✍ Scribed by Klinkel, S.
No coin nor oath required. For personal study only.
This paper represents a macroscopic constitutive law for domain switching e ects, which occur in piezoelectric ceramics. The thermodynamical framework of the law is based on two scalar valued functions: the Helmholtz free energy and a switching surface. In the general sense of a kinematic hardening process, the movement of the centre of the switching surface is controlled by internal variables. In common usage, these are the remanent polarization and the irreversible strain. The novel aspect of the present work is to introduce an irreversible electric ÿeld, which serves besides the irreversible strain as internal variable. The irreversible electric ÿeld has only theoretical meaning, but it makes the formulation very suitable for a ÿnite-element implementation, where displacement and the electric potential are the nodal degrees of freedom. The constitutive model successfully reproduces the ferroelastic and the ferroelectric hysteresis as well as the butter y hysteresis for piezoelectric ceramics. Furthermore, it accounts for the mechanical depolarization e ect, which occurs if the polarized piezoceramic is subjected to a compression stress.
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