A FSDT—MITC Piezoelectric Shell Finite Element with Ferroelectric Non-linearity

A shell finite element based on the Reissner/Mindlin first-order shear deformation theory and integrating a bi-dimensional phenomenological ferroelectric constitutive law for domain switching effects is proposed. An electric switching function is considered to indicate the onset of domain switching. Only one internal variable (the remanent polarization) is used in the model. An implicit integration technique based on the return-mapping algorithm is adopted. The shell element is implemented into the commercial finite element code Abaqus ® via the subroutine user element. Some linear (piezoelectric) and non-linear (ferroelectric) tests are considered to validate first, the element formulation and second, the implementation of the bi-dimensional ferroelectric model. It is shown by studying a complex example (the spiral actuator) that the Reissner/Mindlin kinematic hypothesis (no variation of the displacement across the thickness or no thickness variation) is not sufficient for some electromechanical applications for which the d33 effect is of major importance.