The performance of piezoelectric materials under stress

The mechanics of coupled large field behavior of ferroelectric materials is discussed in this chapter. The models are multiaxial in both stress and electric field, and thus are suitable for implementation in finite element analysis. The material behavior is described in terms of fundamental behavior that takes place at multiple length scales from the atomic level to the macroscopic level. The crystal structure and an example of a lattice defect are introduced at the atomic scale. A simplified model of the unit cell behavior is introduced at the scale of tens of atoms. This leads to domain structures at the single crystal length scale and an explanation of compatibility issues across domain boundaries, phase boundaries, and grain boundaries. The macroscopic behavior is described as a volume average of the behavior at smaller length scales.