Fundamental elastic field in an infinite medium of two-dimensional hexagonal quasicrystal with a planar crack: 3D exact analysis

Guided wave characteristics in the functionally graded two‐dimensional hexagonal quasi‐crystal plate

“…In this section, dispersion curves, phonon and phason stresses and displacements of guided waves in the functionally graded 2‐D quasi‐crystal plates are investigated. The plates are composed of a kind of 2‐D quasi‐crystal material and a kind of crystal material(Al), whose material parameters are listed in the Table 1 [30,31].…”

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

“…As regard to extended stress intensity factors, normal phonon stress loading can only induce Mode I phonon stress intensity factor, as discussed in above sections and the literatures [40,43,44,51], which is a simple case and not addressed here. What we are most concerned is the coupled field intensity factors, related to Mode II, III cases, and thermal case, whose corresponding analytical solutions are given firstly in this paper.…”

“…As an application of the general solution, they dealt with a penny-shaped crack problem with crack surface uniformly distributed temperature loadings. With the help of these general solutions in terms of quasi-harmonic functions [37,39] conjugated with the generalized method of potential theory, some 3D exact analyzes of planar crack in 2D hexagonal QCs were conducted, such as the cases of Model I crack [40] and symmetry temperature loadings [41]. Without considering thermal effects, Li et al [42] took the phonon and phason displacement discontinuities as the unknown variables of generalized potential function method and first derived closed-form exact solutions to the elliptical crack problems for 2D hexagonal QCs.…”

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

“…The expression for the Mode I stress intensity factors, K I p , is known from Wang et al [42], whereas K II p , K III p , K II H , and K III H are new and first given in the present paper.…”

“…Yang et al [41] obtained the general solution of 3D thermoelasticity of 2D hexagonal QCs and investigated a uniformly distributed temperature change on the crack face of a penny-shaped crack. Wang et al [42] studied the Mode I problem of a penny-shaped crack in 2D hexagonal QCs. Following the similar technique, Li et al [43] presented some analytical solutions for penny-shaped and half-infinite plane cracks with symmetry temperature loadings applied on the crack surfaces.…”