Dynamics of a viscoelastic cylinder on a viscoelastic half-space

The deceleration of a viscoelastic cylinder rolling with slipping on a viscoelastic half-space of the same material without driving forces and torques is studied. The interaction of the cylinder and the half-space is described from the solution of the 2D quasistatic contact problem of viscoelasticity (Goryacheva in J Appl Math Mech 37(5):877–885, 1973, Contact mechanics in tribology, Kluwer, Dordrecht, 1998). This solution states that the contact region consists of the slip and stick zones, and it is shifted forward in the direction of motion. Contact normal and shear stresses and, therefore, the resultant force and torque depend on the values of the linear velocity of the cylinder and creep ratio, as well as the mechanical properties of contacting bodies and sliding friction coefficient. The Cauchy problem for dynamical equations of the cylinder’s deceleration was solved numerically. The analysis of the deceleration process and changes in the contact normal and shear stress distributions in time for various initial conditions is presented.