Modeling and Analysis of Butterfly Loops via Preisach Operators and its Application in a Piezoelectric Material

We present modeling and analysis of the so-called butterfly hysteresis behavior, based on the use of the Preisach operator. The desired butterfly loop properties can be obtained under some mild conditions on the weighting function that defines the Preisach operator. The proposed framework is used to model the electric-field dependence of the strain in a piezoelectric material purposely designed to exhibit asymmetric butterfly loops with remnant deformation.