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

Shuai Wang ¹Hengchang Su ¹Min Yi ²Li-Hua Shao¹

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作者信息

1. National Key Laboratory of Strength and Structural Integrity,Institute of Solid Mechanics,School of Aeronautic Science and Engineering,Beihang University,Beijing 100191,People's Republic of China
2. State Key Laboratory of Mechanics and Control for Aerospace Structures and Institute for Frontier Science and Key Laboratory for Intelligent Nano Materials and Devices of Ministry of Education and College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,People's Republic of China
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Abstract

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.

Key words

Flexoelectricity/Phase-field method/Ferroelectrics/Domain configuration

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基金项目

National Natural Science Foundation of China(12272020)

Beijing Natural Science Foundation(JQ21001)

Fundamental Research Funds for the Central Universities(YWF-23-SDHK-L-019)

National Natural Science Foundation of China(12302134)

National Natural Science Foundation of China(12272173)

National Natural Science Foundation of China(11902150)

High-Performance Computing Platform of Beihang University()

出版年

2024

固体力学学报(英文版)

中国力学学会

固体力学学报(英文版)

影响因子：0.214

ISSN：0894-9166

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