Finite element analysis of ferroelectric hysteresis effects in piezoelectric transducers

The acoustic output power of piezoelectric actuators, such as high intensity focused ultrasound transducers used in medical therapy, is more and more increasing. Thus, the nonlinear material behavior of piezoelectric ceramics has to be considered during the design process and, therewith, the need for an appropriate modeling tool arises. In this paper an extension of a recently developed numerical calculation scheme, allowing the precise simulation of the nonlinear behavior of piezoceramic actuators, is presented. The inclusion of a macroscopic ferroelectric hysteresis model in the numerical calculation scheme offers the great advantage to consider changes in the state of electric polarization. Therewith, the nonlinear dependencies of the material parameter on the electric field strength and the mechanical stresses as well as the changes in polarization due to the loading history can be computed.