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A Finite Element Prediction Method for Ferroelectric Single Crystals Containing Electrodes Based on Phase Field Analysis

A ferroelectric single crystal and prediction method technology, applied in electrical digital data processing, special data processing applications, instruments, etc., can solve the problems of evolution, not considering the mutual influence of multiple electrodes, calculation difficulties, etc., and achieve a simple and good process. The effect of adaptability and stability

Active Publication Date: 2017-09-05
NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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Problems solved by technology

[0009] (1) The ferroelectric single crystal with electrodes is mainly simulated under the environment of an external electric field. For the calculation and simulation under the complex environment of force, electricity and heat, the calculation is difficult and the calculation time is long
[0010] (2) At present, most of the ferroelectric single crystal models based on the phase field method simulation are mainly aimed at the finite element simulation of a single electrode or a single crack, and do not consider the interaction between multiple electrodes in the ferroelectric layer capacitor
Therefore, there is a problem that it cannot accurately reflect the physical essence.
[0011] (3) At present, for the finite element method to solve the problem of ferroelectric multi-field coupling with electrodes, the existing commercial finite element software cannot simulate the evolution of ferroelectric microstructure with spontaneous polarization as the first order parameter, and cannot describe clearly and systematically whole physical image

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  • A Finite Element Prediction Method for Ferroelectric Single Crystals Containing Electrodes Based on Phase Field Analysis
  • A Finite Element Prediction Method for Ferroelectric Single Crystals Containing Electrodes Based on Phase Field Analysis
  • A Finite Element Prediction Method for Ferroelectric Single Crystals Containing Electrodes Based on Phase Field Analysis

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Embodiment Construction

[0029] The technical solution of the present invention will be further described below in conjunction with the accompanying drawings.

[0030] This embodiment includes the following steps:

[0031] First of all, D. i is the electric displacement, u i is the displacement vector.

[0032] (1) Establish the phase field model of ferroelectric single crystal, and its electric enthalpy form is:

[0033]

[0034] In the formula, α i , alpha ijk is the dielectric coefficient, As the high-order permittivity of the material in the unstrained state, the parameter material parameter α in the free stress state can be used ij to represent that P i is the spontaneous polarization, G ijkl is the gradient energy coefficient, c ijklis the elastic stiffness of the material, ε ij is the elastic strain and ε ij =1 / 2(u i,j + u j,i ), the ferroelectric material will appear electrostrictive phenomenon q during the polarization process ijkl is the electrostriction coefficient, κ 0...

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Abstract

The invention discloses a finite element prediction method for a ferroelectric single crystal containing an electrode under the coupling action of force-electricity-heat multi-field coupling based on phase field method analysis, comprising the following steps: establishing multi-field coupling based on Landau theory and diffusion interface model The new phase field model; use the ANSYS finite element software to obtain the model modeling and grid division of the ferroelectric single crystal with electrodes, and extract the node information and element information; import the obtained node information, element information and information of different boundary conditions considered , using the FEAP fast solver to realize the solution of the nonlinear force-electric-thermal coupling problem of ferroelectric single crystal with electrodes; the field variables obtained from the FEAP finite element solution are imported into the post-processing program written in Fortran, and visualized by TECPLOT software Field variable results. The method of the invention is not only simple in process, but also has good adaptability and stability, and can be developed into a commercial finite element program to flexibly adapt to changes in problems.

Description

technical field [0001] The invention belongs to an analysis method for a ferroelectric single crystal containing an electrode, in particular to a finite element prediction method for a ferroelectric single crystal containing an electrode under the coupling action of force-electricity-thermal multi-field coupling based on the phase field method analysis, and at the same time relates to a method A predictive system implementing the method. [0002] technical background [0003] Ferroelectric materials refer to a class of materials with ferroelectricity. Ferroelectricity was first discovered by the Frenchman Valasek in 1920. Substances with ferroelectricity are called ferroelectrics. Among the 32 crystallographic point groups in solid state physics, only 10 point groups of l, 2, m, mm2, 4, 4mm, 3m, 6, and 6m have special polarity directions that can produce spontaneous polarization. In ferroelectric crystals, there is usually an electric domain structure, and the domains and th...

Claims

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Application Information

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Patent Type & Authority Patents(China)
IPC IPC(8): G06F17/50
Inventor 黄成戴明高存法余传斌李民祁陆乔
Owner NANJING UNIV OF AERONAUTICS & ASTRONAUTICS
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