Constitutive equations for 0-3 polarized PLZT actuators

This article presents constitutive equations of transparent lead lanthanum zirconate titanate (PLZT) materials poling along thickness direction or with 0-3 polarization. Discussed first are the Beer’s law of light transmission in transparent solid and the photovoltaic current density in PLZT materials. Formulas for field strength and electrical potential between two electrodes of a PLZT wafer are then derived from the basic photovoltaic equations. By superposing the photovoltaic and the converse piezoelectric effects, we formulate a novel expression for photo-induced strain that is nonlinearly dependent of incident light intensity and varies with light penetration depth in through-thickness direction. On the basis of the derived photo-induced strain, linear and nonlinear constitutive equations of 0-3 polarized PLZT actuators are formulated. The present model is validated by using the available experimental data in the literature. By using the present model with an exponential variation of strain through the thickness, closed-form solutions for the equivalent loads acting on a PLZT unimorph, bimorph and intelligent beam are obtained and then compared with numerical results available in the literature.