electric flux density

A singular electric flux density field may occur when mechanical compression or electrical load to piezoelectric joints causes a singular electric flux density field is applied in piezoelectric material corners. This means that a large electric displacement occurs arround a singular point. It can be thought that there are many possible applications of this local large electric displacement. Hence, electric singularity characteristics should be investigated to increase the performance of piezoelectric joints. It is known that the intensity of stress singularity reduces with decreasing the thickness of piezoelectric joints; conversely, the intensity of electric singularity increases under a constant external voltage and load. This implies that there is a relationship between electric singularity and stress singularity. In the present paper, the electric singularity on piezoelectric joints is investigated numerically. Usefulness of piezoelectric joints will then be discussed from the results of analysis.

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Measurement of specific heat at constant electric flux density CD of ferroelectrics by AC method

Ferroelectrics ◽

10.1080/00150197808237208 ◽

1978 ◽

Vol 20 (1) ◽

pp. 193-194 ◽

Cited By ~ 1

Author(s):

K. Ema ◽

K. Hamano

Keyword(s):

Specific Heat ◽

Flux Density ◽

Electric Flux

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M -Integral for Calculating Intensity Factors of Cracked Piezoelectric Materials Using the Exact Boundary Conditions

Journal of Applied Mechanics ◽

10.1115/1.2998485 ◽

2008 ◽

Vol 76 (1) ◽

Cited By ~ 11

Author(s):

Yael Motola ◽

Leslie Banks-Sills

Keyword(s):

Intensity Factor ◽

Boundary Conditions ◽

Flux Density ◽

Electric Permittivity ◽

Intensity Factors ◽

Exact Boundary ◽

Poling Direction ◽

Electric Flux ◽

Crack Faces ◽

M Integral

In this paper, the M-integral is extended for calculating intensity factors for cracked piezoelectric ceramics using the exact boundary conditions on the crack faces. The poling direction is taken at an angle to the crack faces within the plane. Since an analytical solution exists, the problem of a finite length crack in an infinite body subjected to crack face traction and electric flux density is examined. In this case, poling is taken parallel to the crack faces. Numerical difficulties resulting from multiplication of large and small numbers were treated by normalizing the variables. This problem was solved with the M-integral and displacement-potential extrapolation methods. With this example, the superiority of the conservative integral is observed. The values for the intensity factor obtained with the M-integral are found to be more accurate than those found by means of the extrapolation method. In addition, a crack parallel to the poling direction in a four-point bend specimen subjected to both an applied load and an electric field was analyzed and different electric permittivity values in the crack gap were assumed. It is seen that the electric permittivity greatly influences the stress intensity factor KII and the electric flux density intensity factor KIV. The absolute value of these intensity factors increases with an increase in the value of the electric permittivity in the crack. The influence of the permittivity on KI is rather small.

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The Maxwell Equations and Constitutive Relations

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics ◽

10.23943/princeton/9780691142173.003.0002 ◽

2012 ◽

Author(s):

G. F. Roach ◽

I. G. Stratis ◽

A. N. Yannacopoulos

Keyword(s):

Differential Equations ◽

Flux Density ◽

Time Domain ◽

Maxwell Equations ◽

Constitutive Relations ◽

Magnetic Flux Density ◽

Scattering Problems ◽

Stochastic Problems ◽

Time Harmonic ◽

Electric Flux

This chapter first introduces the constitutive relations which are commonly used in electromagnetic theory for the mathematical modelling of complex electromagnetic media. These constitutive relations are to be understood as operators connecting the electric flux density and the magnetic flux density with the electric and the magnetic fields. When they are introduced into the Maxwell equations, this chapter obtains differential equations (PDEs) that govern the evolution of the electromagnetic fields. This chapter also seeks to formulate and discuss the scope of the various problems related to the Maxwell equations that will be treated in this volume. It introduces and formulates in terms of differential equations various problems of interest related to the Maxwell equations: time-harmonic problems, scattering problems, time-domain evolution problems, random and stochastic problems, controllability problems, homogenisation problems, and others.

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