On the Role of Roughness in the Indentation of Viscoelastic Solids

A numerical boundary element methodology is employed to understand how fractality intervenes when a 1D rigid rough profile indents a linear viscoelastic half-plane. The focus is, in particular, on the viscoelastic dissipation and how this is influenced by the profile statistical parameters, namely, the mean square roughness h(rms) of the profile, the mean square slope m(2) and the Hurst exponent H. Our numerical investigation, properly supported by a dimensional analysis, reveals that, in the one-dimensional case under investigation, the leading role is played by h(rms) and, thus, mainly by the large scales of the rough spectrum. Clearly, on an experimental level, this implies that a simple measure of the roughness parameter h(rms) is sufficient to determine the viscoelastic dissipation.