Indentation on two-dimensional hexagonal quasicrystals

• Boundary integral equation for contact problems for 2D QC body is established.
• Exact phonon–phason fields are derived explicitly for three common indenters.
• Indentation stiffness constants for three indenters are uniformly expressed.
• Numerical calculations are performed to show the phonon–phason coupling effect.

This paper is concerned with contact problem for a half-space of two-dimensional hexagonal quasi-crystal punched by three common indenters (cylindrical flat-ended, conical and spherical punches). Based on the Green’s functions for the half-space subjected to an external phonon source exerted on the surface, the superposition principle is applied to constructing the boundary integral equation. Relations between the indentation force and the penetration depth, and the indentation stiffness constants are explicitly obtained for these three indenters. Complete and exact fields in the half-space are given in terms of elementary functions. The present theoretical solutions can not only serve as benchmark for computational contact mechanics, but also apply to guiding future indentation experiments.