An effective constitutive model for polycrystalline ferroelectric ceramics: Theoretical framework and numerical examples
We present an efficient, physics-based constitutive model for bulk polycrystalline ferroelectric ceramics, which links domain switching mechanisms and phase transitions at the microscale to the observed electro-thermo-mechanically coupled material response at the macroscale. In particular, a convexified energy density is formulated based on domain volume fractions and extended to polycrystals via the common Taylor assumption of uniform strains (alternative descriptions are discussed as well). The chosen kinetic relations admit to account for differences in 90°- and 180°-domain wall motion and rate effects. The model is applied to tetragonal barium titanate (BaTiO_3) and we present results for both material point calculations and finite element simulations, which demonstrate good qualitative agreement with experiments. We deliberately target bulk polycrystalline ferroelectrics in contrast to thin films that have been studied extensively.