The Green's functions of two-dimensional piezoelectric quasicrystal semi-infinite crack and finite crack

Abstract

This paper investigates the interactions of a semi-infinite crack / finite crack with multiple loadings in a two-dimensional piezoelectric quasicrystal under different boundary conditions. Utilizing the Stroh formalism and conformal mapping, Green's functions of generalized displacements and stresses are obtained for two general cases: a semi-infinite crack and a finite crack subject to free-free or fixed-fixed boundary conditions. The stress and electric displacement intensity factors at the crack tip and the image forces on how dislocations are affected by the crack surfaces are given explicitly. The results are analyzed and compared with special cases documented in the scholarly literature. At the same time, the effects of the Burgers vector components on the generalized stresses and image forces numerically illustrate as well as the impacts of line forces on generalized stress intensity factors.