Weight Function Theory for Piezoelectric Materials with Crack in Anti-Plane Deformation

균열을 가진 압전재료에 대한 면외 변형에서의 가중함수이론

  • Son, In-Ho (Department of Mechanical Design Engineering, Pusan National Univ.) ;
  • An, Deuk-Man (Department of Mechanical Design Engineering, Pusan National Univ.)
  • 손인호 (부산대학교 기계설계공학과) ;
  • 안득만 (부산대학교 기계설계공학과)
  • Received : 2009.12.09
  • Accepted : 2010.06.18
  • Published : 2010.06.30


In this paper, an electroelastic analysis is performed on a piezoelectric material with an open crack in anti-plane deformation. Bueckner’s weight function theory is extended to piezoelectric materials in anti-plane deformation. The stress intensity factors and electric displacement intensity factor are calculated by the weight function theory.


Piezoelectric;Complex potential function;Weight function;Stress intensity factor;Electric displacement intensity factor


Supported by : 부산대학교


  1. An, D. (1987). "Weight Function Theory for a Rectilinear Anisotropic Body", Int. J. of Fracture, Vol 34, pp 85-109. https://doi.org/10.1007/BF00019766
  2. An, D. and Son, I. (2007). "Weight Functions for Notched Structures with Anti-Plane Deformation", Int. J. of Precision Engineering and Manufacturing, Vol 8, pp 60-63.
  3. Chen, B.J., Liew, K.M. and Xiao, Z.M. (2004). "Green's Functions for Anti-Plane Problems in Piezoelectric Media with a Finite Crack", Int. J. of Solids and Structures, Vol 41, pp 5285-5300. https://doi.org/10.1016/j.ijsolstr.2004.04.010
  4. Gao, H., Zhang, T. and Tong, P. (1997). "Local and Global Energy Release Rates for an Electrically Yielded Crack in a Piezoelectric Ceramic", J. Mech. Phys. Solids, Vol 45, pp 491-510. https://doi.org/10.1016/S0022-5096(96)00108-1
  5. Li, C. and Weng, G.J. (2002). "Antiplane Crack Problem in Functionally Graded Piezoelectric Materials", J. of Applied Mechanics, Vol 69, pp 481-488. https://doi.org/10.1115/1.1467091
  6. McMeeking, R. and Ricoeur, A. (2003). "The Weight Function for Cracks in Piezoelectrics", Int. J. of Solids and Structures, Vol 40, pp 6143-6162. https://doi.org/10.1016/S0020-7683(03)00366-4
  7. Pak, Y. (1990). "Crack Extension Force in a Piezoelectric Material", J. of Applied Mechanics, Vol 57, pp 647-653. https://doi.org/10.1115/1.2897071
  8. Parton, V.Z. and Kudryavtsev, B.A. (1988). Electromagnetoelasticity Piezoelectrics and Electrically Conductive Solids, Gordon and Breach Science Publishers.
  9. Sosa, H. (1991). "Plane Problems in Piezoelectric Media with Defects", Int. J. of Solids and Structures, Vol 28, pp 491-505. https://doi.org/10.1016/0020-7683(91)90061-J
  10. Suo, Z., Kuo, C.M., Barnett, D.M. and Willis, J.R. (1992). "Fracture Mechanics for Piezoelectric Ceramics", J. of the Mechanics and Physics of Solids, Vol 40, pp 736-765. https://doi.org/10.1016/0022-5096(92)90002-J
  11. Zhang, T. and Hack, J.E. (1992). "Mode-III Cracks in Piezoelectric Materials", J. Appl. Phys., Vol 71, pp 5865-5870. https://doi.org/10.1063/1.350483