Multigrid Methods in Solving Transient and Steady-State Viscoelastic Point Contact Problems

The Standard Linear Solid (SLS) model is used to characterize the viscoelastic behavior of the substrate. Viscoelastic dry transient and steady-state models are proposed based on the differences of the time-dependent response of the viscoelastic materials.

A new viscoelastic deformation modeling equation is derived for viscoelastic steady state model so that the efficiency of the computation of the viscoelastic deformation remains close to that of the elastic case, rather than being much more expensive owing to its time varying nature. For rolling contacts in steady state regime, the viscoelastic contact problem is dominated by two dimensionless parameters: the Deborah number which relates the relaxation time of the viscoelastic material to the characteristic time of the material passing through the contact, and the ratio of the two elastic limits of the SLS viscoelastic material.