Methods of calculating coupling coefficients for electrostrictive materials

Abstract

The definition of the coupling constant for piezoelectric ceramics is straightforward and depends directly on the square of the piezoelectric constant and inversely on the compliance and dielectric constants appropriate for the boundary conditions. However, these definitions are not directly applicable to electrostrictive materials because the material is nonlinear and therefore the equivalent piezoelectric and dielectric constants are not universally defined. Also, the presence of bias voltages about which the material would operate complicates the situation dramatically. In this presentation, energy methods [Hom et al., IEEE Trans. Sonics Ultrason. and Freq. Cont. UFFC-41, 541–545 (1994)] are used to calculate k33 for electrostrictive materials using several different constitutive models for the material. Experimental data on PMN taken at NUWC will be used to characterize the materials. The behavior of the electrostrictive coupling constants in the limit of small drive amplitudes about the bias voltage will be discussed. The effects of prestress, bias voltage, and drive level on the coupling coefficient will be examined for each model. The results will be compared with the equivalent piezoelectric definitions for k33.