An analytical solution of the rebound indentation problem for an isotropic linear viscoelastic layer loaded with a spherical punch

Abstract

A unilateral frictionless axisymmetric contact problem for an isotropic viscoelastic layer attached to a rigid substrate and loaded with a spherical indenter is considered. It is assumed that the indentation protocol is composed of two stages. In the indentation phase, the layer is subjected to displacement loading, while at the end of the first stage, the load is immediately removed and the second stage, called the recovery phase, lasts for a theoretically indefinite time. Under the assumption of time-independent Poisson’s ratio, we derive closed-form analytical expressions for the contact force (in the indentation phase) and for the indentation displacement (in the the recovery phase). The obtained closed-form analytical solution is valid for the indentation phase with an arbitrary monotonic loading displacement and can be used for evaluation of the rebound indentation test for soft biological tissues and originally suggested for assessment of articular cartilage viability.