Nonlinear piezoelectric constitutive relationship and actuation for piezoelectric laminates

A piezoelectric constitutive model is developed to address nonlinear electromechanical coupling. Taking into account the polarization versus electric field hysteresis, a new form of elastic Gibbs energy is proposed to capture the variation of butterfly shaped loop between induced strains and applied electric field. With the introduction of a new material constant, an explicit formulation governing the nonlinear constitutive relationship is obtained by using saturation polarization, remnant polarization, coercive electric field and linear piezoelectric coefficients. The developed nonlinear constitutive relations are applicable in the case of high stroke actuation utilizing the largest possible strain available in piezoceramics. Experiments are conducted to verify the developed model. The nonlinear coupling between the mechanical and the electrical fields obtained using the current constitutive relationship are correlated with experimental results. The present model is then used in the analysis of a cantilevered plate with surface-bonded piezoelectric actuators. To capture transverse shear effects of piezoelectric laminates and nonuniform distribution of electrical field, higher order descriptions of displacement field and electrical potential are used. Incremental variational principle is employed to address the two-way electromechanical interactions. Both direct and converse piezoelectric effects are considered. The nonlinear effects of hysteresis on structural deformation are investigated both numerically and experimentally.