Three-dimensional extended displacement discontinuity method for vertical cracks in transversely isotropic piezoelectric media |
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| Affiliation: | 1. College of Science, China Agricultural University, P.O. Box 74, Beijing 100083, China;2. College of Engineering, China Agricultural University, Beijing 100083, China;1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi’an 710072, PR China;2. Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an 710072, PR China |
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| 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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