Short note: Transformation between different solution methods for general axisymmetric tangential contact problems in Hertz-Mindlin approximation

TL;DR

This paper demonstrates the equivalence and transformation between Jäger's superposition solution and the method of dimensionality reduction for axisymmetric tangential contact problems under Hertz-Mindlin assumptions, facilitating solution conversion.

Contribution

It introduces a method to convert between two different solution procedures for axisymmetric tangential contact problems, enhancing understanding and computational flexibility.

Findings

Unified framework for solution transformation

Explicit relation between superposition weights and MDR displacements

Applicability to finite and infinite superpositions

Abstract

The transition between two conceptionally different solution procedures for general axisymmetric tangential contact problems with arbitrary laoding histories under Hertz-Mindlin assumptions is demonstrated, namely J\"ager's superposition solution and the method of dimensionality reduction. Both finite and ininite superpositions of Cattaneo-Mindlin basis functions are considered. It is shown how the weights in the superposition solution can be easily obtained from the displacements in the MDR model.