A Dugdale-Barenblatt model for elliptical orifice problem with asymmetric cracks in one-dimensional orthorhombic quasicrystals

By means of Muskhelishvili’s method and the technique of generalized conformal mapping, the physical plane problems are transformed into regular mathematical problems in quasicrystals (QCs). The analytical solution of an elliptical orifice problem with asymmetric cracks in one-dimensional (1D) orthorhombic QCs is obtained. By using the Dugdale-Barenblatt model, the plastic simulation at the crack tip of the elliptical orifice with asymmetric cracks in 1D orthorhombic QCs is performed. Finally, the size of the atomic cohesive force zone is determined precisely, and the size of the atomic cohesive force zone around the crack tip of an elliptical orifice with a single crack or two symmetric cracks is obtained.