Simulations of domain switching in ferroelectrics by a three-dimensional finite element model

Li, Faxin; Fang, Daining

doi:10.1016/j.mechmat.2003.01.001

Cited by 67 publications

(37 citation statements)

References 18 publications

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“…The finite element formulation of Li and Fang [55] is employed in this paper. The displacement and electric potential are taken to be the nodal degrees of freedom in the present finite element method.…”

Section: Finite Element Formulationmentioning

confidence: 99%

“…Landis [54] developed a new finite element formulation, the vector potential formulation which uses a charge based potential as the independent variable. Li and Fang [55] carried out 3D finite element simulations on ferroelectric materials. Kim and Jiang [56] and Arockiarajan et al [57] also developed a 3D finite element model for rate-dependent behavior of ferroelectric ceramics.…”

Section: Introductionmentioning

confidence: 99%

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Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

Liu

Wang

2008

Acta Mech

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Summary. Many experimental observations have shown that a single domain in a ferroelectric material switches by progressive movement of domain walls, driven by a combination of electric field and stress. The mechanism of the domain switch involves the following steps: initially, the domain has a uniform spontaneous polarization; new domains with the reverse polarization direction nucleate, mainly at the surface, and grow though the crystal thickness; the new domain expands sideways as a new domain continues to form; finally, the domain switch coalesces to complete the polarization reversal. According to this mechanism, the volume fraction of the domain switching is introduced in the constitutive law of the ferroelectric material and used to study the nonlinear constitutive behavior of a ferroelectric body in this paper. The principle of stationary total potential energy is put forward in which the basic unknown quantities are the displacement u i , electric displacement D i and volume fraction q I of the domain switching for the variant I. The mechanical field equation and a new domain switching criterion are obtained from the principle of stationary total potential energy. The domain switching criterion proposed in this paper is an expansion and development of the energy criterion established by Hwang et al. [1]. Based on the domain switching criterion, a set of linear algebraic equations for determining the volume fraction q I of domain switching is obtained, in which the coefficients of the linear algebraic equations only contain the unknown strain and electric fields. If the volume fraction q I of domain switching for each domain is prescribed, the unknown displacement and electric potential can be obtained based on the conventional finite element procedure. It is assumed that a domain switches if the reduction in potential energy exceeds a critical energy barrier. According to the experimental results, the energy barrier will strengthen when the volume fraction of the domain switching increases. The external mechanical and electric loads are increased step by step. The volume fraction q I of domain switching for each element obtained from the last loading step is used as input to the constitutive equations. Then the strain and electric fields are calculated based on the conventional finite element procedure. The finite element analysis is carried out on the specimens subjected to uniaxial coupling stress and electric field. Numerical results and available experimental data are compared and discussed. The present theoretic prediction agrees reasonably with the experimental results.

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Section: Finite Element Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

Liu

Wang

2008

Acta Mech

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“…The new basic equations for ferroelectrics can overcome the difficulty in the current finite element analysis for ferroelectrics. The good calculation results have been obtained for ferroelectrics using the new basic equations [36,[41][42][43].…”

Section: Introductionmentioning

confidence: 96%

“…According to the above theories and models, some researchers have simulated the electromechanical coupled nonlinear behavior of ferroelectrics by the finite element method which generally implements the displacement and electric potential as the basic nodal variables [35][36][37][38][39][40][41][42][43]. In the solution of the finite element formalization, the researchers have found that the equivalent nodal load produced by spontaneous polarization is large enough to cause illogical simulated results [36,[41][42][43].…”

Section: Introductionmentioning

confidence: 99%

“…In the solution of the finite element formalization, the researchers have found that the equivalent nodal load produced by spontaneous polarization is large enough to cause illogical simulated results [36,[41][42][43]. In order to accomplish the calculation and obtain good simulated results, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization [36,[41][42][43].…”

Section: Introductionmentioning

confidence: 99%

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Energy functions and basic equations for ferroelectrics

Wang

2008

Acta Mech

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Energy functions (or characteristic functions) and basic equations for ferroelectrics in use today are given by those for ordinary dielectrics in the physical and mechanical communications. Based on these basic equations and energy functions, the finite element computation of the nonlinear behavior of the ferroelectrics has been carried out by several research groups. However, it is difficult to process the finite element computation further after domain switching, and the computation results are remarkably deviating from the experimental results. For the crack problem, the iterative solution of the finite element calculation could not converge and the solutions for fields near the crack tip oscillate. In order to finish the calculation smoothly, the finite element formulation should be modified to neglect the equivalent nodal load produced by spontaneous polarization gradient. Meanwhile, certain energy functions for ferroelectrics in use today are not compatible with the constitutive equations of ferroelectrics and need to be modified. This paper proposes a set of new formulae of the energy functions for ferroelectrics. With regard to the new formulae of the energy functions, the new basic equations for ferroelectrics are derived and can reasonably explain the question in the current finite element analysis for ferroelectrics.

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An Optimization-Based Computational Model for Polycrystalline Ferroelastics

2010

IUTAM Symposium on Multiscale Modelling of Fatigue, Damage and Fracture in Smart Materials

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Simulations of domain switching in ferroelectrics by a three-dimensional finite element model

Cited by 67 publications

References 18 publications

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

Energy principle and nonlinear electric–mechanical behavior of ferroelectric ceramics

Energy functions and basic equations for ferroelectrics

An Optimization-Based Computational Model for Polycrystalline Ferroelastics

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