Abstract
This paper derives an exact solution of periodical collinear cracks in a piezoelectric material plane. Two cases have been studied. In the first case, the permittivity of air εais far less than that of piezoelectric material εm. Therefore, the electric induction in the air (Pak, 1990; Suo et al., 1992) may be neglected. In the second case, the permittivity of air is comparable with that of piezoelectric material. This electric induction is considered. Using the conformal mapping method, this problem can be deduced into a Riemann–Hilbert problem and solved in closed form. It is shown that the exact linear theory results (McMeeking, 1989; Gun and Fan, 1999) can be accepted when the remote stress σ∞ 2and ratio εm/εaare small. If they are large, the approximate nonlinear boundary conditions (Deeg, 1980; Pak, 1990; Suo et al., 1992) are suitable.
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Tian-hu, H. Periodical collinear air containing cracks in a piezoelectric material. International Journal of Fracture 112, 197–204 (2001). https://doi.org/10.1023/A:1013588221105
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DOI: https://doi.org/10.1023/A:1013588221105