ABSTRACT

A continuum constitutive model for PbTiO₃ has been obtained from an effective Hamiltonian which was constructed from ab initio calculations. This model contains the nonlinearities necessary for switching from the ground-state tetragonal phase to the metastable rhombohedral and orthorhombic phases. The constitutive model was incorporated into a finite element formulation in order to study the large length-scale electro-mechanical response of this piezoelectric material. We use this approach to study the hysteresis of single-crystal PbTiO₃ as a function of applied electric field and temperature and we analyze the microscopic mechanisms responsible for polarization switching. The model successfully reproduces the qualitative features of a high-strain actuator recently proposed and tested experimentally.