International Journal of Fracture

, Volume 189, Issue 1, pp 111–120 | Cite as

Comparison of several BEM-based approaches in evaluating crack-tip field intensity factors in piezoelectric materials

  • Jun Lei
  • Hongyan Wang
  • Chuanzeng Zhang
  • Tinh Quoc Bui
  • Felipe Garcia-Sanchez
Brief Note


From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular displacement boundary integral equations (BIEs) are applied on the external boundary of the cracked solid, while the hypersingular traction BIEs are used on the crack faces. Three numerical examples are presented to show the path independence and the high accuracy of the J-integral in piezoelectric materials and to analyze the pros and cons of these approaches in evaluating the field intensity factors.


Piezoelectric BEM J-integral Displacement extrapolation MCCI 



This work is supported by the Funding Project (No. 067135300100) for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality and the German Research Foundation (DFG) under the Project No. ZH 15/14-1, which are gratefully acknowledged.


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Jun Lei
    • 1
  • Hongyan Wang
    • 1
  • Chuanzeng Zhang
    • 2
  • Tinh Quoc Bui
    • 2
  • Felipe Garcia-Sanchez
    • 3
  1. 1.Department of Engineering MechanicsBeijing University of TechnologyBeijingPeople’s Republic of China
  2. 2.Department of Civil EngineeringUniversity of SiegenSiegenGermany
  3. 3.Departamento de Ingeniería Civil, de Materiales y Fabricación, E.T.S. de Ingenieros IndustrialesUniversidad de MálagaMálagaSpain

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