基于相场法的铁电材料柔电应变梯度有限元模型

IF 2 3区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY
Shuai Wang, Hengchang Su, Min Yi, Li-Hua Shao
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引用次数: 0

摘要

挠电效应是应变梯度和电场之间的双向耦合效应,存在于所有电介质中,与点群对称性无关。然而,应变梯度涉及的高阶位移导数给解决包含挠电效应的机电耦合问题带来了挑战。在本研究中,我们建立了一个考虑到挠电效应的铁电材料相场模型。在不引入高阶形状函数的情况下,构建了具有 20 个自由度的四节点四边形元素。畴的微观结构演变由一个独立的阶次参数来描述,即受时变金兹堡-朗道理论支配的自发极化。该模型基于热力学框架开发,其中引入了一组微力来构建构成关系和演化方程。对于电焓的柔电部分,应变梯度是通过等参数空间中高斯积分点的值对节点处的机械应变进行内插而确定的。结果表明,该模型能够再现包含挠电贡献的介电材料经典分析解。通过复制圆柱管和截顶金字塔中一些典型的挠电现象,对模型进行了验证。对介电材料和铁电材料中的极化分布进行了比较。该模型可以再现圆柱形挠性电管的边界值问题解,并演示了铁电中考虑挠电效应的畴壁扭曲现象。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Strain Gradient Finite Element Formulation of Flexoelectricity in Ferroelectric Material Based on Phase-Field Method

Strain Gradient Finite Element Formulation of Flexoelectricity in Ferroelectric Material Based on Phase-Field Method

Strain Gradient Finite Element Formulation of Flexoelectricity in Ferroelectric Material Based on Phase-Field Method

Flexoelectricity is a two-way coupling effect between the strain gradient and electric field that exists in all dielectrics, regardless of point group symmetry. However, the high-order derivatives of displacements involved in the strain gradient pose challenges in solving electromechanical coupling problems incorporating the flexoelectric effect. In this study, we formulate a phase-field model for ferroelectric materials considering the flexoelectric effect. A four-node quadrilateral element with 20 degrees of freedom is constructed without introducing high-order shape functions. The microstructure evolution of domains is described by an independent order parameter, namely the spontaneous polarization governed by the time-dependent Ginzburg–Landau theory. The model is developed based on a thermodynamic framework, in which a set of microforces is introduced to construct the constitutive relation and evolution equation. For the flexoelectric part of electric enthalpy, the strain gradient is determined by interpolating the mechanical strain at the node via the values of Gaussian integration points in the isoparametric space. The model is shown to be capable of reproducing the classic analytical solution of dielectric materials incorporating the flexoelectric contribution. The model is verified by duplicating some typical phenomena in flexoelectricity in cylindrical tubes and truncated pyramids. A comparison is made between the polarization distribution in dielectrics and ferroelectrics. The model can reproduce the solution to the boundary value problem of the cylindrical flexoelectric tube, and demonstrate domain twisting at domain walls in ferroelectrics considering the flexoelectric effect.

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来源期刊
Acta Mechanica Solida Sinica
Acta Mechanica Solida Sinica 物理-材料科学:综合
CiteScore
3.80
自引率
9.10%
发文量
1088
审稿时长
9 months
期刊介绍: Acta Mechanica Solida Sinica aims to become the best journal of solid mechanics in China and a worldwide well-known one in the field of mechanics, by providing original, perspective and even breakthrough theories and methods for the research on solid mechanics. The Journal is devoted to the publication of research papers in English in all fields of solid-state mechanics and its related disciplines in science, technology and engineering, with a balanced coverage on analytical, experimental, numerical and applied investigations. Articles, Short Communications, Discussions on previously published papers, and invitation-based Reviews are published bimonthly. The maximum length of an article is 30 pages, including equations, figures and tables
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