Finite element modeling of PMN electrostrictive materials and application to the design of transducers

New electrostrictive lead magnesium niobate ceramics (PMN) are promising materials for realizing actuators or high power transducers for macrosonics or underwater acoustics. Because of their large dielectric permittivity, PMN materials have strains roughly an order of magnitude larger than those of the lead titanate zirconate (PZT) ceramics, However, the use of PMN as active material in actuators or transducers presents some difficulties: highly nonlinear properties, temperature and frequency dependence of dielectric permittivity and DC bias field are needed. To help in the design of PMN-based transducers, a numerical modeling capability is needed. In this paper, the development of electrostrictive finite elements for nonlinear static and time-domain analyses is presented. The model, valid at constant temperature, includes electrostriction and polarization saturation and excludes hysteresis. The validity of the model is demonstrated by comparing computed strain and charge density with measurements for a PMN bar at various electric DC fields and mechanical prestresses. Coupling coefficients are predicted from dynamic responses of the transducer to applied voltage and charge steps. Finally, the finite element modeling is used to design a Langevin-type electrostrictive transducer.