Applied Mathematics and Mechanics

, Volume 20, Issue 1, pp 51–58 | Cite as

An exact solution of crack problems in piezoelectric materials

  • Gao Cunfa
  • Fan Weixun


An assumption that the normal component of the electric displacement on crack faces is thought of as being zero is widely used in analyzing the fracture mechanics of piezoelectric materials. However, it is shown from the available experiments that the above assumption will lead to erroneous results. In this paper, the two-dimensional problem of a piezoelectric material with a crack is studied based on the exact electric boundary condition on the crack faces. Stroh formalism is used to obtain the closed-form solutions when the material is subjected to uniform loads at infinity. It is shown from these solutions that: (i) the stress intensity factor is the same as that of isotropic material, while the intensity factor of the electric displacement depends on both material properties and the mechanical loads, but not on the electric load. (ii) the energy release rate in a piezoelectric material is larger than that in a pure elastic-anisotropic material, i. e., it is always positive, and independent of the electric loads. (iii) the field solutions in a piezoelectric material are not related to the dielectric constant of air or vacuum inside the crack.

Key words

piezoelectric material plane problem crack energy release rate exact solution 


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Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Gao Cunfa
    • 1
  • Fan Weixun
    • 1
  1. 1.Department of AircraftNanjing University of Aeronautics & AstronauticsNanjingP. R. China

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