A three-dimensional nonlinear finite element formulation for ferroelectric materials is developed based on a principle of virtual work. The formulation includes the coupling of three physical fields, namely polarization field, electric field and strain field. The developed finite element formulation is employed to investigate the polarization distribution near a flaw in a ferroelectric single crystal under mechanical loadings. It is found that the polarization switching takes place near the flaw tip if the loadings exceed a critical value. In the simulation, we do not take any prior assumptions, i.e. without any switching criterion, on the polarization switching. The polarization switching is a result of the minimization of the total energy in the simulated system.
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A Nonlinear Multi-Field Coupling Finite Element Method for Polarization Switching in Ferroelectrics
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Wang, J, & Kamlah, M. "A Nonlinear Multi-Field Coupling Finite Element Method for Polarization Switching in Ferroelectrics." Proceedings of the ASME 2008 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Smart Materials, Adaptive Structures and Intelligent Systems, Volume 1. Ellicott City, Maryland, USA. October 28–30, 2008. pp. 173-179. ASME. https://doi.org/10.1115/SMASIS2008-324
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