Phase-Field simulation of ferroelectric domains with material inhomogeneity – A finite element approach

• Main Authors: Kai-Yang Wang, 王凱陽
• Other Authors: Yi-Chung Shu
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/76462036615145212075

碩士 === 國立臺灣大學 === 應用力學研究所 === 101 === The thesis aims to develop numerical algorithms implemented in COMSOL finite element software for phase-field simulations. The conventional phase-field simulations adopt algorithms based on the fast Fourier transform. However, such a method is not suitable for the case with material inhomogeneity. Instead, the algorithms developed here are suitable for both cases with material homogeneity and inhomogeneity. In addition, the algorithms based on COMSOL are much simpler than those implemented in programming languages. The framework is based on the equivalent phase-field models developed by the previous team efforts. It is established by involving the spirit of Eshelby equivalent principle and Hashin-Shtrikman variational formulation. The results are first validated by simulating microstructure patterns in martensitic thin films. Next, the developed algorithms are extended to the case of tetragonal and rhombohedral ferroelectric domain simulations. The results show that many more electromechanical self-accommodation patterns as well as engineered domains are simulated and are consistent with experimental observations. Finally, the effective constants of several engineered domains are calculated and compared with those based on micromechanics calculations.