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点群10mm十次对称二维准晶中的两类接触问题

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

  • 摘要: 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\pm \beta, 其中\beta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\pm \rm i\v, 其中\varepsilon 由准晶体的材料常数确定.

     

    Abstract: By means of the complex variable method, thisinvestigation addresses two kinds of contact problems in decagonalquasicrystalline materials. One kind of contact problem is the frictionalcontact problem, the other one is the adhesive contact problem.Particularly, the explicit expressions of the analytic functionscharacterizing the phonon and phason fields as well as the contact stressdistribution on the indenter are obtained for a flat indenter on a decagonalquasicrystalline half-space. The results show that 1) the contact stressesexhibit the real power type singularities - 1/2\pm \beta in the edge of the contact zone for the frictional contact problem with \beta determined bythe 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 adhesivecontact problem with \varepsilon determined by the material constants ofthe quasicrystal.

     

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