Three-dimensional analysis of a spheroidal inclusion in a two-dimensional quasicrystal body

Abstract

This paper deals with the three-dimensional problem of a spheroidal quasicrystalline inclusion, which is embedded in an infinite matrix consisting of a two-dimensional quasicrystal subject to uniform loadings at infinity. Based on the general solution of quasicrystals in cylindrical coordinates, a series of displacement functions is adopted to obtain the explicit real-form results for the coupled fields both inside the inclusion and matrix, when three different types of loadings are studied: axisymmetric, inplane shear and out-of-plane shear. Furthermore, the present results are reduced to the limiting cases involving inhomogeneities including rigid inclusions, cavities and penny-shaped cracks.

Mixed-mode crack tip loading and crack deflection in 1D quasicrystals

“…Various boundary value problems have been solved applying different methods, providing solutions for e.g. inclusions [15,16], interfaces [17] or Green's functions [18,19]. Some papers deal with crack problems in QC giving solutions for elastic fields in the structure or in the crack tip near field and providing fracture mechanical loading quantities [20,21].…”

Analysis solution method for 3D planar crack problems of two-dimensional hexagonal quasicrystals with thermal effects

“…The material constants are chosen as those given in Ref. [38] and listed in Table 1. Making use of these material constants and the definitions in Re.…”

“…Gao and Ricoeur [38] derived an analytical solution of shear field stress intensity factors according to the limited case of spheroidal inclusion. Making use of ASM, the related crack analytical solutions regarding tangential phonon and phason loadings can also be easily established.…”

“…Only since general solutions for 3D problems of 2D hexagonal QCs were given by Gao and Zhao [37], some research efforts have been made on the 3D crack analysis of 2D hexagonal QCs. Gao and Ricoeur [38] analytically studied the 3D problems associated with a spheroidal quasicrystalline inclusion embedded inside an infinite dissimilar quasicrystalline matrix subject to uniform loadings at infinity. As further developments to the work conducted by Gao and Zhao [37], Yang et al [39] included thermal effect to the problem and presented the associated general solution of 2D hexagonal QCs.…”

Numerical crack path prediction under mixed-mode loading in 1D quasicrystals

“…Various boundary value problems have been investigated applying different methods, providing solutions for e.g. inclusions [15,16], interfaces [17] or Green's functions [18,19]. Some papers address crack problems in QCs giving solutions in the structure or in the crack tip near field and providing fracture mechanical loading quantities [20,21].…”