Axisymmetric contact problem of one-dimensional hexagonal quasicrystal based on couple stress theory

This paper investigates the size-dependent axisymmetric frictionless contact problem between a rigid spherical indenter and a one-dimensional (1D) hexagonal quasicrystal (QC) half-space within the context of couple stress elasticity. By introducing the characteristic material length parameter and employing the Hankel integral transformation, the governing equations for the axisymmetric contact problem of 1D hexagonal QC under the theory of couple stress are derived and solved analytically. The least-squares integral method is also employed to obtain the expression for the contact pressure distribution with size effect. Through numerical examples, the effects of the characteristic material length parameter on the contact radius, contact pressure, and indentation depth are analyzed. The results incorporating the size effects lead to notable departures from classical elasticity predictions. The presence of the phason field leads to a reduction in peak contact pressure with the size effect.