A simple constitutive model for temperature dependent behavior of ferroelectric materials is developed. This model is based on the one-dimensional phase transformation model of shape memory alloys. To model the temperature dependent behavior of the ferroelectric materials, a paraelectric phase is considered in addition to four ferroelectric variants in a ferroelectric phase. These ferroelectric variants are connected in series to each other, whereas the paraelectric phase is connected in parallel to the ferroelectric phase. The internal stress is induced in the material due to this parallel connection, which increases or decreases the driving energy for the switching depending on the switching direction. As the temperature increases up to the Curie temperature, the volume fraction of the paraelectric phase is assumed to increase and the required switching energy is assumed to decrease as observed in experiments. The temperature dependence of the relationships among the electric field, electric displacement, stress, and strain are simulated and compared with published experimental data for a soft PZT. The comparison indicates that the present constitutive model can predict the temperature dependent behavior well. This implies that the proposed model can provide a convenient tool to understand the physical mechanism of the ferroelectric materials and to design smart structures containing the ferroelectric materials.

Date Published: 31 March 2009
PDF: 9 pages
Proc. SPIE 7289, Behavior and Mechanics of Multifunctional Materials and Composites 2009, 72890J (31 March 2009); doi: 10.1117/12.815180

Published in SPIE Proceedings Vol. 7289:
Behavior and Mechanics of Multifunctional Materials and Composites 2009
Zoubeida Ounaies; Jiangyu Li, Editor(s)