A moving interface crack in 1D quasicrystal with piezoelectric effect

A Yoffe-type crack moving along the interface of two one-dimensional hexagonal piezoelectric quasicrystals under the action of antiplane mechanical loading and in-plane electric field was considered. Using the Galilean transformation, a moving coordinate system connected to the speed of the crack is introduced. All required phonon, phason, and electrical parameters are presented in this coordinate system via vector functions analytic in the entire complex plane except the crack region. The subsonic crack regime was studied, and cases of electrically impermeable and electrically permeable crack faces were considered. In both cases, the problems of linear relationships were formulated and solved exactly. Analytical formulas for phonon and phason mechanical factors at the material interface, as well as for electrical components, were found. Formulas for the energy release rate were also obtained. The case of multiple moving cracks at the interface of one-dimensional hexagonal piezoelectric quasicrystals is also considered. A numerical analysis was performed for a certain quasicrystalline bimaterial. The dependence of the phonon, phason, and electric components on the crack speed is demonstrated, and the critical speed for electrically impermeable and electrically permeable crack models is determined. The interaction of the multiple cracks is illustrated.