Boundary integral equation method for conductive cracks in two and three-dimensional transversely isotropic piezoelectric media

Engineering Analysis with Boundary Elements

Volumn 29, Issue 5, 2005, Pages 466-476

  Zhao, Ming Hao ^a   Yang, Feng ^a   Liu, Tong ^a   Liu, Min Shan ^a  

^a ZHENGZHOU UNIVERSITY   (China)

Author keywords

Boundary integral equation; Conductive crack; Intensity factor; Piezoelectric medium

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CRACKS; INTEGRAL EQUATIONS; PIEZOELECTRIC MATERIALS; STRESS CONCENTRATION;

BOUNDARY INTEGRAL EQUATIONS (BIE); CONDUCTIVE CRACKS; INTENSITY FACTOR; PIEZOELECTRIC MEDIUM;

BOUNDARY ELEMENT METHOD;

EID: 18644381670     PISSN: 09557997     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.enganabound.2005.02.004     Document Type: Article

References (30)

1. T-Y. Zhang, M.H. Zhao, and P. Tong Fracture of piezoelectric ceramics Adv Appl Mech 38 2001 147 289
2. Q.H. Qin Fracture mechanics of piezoelectric materials 2001 WIT Press Southampton
3. Y.H. Cheng, and T.J. Lu Cracks and fracture in piezoelectrics Adv Appl Mech 39 2002 121 215
4. R.M. McMeeking The energy release rate for a Griffith crack in a piezoelectric material Eng Fracture Mech 71 2004 1149 1163
5. V. Heyer, G.A. Schneider, H. Balke, J. Drescher, and H-A. Bahr A fracture criterion for conducting cracks in homogeneously poled piezoelectric PZT-PIC 151 ceramics Acta Mater 46 1998 6615 6622
6. R. Fu, C.F. Qian, and T-Y. Zhang Electrical fracture toughness for conductive cracks driven by electric fields in piezoelectric materials Appl Phys Lett 76 2000 126 128
7. T-Y. Zhang, T.H. Wang, and M.H. Zhao Failure behavior and failure criterion of conductive cracks (deep notches) in dielectric ceramics Acta Mater 51 2003 4881 4895
8. T-Y. Zhang, G.N. Liu, and Y. Wang Failure behavior and failure criterion of conductive cracks (deep notches) in piezoelectric ceramics II: experimental verification Acta Mater 52 2004 2025 2035
9. A. Furuta, and K. Uchino Dynamic observation of crack propagation in piezoelectric multilayer actuators J Am Ceram Soc 76 1993 1615 1617
10. R.M. McMeeking On mechanical stresses at cracks in dielectrics with application to dielectric breakdown J Appl Phys 62 1987 3116 3122
11. C.S. Lynch, W. Yang, L. Collier, Z. Suo, and R.M. McMeeking Electric field induced cracking in ferroelectric ceramics Ferroelectrics 166 1995 11 30
12. C.Q. Ru, and X. Mao Conducting cracks in a piezoelectric ceramic of limited electrical polarization J Mech Phys Solids 47 1999 2125 2146
13. M.Y. Chung, and T.C.T. Ting Piezoelectric solid with an elliptical inclusion or hole Int J Solids Struct 33 1996 3343 3361
14. E. Pan, and B.E.M. A analysis of fracture mechanics in 2D anisotropic piezoelectric solids Eng Anal Bound Elem 23 1999 67 76
15. Q.H. Qin, and Y.W. Mai BEM for crack-hole problems in thermopiezoelectric materials Eng Fracture Mech 69 2002 577 588
16. Q.H. Qin, and M. Lu BEM for crack-inclusion problems of plane thermopiezoelectric solids Int J Numer Meth Eng 48 2000 1071 1088
17. H. Schmitz, K. Volk, and W. Wendland Three-dimensional singularities of elastic fields near vertices Num Meth P Diff Eq 9 1993 323 337
18. X.M. Wang, and Y.P. Shen Theorem of work reciprocity for piezoelectric elastic media with application Acta Mech Sinica 28 1996 244 250 (in Chinese)
19. N.I. Ioakimidis Validity of the hypersingular integral equation of crack problems in three-dimensional elasticity along the crack boundary Eng Fracture Mech 26 1987 783 788
20. A. Lin'kov, and S.G. Mogilevshaya Finite-part integrals in problems of three-dimensional crack Appl Math Mech (PMM) 50 1986 652 658
21. M.H. Zhao, C.J. Cheng, and Y.J. Liu Boundary integral equations and boundary element method for three-dimensional fracture mechanics Eng Anal Boundary Elem 13 1994 333 338
22. G.M.L. Gladwell Contact problems in the classical theory of elasticity 1980 Alphen aanden Rijn Sijthoff and Noordhoff
23. K.L. Johson Contact mechanics 1985 Cambridge University Press Cambridge
24. M.H. Aliabadi, and C.A. Brebbia Advances in boundary element methods for fracture mechanics 1993 Computational Mechanics Publications Southampton
25. C.A. Brebbia, J.C.F. Telles, and L.C. Wrobel Boundary element techniques 1984 Springer Berlin
26. P.H. Wen Displacement discontinuity method Topic in engineering vol. 29 1996 Computational Mechanics Publication Southampton
27. N.I. Ioakimids, and M.S. Pita Remarks on the Gauss quadrature rule for finite-part integrals with a second-order singularity Comp Meth Appl Mech Eng 69 1988 325 343
28. Kutt HR. On the numerical evaluation of finite part integrals involving an algebraic singularity. Special report WISK 179. National Research Institute for Mathematical Sciences. P.O. Box 395, Pretoria 0001, South Africa; 1975.
29. H.J. Ding, B. Chen, and J. Liang On the Green's functions for two-phase transversely isotropic piezoelectric media Int J Solids Struct 34 1997 3041 3057
30. M.H. Zhao, Y.P. Shen, Y.J. Liu, and G.N. Liu Fundamental solutions for infinite transversely isotropic piezoelectric media Proceedings of the first international seminar on the computational methods for smart structures and materials 1998 Computational Mechanics Publications Southampton