An analytical approach to the analysis of an electrically permeable interface crack in a 1D piezoelectric quasicrystal

A plane problem is analysed for an electrically permeable crack in a bi-material composed of two semi-infinite 1D piezoelectric quasicrystals bonded together. The polarization direction coincides with the quasiperiodic direction of the materials and is orthogonal to the interface. Uniformly distributed phonon normal and shear in-plane stresses and also phason stress and electric displacement are applied at infinity. The matrix-vector representations for the phonon and phason stresses, the electrical displacement and for the derivatives of the phonon and phason displacements and electrical potentials jumps via the sectional-holomorphic vector-function are derived. Using these relations and satisfying the conditions at the crack faces, the problems of linear relationship are formulated and solved exactly. All required phonon and phason characteristics are given in the form of simple analytical expressions. A numerical analysis is carried out for two different 1D piezoelectric quasicrystals bonded together. The obtained results are presented in graph and table forms.