Abstract: A set of new stress functions are introduced for analyzing the elasticity of pentagonal quasicrystals.By which the 18 basic equations on coupling phonon-phason fields are reduced to a single higher-order partial differential equation and its solution for a Griffith crack boundary problem of pentagonal quasicrystals is obtained by applying Fourier transform and dual integral equations.The stress intensity factor and strain energy release rate areworked out which are the key physical quantities for studying the deformation and fracture of the material.

Key words: stress intensity factor, quasicrystal, griffith crack, stress function, energy release rate