Exact solutions of the generalized Dugdale model of two-dimensional decagonal quasicrystals

The basic properties of the generalized Dugdale model of quasicrystals have significance in the theory of fracture mechanics of this solids. This study suggests a conformal mapping which transforms the complicated region in physical plane onto the exterior of the unit circle in the ζ plane, then in terms of Cauchy integral theory, the complicated boundary value problem is solved, and the solutions are expressed in close form exactly. The crack tip opening displacement (CTOD), cohesive force zone and the most important physical quantity, stress intensity factor, are obtained with exact analytic form, which are useful in materials science and engineering.