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首页> 外文期刊>International Journal of Solids and Structures >An invariant formulation for phase field models in ferroelectrics
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An invariant formulation for phase field models in ferroelectrics

机译：铁电相场模型的不变公式

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摘要

This paper introduces an electro-mechanically coupled phase field model for ferroelectric domain evolution based on an invariant formulation for transversely isotropic piezoelectric material behavior. The thermodynamic framework rests upon Gurtin’s notion of a micro-force system in conjunction with an associated micro-force balance. This leads to a formulation of the second law, from which a generalized Ginzburg–Landau evolution equation is derived. The invariant formulation of the thermodynamic potential provides a consistent way to obtain the order parameter dependent elastic stiffness, piezoelectric, and dielectric tensor. The model is reduced to 2d and implemented into a finite element framework. The material constants used in the simulations are adapted to meet the thermodynamic condition of a vanishing micro-force. It is found that the thermodynamic potential taken from the literature has to be extended in order to avoid a loss of positive definiteness of the stiffness and the dielectric tensor. The small-signal response is investigated in the presence and in the absence of the additional regularizing terms in the potential. The simulations show the pathological behavior of the model in case these terms are not taken into account. The paper closes with microstructure simulations concerning a ferroelectric nanodot subjected to an electric field, a cracked single crystal, and a ferroelectric bi-crystal.
机译：本文基于横向各向同性压电材料行为的不变公式，介绍了一种用于铁电畴演化的机电耦合相场模型。热力学框架基于Gurtin的微力系统概念以及相关的微力平衡。这导致了第二定律的制定，从中得出了广义的Ginzburg-Landau演化方程。热力学势的不变公式提供了一种获得依赖于阶次参数的弹性刚度，压电和介电张量的一致方法。该模型被简化为2d，并实现为有限元框架。模拟中使用的材料常数适合于消失的微力的热力学条件。已经发现，必须扩展从文献中获得的热力学势，以避免损失刚度和介电张量的正定性。在存在和不存在潜在的其他正则项的情况下研究小信号响应。仿真显示了在不考虑这些术语的情况下模型的病理行为。本文以微观结构模拟作为结尾，该模拟涉及受电场作用的铁电纳米点，破裂的单晶和铁电双晶。

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