Determination of the stress state beneath arbitrary axisymmetric tangential contacts in Hertz-Mindlin approximation based on the superposition of solutions for parabolic contact

TL;DR

This paper improves the method for calculating stress beneath axisymmetric tangential contacts by using superposition of solutions for parabolic contact, offering easier implementation and increased stability over flat-punch solutions.

Contribution

It demonstrates the use of parabolic contact solutions for stress analysis, enhancing numerical stability and simplicity compared to flat-punch approaches.

Findings

Superposition of parabolic contact solutions is effective for stress determination.

The method avoids stress singularities present in flat-punch solutions.

Numerical example confirms the method's applicability to power-law profiles.

Abstract

As an improvement to the recently proposed procedure for the determination of the stress state beneath axisymmetric tangential contacts in Hertz-Mindlin approximation via an appropriate superposition of solutions for the respective flat-punch problem, the determination via the superposition of solutions for parabolic contact is demonstrated. It has two advantages over the flat-punch formulation: the numerical implementation is slightly easier and more stable, due to the absence of stress singularities for the smooth parabolic profile. As a numerical example, the oscillating tangential contact between a rigid indenter with a profile in the form of a power-law (with exponent 4) and an elastic half-space is considered in detail.