Rebound indentation problem for a viscoelastic half-space and axisymmetric indenter - Solution by the method of dimensionality reduction

TL;DR

This paper extends the method of dimensionality reduction to solve the rebound indentation problem for a viscoelastic half-space with an axisymmetric indenter, providing a shape-independent analytical solution for the displacement during recovery.

Contribution

The paper introduces an extended MDR approach for viscoelastic contact problems with arbitrary axisymmetric indenters, including a detailed solution for rebound indentation.

Findings

Closed-form analytical solution for rebound displacement

Solution independence from indenter shape

Application to viscoelastic half-space contact problems

Abstract

The method of dimensionality reduction (MDR) is extended for the axisymmetric frictionless unilateral Hertz-type contact problem for a viscoelastic half-space and an arbitrary axisymmetric rigid indenter under the assumption that an arbitrarily evolving in time circular contact area remains singly connected during the whole process of indentation. In particular, the MDR is applied to study in detail the so-called rebound indentation problem, where the contact radius has a single maximum. It is shown that the obtained closed-form analytical solution for the rebound indentation displacement (recorded in the recovery phase, when the contact force vanishes) does not depend on the indenter shape.