Finite Element Analysis for Nonlinear Time Dependent Response of Piezoelectric Materials

Piezoelectric materials show nonlinear response under high electric field. In addition, recent experiments showed that the electromechanical coupling coefficients of polarized piezoelectric materials, such as PZT ceramics, change with time, leading to history dependent and hysteretic responses in these materials. In this study, the coupling behavior of piezoelectric material under high electric field is investigated. The electromechanically coupled constitutive equation that accounts for history of mechanical loading and electric field is used for the piezoelectric materials. Effect of high electric field which causes nonlinearity in response of piezoelectric material is modeled by taking the material’s electromechanical coupling coefficients to be dependent on applied electric field and single time integration model is employed to incorporate history-dependent behavior. A continuum finite element with displacement and electric potential degrees of freedom that incorporates nonlinear history dependent effect is developed. Nonlinear finite element solver is formulated by using direct iteration method at element level and recursive iterative method at material (Gaussian) integration points. Nonlinear time-dependent finite element formulation is validated by comparing its response with experimental data on PZT ceramics. History dependent and nonlinear response of PZTs due to electric field and stress is discussed. Developed finite element is capable of modeling behavior of smart structures with piezoelectric sensors and actuators.