Nonlinear finite element modeling of polycrystalline ferroelectrics based on constrained domain switching

A review of the nonlinear finite element formulations for ferroelectrics shows that instability related to domain switching may arise in formulations using a phenomenological constitutive model or micromechanical domain switching criterion. To overcome the instability problems and to predict the experimentally observed incomplete non-180° switching in ferroelectrics, a constrained domain switching model for polycrystalline ferroelectrics is proposed in this paper and implemented in a finite element code. In the proposed model, a ferroelectric polycrystalline is made up of numerous random oriented grains, each of which contains multi-domains and is represented by a finite element. Charge screening effect in real ferroelectrics is also taken into account in the model, thus 180° domain switching is not constrained. While the internal stress induced by non-180° switching cannot be compensated in a similar manner and is considered naturally by the finite element method. The fraction of non-180° switching in each grain is obtained through a dichotomy approximation. Selected numerical results show that during electrical poling, 180° switching is usually complete while 90° switching is only about 2% for both BaTiO3 and tetragonal PZT ceramics, which agree well with the experimental results.