Anti-plane analysis on a finite crack in a one-dimensional hexagonal quasicrystal strip

Crack tip plasticity of a half-infinite Dugdale crack embedded in an infinite space of one-dimensional hexagonal quasicrystal

“…The constants g mi and A in (5) This section is dedicated to evaluating the integrals involved in (15).…”

“…Later, Fan and Mai [9] gave a comprehensive review of the mathematical theory and methodology of elasticity of QCs and their applications to dislocations and cracks. For the anti-plane crack problems in 1D hexagonal QCs, some works [31,14,15] have been achieved under the framework of elasticity of QCs, to explore the effect of phason field on the deformations of the cracked materials. For the plane problems of an elliptic hole and a crack in three-dimensional (3D) QCs, Gao et al [12,13] derived the explicit solutions for the phononphason coupled fields are obtained in closed forms, by a complex potential approach and the generalized Stroh formalism.…”

Bending Analysis of Laminated Two-Dimensional Piezoelectric Quasicrystal Plates with Functionally Graded Material Properties

“…As new-type solid materials, quasicrystals (QCs) were discovered from the diffraction image of rapidly cooled Al-Mn alloys by Shechtman in early 1980s [10]. QCs have a long-range quasiperiodic translational order and a longrange orientational order [11,12]. Two lower frequency excitations, which are phonon and phason, are considered in the elastic energy theory of QCs [13].…”

An exact closed-form solution for a multilayered one-dimensional orthorhombic quasicrystal plate

“…For 1D QCs, many efforts have been made involving defect problems, such as dislocation and crack problems in infinite space [19][20][21][22][23]. Based on the general solutions of 1D QCs [24,25], Gao et al [26,27] solved exactly plane problems for both a QC beam and QC plate by introducing a refined theory.…”