1Simon Fraser University, Burnaby, British Columbia, Canada
2Dublin Institute of Technology, Dublin, Ireland
We consider a smooth rigid cylindrical indentor rolling across a viscoelastic half-space in one direction. The Coulomb friction on the boundary is neglected and the standard linear model is adopted to describe viscoelastic material response. The interval of contact between the indentor and the half-space, $C(t)$, depends on time and is to be determined together with {\em hysteretic friction} (~internal losses in the viscoelastic half-space~) and stress. To solve the governing integral equation for a ``pressure-like'' function $v(x,t), \, x \in C(t) \, \forall t>0$, subject to appropriate subsidiary conditions, an adaptive numerical algorithm is constructed. The results obtained with the help of this algorithm are compared and found consistent with those for the available steady-state analytic solution. It is observed that more pronounced viscoelastic properties of the material of the half-space lead to longer contact intervals, higher hysteretic friction and more asymmetric pressure distribution. The shapes of the graphs of transient and steady-state hysteretic friction for variable {\em speed} are substantially different. After a period of acceleration, the transient value of the hysteretic friction exceeds the corresponding steady-state value. The stress tensor components $\sigma_{11}$, $\sigma_{12}$ and $\sigma_{22}$ are computed and analyzed. Results for the case of a time-dependent load are also obtained.