#### Vol. 3, No. 4, 2008

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Interaction between a screw dislocation and a piezoelectric circular inclusion with viscous interface

### Xu Wang, Ernian Pan and A. K Roy

Vol. 3 (2008), No. 4, 761–773
##### Abstract

Exact closed-form solutions in terms of elementary functions are derived for the problem of a screw dislocation embedded in an unbounded piezoelectric matrix interacting with a piezoelectric circular inclusion with a linear viscous interface. By means of the complex variable method, the original boundary value problem is reduced to an inhomogeneous first-order partial differential equation whose solution can be expressed in terms of elementary functions. The time dependent electroelastic fields such as stresses, strains, electric fields, and electric displacements are then obtained. In particular the image force acting on the piezoelectric screw dislocation, due to its interaction with the circular viscous interface, is presented. Some special cases of practical importance are discussed to verify and to illustrate the obtained solution. Finally we present a specific example of a screw dislocation located in a piezoelectric PZT-5 matrix interacting with a piezoelectric BaTiO${}_{3}$ fiber to graphically demonstrate the influence of the viscosity of the interface on the mobility of the screw dislocation.

##### Keywords
piezoelectricity, circular inclusion, screw dislocation, viscous interface, image force
##### Supplementary material

Online supplement

##### Milestones
Received: 27 September 2007
Accepted: 3 February 2008
Published: 1 June 2008
##### Authors
 Xu Wang Deparment of Civil Engineering University of Akron Akron, OH 44325-3905 United States Department of Applied Mathematics University of Akron Akron, OH 44325-3905 United States Ernian Pan Department of Civil Engineering University of Akron Akron, OH 44325-3905 United States Department of Applied Mathematics University of Akron Akron, OH 44325-3905 United States A. K Roy Air Force Research Laboratory AFRL/MLBCM, Bldg 654 2941 Hobson Way Wright-Patterson AFB, OH 45433-7750 United States