Elasto-hydrodynamics of quasicrystals with a crack under sudden impacts

In this paper, a mode-III crack in one-dimensional (1D) hexagonal quasicrystals subjected to anti-plane impact loading is analyzed. The elasto-hydrodynamics of quasicrystals is adopted, where the phonon field obeys wave equation, and the phason field obeys diffusion equation. By introducing a new auxiliary function, the coupled wave-diffusion equations are converted to a single higher-order partial differential equation. With the aid of the Laplace transform, an associated mixed initial-boundary value problem is reduced to two sets of dual integral equations, and then transformed into two coupled Fredholm integral equations of the second kind. Numerical results of transient phonon and phason stress intensity factors and crack-centre displacement jump are obtained through the numerical inversion of the Laplace transform and are presented graphically to show the influences of the phason.