Two kinds of contact problems for two-dimensional hexagonal quasicrystals

Abstract

By means of the displacement potential function method, the plane elastic control equation of two-dimensional hexagonal quasicrystals is reduced to a quadruple harmonic equation. The stress and displacement components of the plane elasticity are obtained by complex functions. The frictional contact problem and half-plane adhesive contact problem for a rigid flat indenter on two-dimensional hexagonal quasicrystals materials half-space are investigated. Analytical expressions of the stress components are obtained. The results show that the contact stresses exhibit 1/2 order singularity at the edge of the contact zone and 1/2 order singularity at the bottom of the indenter with k = 0. The stress of the phonon field is independent of the material constants for the frictional contact problem. For the half-plane adhesive contact problem, the stress distribution at the bottom of the contact zone has 1/2order singularity, the normal stresses are zero, and only shear stresses exist. Finally, a solution for the relation between load and penetration for the frictional and adhesive contact problems for the flat indenter is derived. Numerical calculations are presented, and the validity of the solution is verified.