ZHOU Zhen-gong, WANG Biao. Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method[J]. Applied Mathematics and Mechanics, 2006, 27(7): 765-774.
Citation: ZHOU Zhen-gong, WANG Biao. Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method[J]. Applied Mathematics and Mechanics, 2006, 27(7): 765-774.

Investigation of the Behavior of a Model-Ⅰ Interface Crack in Piezoelectric Materials by Using the Schmidt Method

  • Received Date: 2005-01-06
  • Rev Recd Date: 2006-03-21
  • Publish Date: 2006-07-15
  • The behavior of a Mode-Ⅰ interface crack in piezoelectric materials is investigated under the assumptions that the effect of the crack surface overlapping very near the crack tips is negligible. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Contrary to the previous solution of the interface crack in piezoelectric materials, it is found that the stress and the electric displacement singularities of the present interface crack solution are the same as those of the ordinary crack in homogenous materials. The solution can be returned to the exact solution when the upper half plane material is the same as the lower half plane material.
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