Three-dimensional steady-state indentation problem for a general viscoelastic material

The steady-state problem is considered for periodic normal loading by a smooth, rigid indentor on a half-space exhibiting general viscoelastic behaviour. A technique is developed for summing the infinite series that arise. The method is applicable to the case in which the viscoelastic behaviour is described by a discrete spectrum model, in other words, by a finite sum of decaying exponentials. Numerical results are presented for two decay times. The extension to any number of decay times is straightforward.