点群10mm十次对称二维准晶中的两类接触问题

采用复变函数法探讨了在一个刚性压头作用下十次对称二维准晶材料的两类接触问题,即具有有限摩擦的接触问题以及粘结接触问题.特别地对于平底压头,获得了表征声子场和相位子场的全纯函数的显式表达式,以及在压头上的接触应力分布.结果显示,对于具有有限摩擦的接触问题,接触应力在接触区边缘具有实指数奇异性-1／2±β,其中β由准晶体的材料常数及静摩擦系数确定;而对于粘结接触问题,接触应力在接触区边缘具有振荡型奇异性-1／2±iε,其中ε由准晶体的材料常数确定.

Two kinds of contact problems in decagonal quasicrystalline materials of point group 10mm

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.