Analysis of cracks in one-dimensional hexagonal quasicrystals with the heat effect

The extended displacement discontinuity (EDD) method is proposed to analyze cracks in the periodical plane of one-dimensional (1D) hexagonal quasicrystals with the heat effect. Based on the operator theory and the Fourier transform, the fundamental solutions for EDDs are derived, where the EDDs include phonon and phason displacement discontinuities and the temperature discontinuity. The EDD boundary integral equation method is used to analyze the singularities of the near-crack tip fields, and the extended stress intensity factor (ESIF) expressions are obtained in terms of the EDDs across the crack faces. The EDD boundary element method is proposed to calculate the ESIFs of cracks in 1D hexagonal quasicrystals. COMSOL software is used to validate the developed method. The influences of applied mechanical and heat loads on cracks in a finite plate are investigated.