Line Force, Charge, and Dislocation in Anisotropic Piezoelectric Composite Wedges and Spaces

1995 ◽  
Vol 62 (2) ◽  
pp. 423-428 ◽  
Author(s):  
M. Y. Chung ◽  
T. C. T. Ting
Keyword(s):  
Electric Displacement ◽  
Form Solution ◽  
Piezoelectric Composite ◽  
Real Form ◽  
Line Charge ◽  
Radial Plane ◽  
Line Force ◽  
Line Dislocation ◽  
Charge Line ◽  
Composite Wedge

Two-dimensional problems of anisotropic piezoelectric composite wedges and spaces are studied. The Stroh formalism is employed to obtain the basic real-form solution in terms of two arbitrary constant vectors for a particular wedge. Explicit real-form solutions are then obtained for (i) a composite wedge subjected to a line force and a line charge at the apex of the wedge and (ii) a composite space subjected to a line force, line charge, line dislocation, and an electric dipole at the center of the composite space. For the composite wedge the surface traction on any radial plane θ = constant and the electric displacement Dθ normal to the radial plane θ = constant vanish everywhere. For the composite space these quantities may not vanish but they are invariant with the choice of the radial plane.

Interaction Between a Semi-Infinite Crack and a Screw Dislocation in a Piezoelectric Material

1999 ◽  
Vol 67 (1) ◽  
pp. 165-170 ◽  
Author(s):  
Kang Yong Lee ◽  
Won Gyu Lee ◽  
Y. Eugene Pak
Keyword(s):  
Screw Dislocation ◽  
Piezoelectric Material ◽  
Electric Displacement ◽  
Crack Tip ◽  
Linear Elasticity Theory ◽  
The Core ◽  
Line Charge ◽  
Extension Force ◽  
Line Force ◽  
Field Intensity Factors

The interaction between a semi-infinite crack and a screw dislocation under antiplane mechanical and in-plane electrical loading in a linear piezoelectric material is studied in the framework of linear elasticity theory. A straight dislocation with the Burgers vector normal to the isotropic basal plane near a semi-infinite crack tip is considered. In addition to having a discontinuous electric potential across the slip plane, the dislocation is subjected to a line-force and a line-charge at the core. The explicit solution for the model is derived by means of complex variable and conformal mapping methods. The classical 1/r singularity is observed for the stress, electric displacement, and electric field at the crack tip. The force on a screw dislocation due to the existence of a semi-infinite crack subjected to external electromechanical loads is calculated. Also, the effect of the screw dislocation with the line-force and line-charge at the core on the crack-tip fields is observed through the field intensity factors and the crack extension force. [S0021-8936(00)01501-4]

Interaction Between A Permeable Crack And Piezoelectric Screw Dislocations, Line Forces And Line Charges In A Finite Piezoelectric Cylinder

2014 ◽  
Vol 44 (4) ◽  
pp. 51-68 ◽  
Author(s):  
H. P. Song ◽  
C. F. Gao
Keyword(s):  
Dislocation Line ◽  
Electric Displacement ◽  
Complex Function ◽  
Image Force ◽  
Stress Fields ◽  
Shielding Effect ◽  
Permeable Crack ◽  
Piezoelectric Cylinder ◽  
Line Charge ◽  
Line Force

Abstract The problem of a piezoelectric screw dislocation, line force and line charge around a permeable crack in a finite piezoelectric cylinder is dealt with in this paper. Utilizing the complex function and conformal mapping methods, the closed form solutions of the stress fields and the electric displacement fields are derived. The stress intensity factor and the image force are discussed in detail. The results show that the stress fields are in direct proportion to the line force, but independent of the line charge. The shielding effect produced by the dislocation increases with the increasing of the radius of the piezoelectric cylinder. Moreover, the unstable equilibrium point and the image force are also severely affected by the radius of the piezoelectric cylinder.

scholarly journals Singularity of Electromechanical Coupling Field in Piezoelectric Composite Junctions

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Li Jiang ◽  
Renyu Ge ◽  
Jinlun Zhang
Keyword(s):  
Electromechanical Coupling ◽  
Electric Displacement ◽  
Dissimilar Materials ◽  
Singularity Analysis ◽  
Variable Coefficients ◽  
Piezoelectric Composite ◽  
Fiber Direction ◽  
Singular Stress ◽  
Coupling Field ◽  
Interpolation Matrix

The double singularities including singular stress field and singular electric displacement field, in the tips of piezoelectric composite junctions, are analyzed by the interpolation matrix method (IMM). The double singularity analysis problem of piezoelectric composite junctions is converted into eigenvalue solution problem of ordinary differential equations with variable coefficients under corresponding boundary conditions. In numerical examples, the first couple of singularity orders and the corresponding characteristic angular functions of displacement and electric potential for the electromechanical coupling field are obtained and comparisons are presented to validate the accuracy of the proposed method. The singularity of the electromechanical coupling field at the tip of piezoelectric composite material junctions is closely related to the bonding angle and fiber direction. According to the numerical results, the best scheme can be configured for the combination of dissimilar materials.

scholarly journals Multiscale instabilities in soft heterogeneous dielectric elastomers

2014 ◽  
Vol 470 (2162) ◽  
pp. 20130618 ◽  
Author(s):  
S. Rudykh ◽  
K. Bhattacharya ◽  
G. deBotton
Keyword(s):  
Large Volume ◽  
Electric Displacement ◽  
Closed Form Solution ◽  
Form Solution ◽  
Dielectric Elastomers ◽  
Layered Composites ◽  
Volume Fractions ◽  
Moderate Volume ◽  
Layered Dielectrics ◽  
New Type

The development of instabilities in soft heterogeneous dielectric elastomers is investigated. Motivated by experiments and possible applications, we use in our analysis the physically relevant referential electric field instead of electric displacement. In terms of this variable, a closed form solution is derived for the class of layered neo-Hookean dielectrics. A criterion for the onset of electromechanical multiscale instabilities for the layered composites with anisotropic phases is formulated. A general condition for the onset of the macroscopic instability in soft multiphase dielectrics is introduced. In the example of the layered dielectrics, the essential influence of the microstructure on the onset of instabilities is revealed. We found that: (i)  macroscopic instabilities dominate at moderate volume fractions of the stiffer phase, (ii) interface instabilities appear at small volume fractions of the stiffer phase and (iii) instabilities of a finite scale, comparable to the microstructure size, occur at large volume fractions of the stiffer phase. The latest new type of instabilities does not appear in the purely mechanical case and dominates in the region of large volume fractions of the stiff phase.

scholarly journals Analysis of Wave Propagation in Infinite Piezoelectric Plates

2005 ◽  
Vol 21 (2) ◽  
pp. 103-108 ◽  
Author(s):  
C. Y. Wu ◽  
J. S. Chang ◽  
K. C. Wu
Keyword(s):  
Wave Propagation ◽  
Piezoelectric Materials ◽  
Electric Displacement ◽  
Low Frequency ◽  
Elastic Plates ◽  
Real Form ◽  
Long Wavelength ◽  
Anisotropic Elastic ◽  
Physical Quantities ◽  
Frequency Approximation

ABSTRACTAn analysis is presented for wave propagation in infinite homogeneous elastic plates of piezoelectric materials. The analysis is an extension to the work by Shuvalov [1] on wave propagation in general anisotropic elastic plates. A real form of dispersion equation is provided for a piezoelectric plate subjected to different boundary conditions on the plate surfaces. Perturbation theory [2] is exploited to obtain long-wavelength low-frequency approximation for physical quantities of wave propagation, including wave amplitude, stress, electric potential, electric displacement and velocity.

Green’s Functions for a Half-Space and Two Half-Spaces Bonded to a Thin Anisotropic Elastic Layer

2008 ◽  
Vol 75 (5) ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Thin Layer ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Elastic Material ◽  
The Body ◽  
Reference Length ◽  
Line Force ◽  
Line Dislocation ◽  
Anisotropic Elastic

The Green’s function for an anisotropic elastic half-space that is bonded to a thin elastic material of different anisotropy subject to a line force and a line dislocation is presented. Also presented is the Green’s function for two different anisotropic elastic half-spaces that are bonded to a thin elastic material of different anisotropy subject to a line force and a line dislocation in one of the half-spaces. The thickness h of the thin layer is assumed to be small compared with a reference length. Thus, instead of finding the solution in the thin layer and imposing the continuity conditions at the interface(s), we derive and apply effective boundary conditions for the interface between the layer and the body that take into account the existence of the layer.

Green’s Function for Piezoelectricity with an Elliptical Inclusion in Multi-Field Circumstance

2013 ◽  
Vol 650 ◽  
pp. 350-355
Author(s):  
Long Chao Dai ◽  
Jun Jie Gong
Keyword(s):  
Conformal Mapping ◽  
Elastic Solid ◽  
Analytical Continuation ◽  
Stroh Formalism ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Elliptic Inclusion ◽  
Elliptical Inclusion ◽  
Line Force ◽  
Line Dislocation

The two-dimensional problem of an elliptic inclusion embedded into an anisotropic magneto-electro-elastic solid is studied. Based on the Stroh formalism combined with the technique of conformal mapping and the method of analytical continuation, general solutions for the stress and deformations in the entire domain are obtained when a generalized line force and a generalized line dislocation is located at a point outside, inside, or on the interface of an elliptical inclusion. Comparisons with some related solutions show that the present solutions are valid and general.

Mode III Interfacial Edge Crack in a Magnetoelectroelastic Bimaterial

2004 ◽  
Vol 261-263 ◽  
pp. 393-398 ◽  
Author(s):  
Ai Kah Soh ◽  
Jin Xi Liu
Keyword(s):  
Edge Crack ◽  
Electric Displacement ◽  
Mapping Technique ◽  
Mode Iii ◽  
Variable Approach ◽  
Out Of Plane ◽  
Line Force ◽  
Closed Form Analytical Solution ◽  
Line Singularities ◽  
Magnetoelectroelastic Bimaterial

This paper deals with a Mode III interfacial edge crack in a magnetoelectroelastic bimaterial subjected to line singularities such as an out-of-plane line force, a line electric charge, a line magnetic charge and a straight screw dislocation. The surfaces (including crack surfaces) of the bimateral are assumed to be electrically open and magnetically closed. The closed-form analytical solution to the problem is obtained by employing the complex variable approach in conjunction with the conformal mapping technique. The intensity factors of stress, electric displacement and magnetic induction are given explicitly. The obtained results can be used as the Green's function to solve more complicated problems.

Electromechanical Effects of a Screw Dislocation Around a Finite Crack in a Piezoelectric Material

2001 ◽  
Vol 69 (1) ◽  
pp. 55-62 ◽  
Author(s):  
J. H. Kwon ◽  
K. Y. Lee
Keyword(s):  
Screw Dislocation ◽  
Electric Displacement ◽  
Piezoelectric Medium ◽  
Electromechanical Effects ◽  
Out Of Plane ◽  
Finite Crack ◽  
Line Force ◽  
Field Intensity Factors ◽  
Electrical Loads ◽  
As Stress

The interaction between a screw dislocation and a finite crack in an unbounded piezoelectric medium is studied in the framework of linear piezoelectric theory. A straight screw dislocation with the Burgers vector, which is normal to the isotropic basal plane, positioned around the tip of a finite crack is considered. In addition to having a discontinuous electric potential across the slip plane, the dislocation is assumed to be subjected to a line force and a line charge at the core. The explicit solution is derived by means of complex variable and conformal mapping methods. All field variables such as stress, strain, electric field, electric displacement near the crack tip, and the forces on a screw dislocation, the field intensity factors, and the energy release rate are determined under the combined out-of-plane mechanical and in-plane electrical loads. Also, the effects of screw dislocation and electrical loads are numerically analyzed.

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