Mode-I penny-shaped crack problem in an infinite space of one-dimensional hexagonal piezoelectric quasicrystal: exact solutions

This paper aims to study the Mode-I penny-shaped crack problem of an infinite body of one-dimensional hexagonal piezoelectric quasicrystal. The problem is transformed into a mixed-boundary value problem in the context of electro-elasticity of quasicrystals, and the corresponding integro-differential equations are analytically solved. Two extreme cases of electrically impermeable and permeable crack surface are considered. By virtue of the generalized potential theory method, the three-dimensional complete analytical solutions of three-dimensional crack problems under symmetric concentrated and uniform loads are expressed in terms of elementary functions. Important parameters in fracture mechanics are explicitly derived, such as crack surface displacements, the distributions of generalized stresses at the crack tip and the corresponding generalized stress intensity factors. The validity of the proposed solutions and the coupling effect of phonon-phason-electric fields are investigagted through numerical examples.