Finite Element Modeling of Polarization Rotation Around an Elongated Elliptic Cavity

Electromechanical loading of piezoelectric devices with high electric field and mechanical stress concentrations near electrode and crack tips may lead to a localized inhomogeneous polarization switching response which is responsible for device degradation. We present an approximate constitutive law for polarization rotation of fully poled materials in load cases which do not initiate depolarization of the material. In other words, the local poling direction is changed but the material remains poled to saturation. The structure of the constitutive law resembles incremental plasticity theory: The “yield surface” is postulated, based on an energy criterion for 90°-switching of the randomly oriented crystallites in a material point, and the energy barrier of polarization switching corresponds to the yield stress. The constitutive model is implemented into the finite element code PSU and validated for the plane sample problem of an elongated elliptic cavity in a ferroelectric material. Some implications for crack shielding models are discussed.