Fundamental solution for extended dislocation in one‐dimensional piezoelectric quasicrystal and application to fracture analysis

In this paper, we derive a undamental solution for extended dislocations of one-dimensional (1D) hexagonal piezoelectric quasicrystals. Based on the Stroh formalism, the fundamental solutions for (1D) hexagonal piezoelectric quasicrystals expressing by extended dislocations, including phonon, electric, and phason dislocations, are obtained. Then, by considering the continuously distributed dislocations to be a crack, the crack opening displacement, intensity factor, and energy release rate of the extended dislocation are expressed. Numerical calculations are used to confirm the validity of the theory and to investigate the effect of different parameters on the energy release rate.