Partially debonded circular inclusion in one-dimensional quasicrystal material with piezoelectric effect

In this first effort, a partially-debonded circular inclusion in a one-dimensional quasicrystal material with piezoelectric effect is studied. This mixed boundary value problem of a circular interface crack is reduced to solving three Riemann–Hilbert problems with the use of analytical continuation theory. The crack-tip singularity of the circular interface crack is investigated and the intensity factors of the stresses in the phonon and the phason fields and electric displacements are derived explicitly. Some particular cases are provided to show the effect of the crack angle, material properties and loadings on the field singularities at the tips of the circular interface crack.