Two kinds of contact problems in decagonal quasicrystalline materials of point group 10mm
点群10mm十次对称二维准晶中的两类接触问题

By means of the complex variable method, this investigation addresses two kinds of contact problems in decagonal quasicrystalline materials. One kind of contact problem is the frictional contact problem, the other one is the adhesive contact problem. Particularly, the explicit expressions of the analytic functions characterizing the phonon and phason fields as well as the contact stress distribution on the indenter are obtained for a flat indenter on a decagonal quasicrystalline half-space. The results show that 1) the contact stresses exhibit the real power type singularities $ - 1/2\pm \beta$ in the edge of the contact zone for the frictional contact problem with $\beta $ determined by the material constants of the quasicrystal and the static frictional factor; and 2) the contact stresses exhibit the oscillatory singularities $ - 1/2 \pm {\rm i} \v$ in the edge of the contact zone for the adhesive contact problem with $\varepsilon $ determined by the material constants of the quasicrystal.