研究目的
To propose a non-isothermal phase-field model for piezo-ferroelectric materials that incorporates hysteresis phenomena and thermodynamic consistency.
研究成果
The paper presents two thermodynamically consistent models for non-isothermal phase-field descriptions of piezo-ferroelectric materials, capturing hysteresis effects through Ginzburg–Landau equations and dissipation mechanisms. The models provide a foundation for simulating electromechanical coupling and phase transitions, with potential applications in sensor and actuator design.
研究不足
The model assumes small displacement approximation and linearized elasticity. The inelastic deformation is directly related to polarization, which may be a simplification at macroscopic scales. Crystal anisotropy is handled in the first model but not in the second, and rate-independent hysteresis requires specific assumptions.
1：Experimental Design and Method Selection:
The methodology involves developing a phenomenological model based on the Ginzburg–Landau approach for phase transitions, incorporating energy balance equations and thermodynamic restrictions (Coleman–Noll procedure). Two models are proposed: one with a vector order parameter and another with a scalar order parameter and unit vector evolution.
2：Sample Selection and Data Sources:
No specific samples or datasets are mentioned; the study is theoretical and based on mathematical modeling.
3：List of Experimental Equipment and Materials:
No experimental equipment or materials are listed; the paper is purely theoretical.
4：Experimental Procedures and Operational Workflow:
The procedures involve deriving and solving differential equations (e.g., Ginzburg–Landau equations, energy balance) with boundary conditions, as summarized in Eq. (31). Numerical experiments, such as one-dimensional simulations, are mentioned but not detailed.
5：1). Numerical experiments, such as one-dimensional simulations, are mentioned but not detailed.
Data Analysis Methods:
5. Data Analysis Methods: Analysis is based on solving the derived equations and interpreting results, such as hysteresis loops from ODE solutions (e.g., Fig. 1).
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