Phenomenological Modeling for Large-Signal Behavior of Ferroelectric Materials

Abstract

This chapter primarily deals with Preisach hysteresis modeling, which represents a phenomenological modeling approach for the large-signal behavior of ferroelectric materials. Before we study in Sect. 6.3 alternative phenomenological modeling approaches that also focus on the macroscopic transfer behavior of ferroelectric materials, hysteresis will be mathematically defined. Moreover, an overview of material models on different length scales (e.g., atomistic scale) is given in Sect. 6.2. Contrary to phenomenological modeling approaches, those material models aim at describing the physical behavior of ferroelectric as accurate as possible. In Sect. 6.4, we will introduce the classical Preisach hysteresis operator \(\mathcal {H}_\text {P}\), which comprises weighted elementary switching operators. Section 6.5 details different weighting procedures for the elementary switching operators. Because the classical Preisach hysteresis operator is only suitable to a limited extent for predicting hysteretic behavior of ferroelectric actuators in practical applications, a so-called generalized Preisach hysteresis model (operator \(\mathcal {H}_\text {G}\)) will be introduced in Sect. 6.6. This extended Preisach hysteresis model enables, e.g., the consideration of asymmetric behavior in hysteresis curves. After that, a parameter identification strategy is presented which allows reliable predictions of electrical and mechanical quantities through Preisach hysteresis modeling. To apply Preisach hysteresis modeling in practical applications of ferroelectric actuators (e.g., in high precision positioning systems), it is of utmost importance to invert the Preisach hysteresis operator. Owing to this fact, Sect. 6.8 finally addresses an iterative inversion procedure, which enables efficient determinations of the aimed electrical excitation signals in a reasonable time.