Non-linear modelling of multilayer piezoelectric actuators in non-trivial configurations based on actuator design parameters and piezoelectric material properties

Current models of non-linear electromechanical behaviours of piezoactuators are mostly intended for actuator configurations where the strain of the piezoelectric material is directly used as the linear output. On the other hand, in the design of piezoactuators, there exist non-trivial configurations where the internal strains of the piezoelectric materials manifest externally in the form of bending and curving rather than simple elongation or contraction, it is also important to predict the non-linear performance of the actuator based on the design parameters. Therefore, it is the intent of this article to present a model that enables calculation of the quasi-static mechanical response of piezoelectric multilayer actuators in non-trivial configurations. It is based on the polarization hysteresis loop and butterfly curve of its constituent piezoelectric material. Using an energy-based formulation, the model takes into account the non-piezoelectric sections as well as the mechanical boundary conditions of the actuator. Furthermore, a three-layer lead zirconium titanate bimorph with both ends clamped is considered in this study. Model calculation of its relationship between input voltage V and midpoint vertical displacement X is carried out based on ferroelectric hysteresis data of the bimorph material from the literature. The calculation results are then validated by measurements.