Nonlinear finite element analysis of piezoelectric transducers

In this paper a newly developed finite element method (FEM) is presented, which allows the numerical simulation of the nonlinear behavior of piezoelectric materials. Since both, material as well as geometric nonlinearities are taken into account, full large-signal analysis of the piezoelectric effect is provided. In the implemented constitutive model, the mechanical, piezoelectric, and dielectric tensor elements may depend in a multifunctional way on the current states of the mechanical stresses and the electric field. Therewith, measured material data can be directly used as input for the numerical simulations. In the case of geometric nonlinearities, both large displacements and strains can be modeled. As a practical application, the electric input impedance of an ultrasonic transducer being subjected to mechanical and electric prestressing is considered. Comparisons of simulated and measured resonance frequency shifts due to the nonlinear dependency of the material coefficients on the electric field as well as mechanical stress is presented.