Simulation of precipitate hardening in ferroelectric material

Precipitate hardening is introduced as a mechanism to tune the reaction of ferroelectric materials to the application of an external electric field. For this purpose, a phase field model for polarization in ferroelectric material is presented in this paper. Different materials with and without precipitates are simulated and the respective hysteresis curves for charge and macroscopic strain are derived. The results show a reduction of the hysteresis curves if precipitates are present in the material, which confirms the experimental observation of recent material studies.