International Journal of Fracture

, Volume 194, Issue 2, pp 107–122 | Cite as

Analysis of a nonlinear crack in a piezoelectric half-space via displacement discontinuity method

  • QiaoYun Zhang
  • MingHao Zhao
  • Ernian Pan
  • CuiYing Fan
Original Paper


In this paper, we derive the exact closed-form fundamental solutions due to uniform extended displacement discontinuities over a triangular element in a piezoelectric half-space. Using the triangular elements to partition the penny-shaped crack, the triangular element fundamental solutions are verified by comparing with the existing analytical solution associated with the penny-shaped crack. The polarization saturation model is then applied to an elliptical crack in the piezoelectric half-space, and the resulting nonlinear fracture problem is solved by combing the triangular element fundamental solutions and the displacement discontinuity method. The electric yielding zone and the extended field intensity factors are obtained by an iterative approach. The effects of the applied mechanical load and electric displacement, the polarization saturation in the yielding zone, and the aspect ratio of the elliptical crack on the yielding zone size and field intensity factors are discussed through numerical examples.


Piezoelectric half-space Displacement discontinuity solutions Polarization saturation Nonlinear crack Field intensity factor 



The work was supported by the National Natural Science Foundation of China (Nos. 11172273, 11272290), the Construction Project of Key Laboratory in Henan Colleges, and Henan Bairen Program.


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • QiaoYun Zhang
    • 1
  • MingHao Zhao
    • 2
    • 3
  • Ernian Pan
    • 4
  • CuiYing Fan
    • 2
    • 3
  1. 1.School of Mechanics and Engineering ScienceZhengzhou UniversityZhengzhouChina
  2. 2.School of Mechanical EngineeringZhengzhou UniversityZhengzhouChina
  3. 3.Henan Key Engineering Laboratory for Anti-fatigue Manufacturing TechnologyZhengzhouChina
  4. 4.Department of Civil EngineeringUniversity of AkronAkronUSA

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