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Three-dimensional extended displacement discontinuity method for vertical cracks in transversely isotropic piezoelectric media

Authors
Journal
Engineering Analysis with Boundary Elements
0955-7997
Publisher
Elsevier
Volume
36
Issue
9
Identifiers
DOI: 10.1016/j.enganabound.2012.03.005
Keywords
  • Piezoelectric Medium
  • Displacement Discontinuity Method
  • Extended Green'S Function
  • Boundary Integral Equation
  • Vertical Crack
  • Extended Field Intensity Factor

Abstract

Abstract The conventional displacement discontinuity method is extended to study a vertical crack under electrically impermeable condition, running parallel to the poling direction and normal to the plane of isotropy in three-dimensional transversely isotropic piezoelectric media. The extended Green's functions specifically for extended point displacement discontinuities are derived based on the Green's functions of extended point forces and the Somigliana identity. The hyper-singular displacement discontinuity boundary integral equations are also derived. The asymptotical behavior near the crack tips along the crack front is studied and the ordinary 1/2 singularity is obtained at the tips. The extended field intensity factors are expressed in terms of the extended displacement discontinuity on crack faces. Numerical results on the extended field intensity factors for a vertical square crack are presented using the proposed extended displacement discontinuity method.

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