Stress induced polarization switching and coupled hysteretic dynamics in ferroelectric materials
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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.