Identification of a multi-variate Preisach-based model, through the Everett Integral Formalism and ‘thermodynamic’ constraints

The paper presents a new paradigm to describe, from a macroscopic viewpoint, the magneto-elastic or piezo-electric and in principle the macroscopic behavior of a multi-functional material, i.e. a material where variables of different nature are coupled. The model has the important feature that fulfills a constraint that formally coincides to the Clausius-Duhem inequality and so is thermodynamic consistent and at the same time is quite general to be applied to several kinds of multi-functional materials (e.g. Piezo-electric or Magneto-elastic materials). The model is based on the simultaneous use of two hysteresis operators, i.e. the Preisach Operator and the Preisach Potential. Conversely to its apparent complex structure, the manuscript will show that the handling effort is reduced to the determination of the Everett integrals, through a usual procedure of identification, based on first order reversals.