Indentation on a half-infinite one-dimensional hexagonal quasi-crystal space by a rigid flat-ended cylindrical indenter with uniform heat flux or temperature

The present paper analytically investigates the contact problem of a half-infinite one-dimensional hexagonal quasi-crystal medium punched by a rigid flat-ended cylindrical indenter with uniform heat flux or temperature. The contact between the two objects is assumed to be frictionless. Based on the general solution, the three-dimensional thermo-elastic coupling field variables in the half-space are explicitly obtained by the generalized potential theory method. For the case of heat flux load, the thermo-elastic field variables are expressed in terms of elementary functions and in closed-forms. In contrast, for the case of uniform temperature load, the corresponding variables are in terms of linear integrals, all the integrands are elementary functions. Furthermore, the maximum shear stress and the von Mises stress in the half-space are also obtained. Some significant physical quantities on the contact plane, such as vertical and radial displacements, normal stresses, temperature and heat flux, are presented as well. An illustrative numerical calculation is performed to show the distributions of the thermo-elastic fields in the vicinity of the contact area. The present solution could be served as the theoretical basis for scanning probe microscopy technology to explore the material properties of one-dimensional hexagonal quasi-crystals.