Micro-electromechanically Informed Phenomenological Constitutive Models for Ferroelectrics

Accurate phenomenological constitutive laws for ferroelectric ceramics that can be rapidly integrated are required for finite element models aiming to resolve the complex fields in ferroelectric devices. At best, phenomenological theories can provide a framework within which thermodynamic restrictions are satisfied and undetermined functions exist for “fitting” material behavior. The ultimate challenge in deriving a final constitutive law is to capture the physics of the material deformation and polarization processes within these undetermined functions. A number of microelectromechanical models exist in the literature. These models are based on domain switching events at the domain/grain level and then are generalized to polycrystalline behavior by averaging over many different domain/grain orientations. In this work it will be shown how information obtained from these micro-electromechanical models can be incorporated directly into the undetermined functions of a phenomenological theory.