Plane problems of cubic quasicrystal media with an elliptic hole or a crack

► Lekhnitskiiʼs formalism is extended to cubic QC solids. ► The plane problem of an elliptic hole or crack is investigated. ► Analytical expressions for both entire and asymptotic fields are determined. ► The stress intensity factors are independent of material constants. ► The coupled field strongly affects the configuration and strain energy of the crack.