Closed-form solution of axisymmetric contact problem for a viscoelastic base within cycle of increasing and decreasing of load on the indenter

Abstract

The axisymmetric contact problem for a spherical indenter and viscoelastic base has been considered within a cycle of increasing and decreasing of load. The loading-unloading cycle has been performed at a constant speed of indenter movment. The quasi-static approximation has been used. The study has been carried out according to linear viscoelasticity theory, while the material model allows one to take into account an arbitrary number of relaxation times. The dependence of load on the indenter on time has been defined. Expressions for determining the unknown boundary of the contact area in the loading–unloading process has been given. The hysteretic loop area at different values of the material relaxation time has been analyzed. The applicability of the offered analytical model of elastomer indentation experiments data processing has been discussed.