Sliding of a smooth indentor over a viscoelastic half-space when there is friction

The spatial contact problem of the sliding, at a constant velocity, of a smooth indentor along the boundary of a viscoelastic half-space is considered. Shear stresses, related to the contact pressure by the Coulomb–Amonton friction law and due to surface adhesion interaction forces, act in the contact area. Shear deformation of the base is described by an integral operator with an exponential kernel, which is characterized by a single relaxation time. An integral equation is constructed for determining the unknown contact pressures, to solve which the boundary elements method is employed. Calculations are carried out for two forms of indentor: in the form of a paraboloid of revolution and in the form of an elliptic paraboloid. The dependence of the pressure distribution, the dimensions and displacement of the contact area with respect to the axis (or plane) of symmetry of the indentor, and also the dependence of the mechanical component of the friction force on the rate of sliding, the parameters of the viscoelasticity and the adhesion friction coefficient in the region of the contact interaction, are analysed.