function can be approximated with an analytical function. By means of a quasi-Newton method algorithm, the small number of parameters in this function can be directly determined from major loops. Iterative procedure is circumvented in the implementation of this model in finite-element analysis. The simulated hysteresis loops, such as minor loops and reversal curves, show good agreement to the measurement data. To realize efficient numerical calculation, the integral expression of the inverted model is rewritten in a discrete form. The double integration of the weight function is numerically approximated in the precalculation stage. In this way, it costs low memory usage and short calculation time during the calculation procedure.