Electromechanical models of ferroelectric materials

Models of the electromechanical behaviour of ferroelectric materials are reviewed. Starting from the constitutive relationships for piezoelectrics and estimates of the response of piezoelectric composites, the development of models is traced from the macro-scale through to the micro-scale. Derivations of models based on extensions of classical plasticity and crystal plasticity theory are given, following the literature, and example applications of these models are shown. The formation of domain patterns is discussed and minimum energy methods based on the concept of compatibility are used to derive typical domain patterns for tetragonal and rhombohedral ferroelectrics. Methods for modelling the evolution of domain patterns are described. Finally the outlook for future directions in modelling of ferroelectrics is discussed