Adhesive Contact of a One-Dimensional Hexagonal Quasicrystal Half-Space Punched by a Spherical Indenter

This paper develops the adhesive contact theory for a one-dimensional hexagonal quasicrystal half-space punched by a spherical indenter on the basis of the classical adhesive contact models involving the Johnson–Kendall–Roberts (JKR) model, the Maugis–Dugdale (MD) model and the Derjaguin–Muller–Toporov (DMT) model. By using the superposition principle combined with the Griffith energy balance, all the significant physical quantities for adhesive contact, such as the energy release rate, indentation force, penetration depth, contact radius and pull-out force, are obtained for different models. The result for the DMT model is derived from the MD solution through a limiting procedure. A numerical calculation is carried out to verify the present analytical solutions, to compare different contact models, and to analyze the influence of the phason field on the results. It is indicated that the effect of the phason field on the result for the MD model is pronounced, especially for a small contact radius. However, the phason effect on the JKR and DMT results is not significant. The present solution can serve as a theoretical basis for nano-indentation and atomic force microscopy to measure the material properties of quasicrystals.