Plane elasticity problem of two-dimensional octagonal quasicrystals and crack problem

The plane elasticity theory of two-dimensional octagonal quasicrystals is d eveloped in this paper. The plane elasticity problem of quasicrystals is re duced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a M ode I Griffith crack in the material is obtained by using the Fourier trans form and dual integral equations theory, then the displacement and stress f ields, stress intensity factor and strain energy release rate can be calcul ated. The physical significance of the results relative to the phason and t he difference between the mechanical behaviours of the crack problem in cry stals and quasicrystals are figured out. These provide important informatio n for studying the deformation and fracture of the new solid phase.