The Anti-Plane Shear Problem of Two Symmetric Cracks Originating from an Elliptical Hole in 1D Hexagonal Piezoelectric QCs

Using the complex variable function method and the technique of conformal mapping, the fracture mechanics of two symmetric collinear cracks originating from an elliptical hole in a one-dimensional (1D) hexagonal piezoelectric quasicrystals (QCs) are investigated under anti-plane shear loading and electric loading. The crack is assumed to be either electrical impermeable or permeable. The exact solutions in closed-form of the stress intensity factors (SIFs) of the phonon field and the phason field, and the electric displacement intensity factors (EDIFs) are obtained. In the limiting cases, the new results such as Griffith crack, a circular hole with equal two edge cracks and cross crack can be obtained from the present solutions. In the absence of the phason field, the obtainable results in this paper match with the classical results.