Nonlinear piezoelectric material properties and non-uniform poling in a flexible electro-active composite finite element model

Active Fiber Composites (AFCs) are piezoelectric devices comprised of long cylindrical fibers, typically made of ceramic lead zirconate titanate (PZT), embedded in an epoxy polymer. AFCs use interdigitated electrodes to produce electric field lines parallel to the fibers (33-mode) rather than across the diameter, exploiting the stronger out-of-plane electromechanical coupling. Nonlinear piezoelectric and dielectric terms and nonuniform poling are often neglected in modeling AFCs due to the added complexity, however including the terms improves accuracy for strong electric fields and where the electrode geometry causes non-uniform electric fields. For that reason, a new finite element model of the AFC is developed which includes the effect of nonlinearities in piezoelectric strain constants and electric permittivity due to a non-uniform applied electric field resulting from two sets of interdigitated electrodes. The methods used to apply the nonlinear constitutive equations and poling are described. A comparison of the AFC response with linear and nonlinear material properties, with non-uniform poling, is shown for increasing applied electric fields. The difference in AFC response illustrates the necessity to include Rayleigh Law terms and non-uniform poling in the model.