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Dynamic Crack Propagation in Piezoelectric Materials Subjected to Dynamic Body Forces for Vacuum Boundary

Published online by Cambridge University Press:  05 May 2011

X.-H. Chen ,
C.-C. Ma  and
Y.-S. Ing
X.-H. Chen*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
C.-C. Ma*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Y.-S. Ing*
Affiliation:
Department of Aerospace Engineering, Tamkang University, Tamsui, Taiwan 25137, R.O.C.
*
*Ph.D. candidate
**Professor, corresponding author
***Professor
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Abstract

The problem of a semi-infinite propagating crack in the piezoelectric material subjected to a dynamic anti-plane concentrated body force is investigated in the present study. It is assumed that between the growing crack surfaces there is a permeable vacuum free space, in which the electrostatic potential is nonzero. It is noted that this problem has characteristic lengths and a direct attempt towards solving this problem by transform and Wiener-Hopf techniques [1] is not applicable. This paper proposes a new fundamental solution for propagating crack in the piezoelectric material and the transient response of the propagating crack is determined by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution represents the responses of applying exponentially distributed loadings in the Laplace transform domain on the propagating crack surface. Exact analytical transient solutions for the dynamic stress intensity factor and the dynamic electric displacement intensity factor are obtained by using the Cagniard-de Hoop method [2,3] of Laplace inversion and are expressed in explicit forms. Finally, numerical results based on analytical solutions are calculated and are discussed in detail.

Keywords

Crack propagationPiezoelectric materialSuperpositionDynamic stress intensity factorDynamic electric displacement intensity factor.
Type
Articles
Information
Journal of Mechanics , Volume 23 , Issue 3 , September 2007 , pp. 229 - 238
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2007

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