Dynamical hysteresis model of ferroelectric ceramics under electric field using fractional derivatives

This paper presents a model describing the hysteresis in ferroelectric materials at moderate to high driving levels and from quasi-static frequency to high dynamics. To a quasi-static model, based on a simple mechanism related to the dry-friction concept, is added a polarization fractional derivative term to take into account the dynamical effects through the ferroelectric material. The fractional derivative term allows us to describe slow dynamical variations for the hysteresis area (frequency) loop on a large frequency bandwidth. These variations cannot be described using the usual dynamical term (ρ · d P /d t ) physically linked to resistive damping. In the paper, an equivalent electrical circuit of the model is proposed. Finally, the new approach and the physical insights are developed and discussed. Large numbers of simulated behaviour are compared with experimental results on a typical soft PZT ferroelectric ceramic (type Navy II piezoelectric transducer ceramic).