Stress induced polarization switching and coupled hysteretic dynamics in ferroelectric materials

Abstract

The dynamic responses of ferroelectric materials upon external mechanical and electrical stimulations are inherently nonlinear and coupled. In the current paper, a macroscopic differential model is constructed for the coupled hysteretic dynamics via modeling the orientation switching induced in the materials. A non-convex potential energy is constructed with both mechanic and electric field contributions. The governing equations are formulated as nonlinear ordinary differential equations by employing the Euler-Lagrange equation, and can be easily recast into a state space form. Hysteresis loops associated with stress induced polarization switching and butterfly-shaped behavior in ferroelectric materials are also successfully captured. The effects of mechanical loadings on the electrically induced switching are numerically investigated, as well as the mechanically-induced switching with various bias electric fields.

Key words： differential model; state space; electromechanical switching; butterfly effects; hysteresis

Acknowledgements

L. X. Wang acknowledged the support from the National Natural Science Foundation of China (Grant No. 10872062), and the support by the open research fund of the State Key Laboratory of Fluid Power Transmission and Control (No. GZKF-201003).

References

1 Hall D A. Nonlinearity in piezoelectric materials. Journal of Materials Science, 2001, 36(19): 4575-4601

2 Yen H H, Shu Y C, Shieh J, Yeh J H.A study of electromechanical switching in ferroelectric single crystals. Journal of the Mechanics and Physics of Solids, 2008, 56(6): 2117-2135

3 Chen W, Lynch C S. A Micro-electro-mechanical model for polarization switching of ferroelectric materials. Acta Materialia, 1998, 46(15): 5303-5311

4 Ball B C, Smith R C, Kim S J, Seelecke S. A stress-dependent hysteresis model for ferroelectric materials. Journal of Intelligent Material Systems and Structures, 2006, 18(1): 69-88

5 Smith R C, Seelecke S, Dapino M, Ounaies Z. A unified framework for modeling hysteresis in ferroic materials. Journal of the Mechanics and Physics of Solids, 2006, 54(1): 46-85

6 Wang L X, Liu R, Melnik R V N. Modeling large reversible electric-field-induced strain in ferroelectric materials using 90° orientation switching. Science in China Series E: Technological Sciences, 2009, 52(1): 141-147

7 Wang L X. Hysteretic dynamics of ferroelectric materials under electromechanical loadings. In: Proceedings of SMASIS08 ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, 2008,

8 Brown S A, Hom C L, Massuda M, Prodey J D, Bridger K, Shankar N, Winzer S R. Electromechanical testing and modeling of a PbO₃-PbTiO₃-BaTiO₃ relaxor ferroelectric. Journal of the American Ceramic Society, 1996, 79(9): 2271-2282

9 Wang L X, Chen Y, Zhao W L. Macroscopic differential model for hysteresis and buttery-shaped behavior in ferroelectric materials, Advanced Materials Research, 2008, (47-50): 65-68

10 Wang L X, Melnik R. Control of coupled hysteretic dynamics of ferroelectric materials with a Landau-type differential model and feedback linearization. Smart Materials and Structures, 2009, 18(7): 074011

11 Falk F. Model free energy, mechanics, and thermomechanics of shape memory alloys. Acta Metallurgica, 1980, 28(12): 1773-1780