Coupled effect of viscoelasticity and roughness scales on hysteretic friction in sliding periodic contact

This paper proposes a numerical approach to investigate the hysteretic friction phenomenon occurring in sliding contact of viscoelastic materials on rough surfaces. This formulation is implemented in both transient and steady-state regime assuming periodic contact: the rough surface is reduced to a representative unit-cell, which reduces computational effort as the contact is computed within a window of fixed dimensions. This work first investigates on the parameters that drive friction and confirms that the frequency ratio and the amplitude-to-wavelength ratio are of primary influence. This is particularly stressed when considering multi-scale surfaces with different levels of roughness. The transient formulation is then employed to investigate the evolution of the friction coefficient over time. We show that depending on contact conditions, friction can exhibit unusual non-monotonic behaviour, at times exceeding the steady-state asymptotic value.