Nonlinear time‐domain analysis of electrostrictive materials by the finite element method

Lead magnesium niobate ceramics (PMN) are promising materials for applications in the field of underwater acoustic projectors. A finite element procedure has been developed in the ATILA code to model the static deformation of these materialss [J. C. Debus et al., J. Acoust. Soc. Am. 100, 2584(A) (1996)]. Two different elements are available according to whether or not the saturation of polarization is included. An extension of this model to nonlinear transient analysis is presented in this paper. The procedure is derived for time stepping by finite difference, using a central difference scheme. This new capability is demonstrated by analyzing the transient response of an electrostrictive bar submitted to different electrical excitations (voltage step, charge step, continuous sine). The validation of the model is carried out by comparing the results obtained with the analytical results for a lumped constants model. The validity of commonly used transducer characteristics is discussed to describe electrostr...