The fracture behavior of two asymmetrical limited permeable cracks emanating from an elliptical hole in one-dimensional hexagonal quasicrystals with piezoelectric effect

By modeling that the surfaces of the cracks and hole are in limited permeable boundary conditions, the anti-plane problem of an elliptical hole with two asymmetrical cracks in one-dimensional (1D) hexagonal quasicrystals (QCs) with piezoelectric effect is investigated by adopting the technique of conformal mapping and the Stroh-type formulism. The analytic solutions of the field intensity factors and energy release rate are presented. With the variation of the hole-size and the crack length, the proposed model can be reduced to some classic crack models. In the absence of the electric load or the phason field, the present results match with the classical results of 1D hexagonal QCs or piezoelectric materials provided in the open literature. Numerical examples are then conducted to reveal the effects of the hole-size, the crack length, the coupling coefficient and applied mechanical/electric loads on the field intensity factors and the energy release rate.