General procedure for solution of contact problems under dynamic normal and tangential loading based on the known solution of normal contact problem

TL;DR

This paper presents a general method to solve contact problems involving elastic bodies under dynamic normal and tangential loads by transforming them into equivalent indentation problems using known solutions, applicable to various shapes and loading histories.

Contribution

It introduces a universal procedure that transforms complex contact problems into simpler equivalent problems, leveraging known normal contact solutions for diverse geometries and loading conditions.

Findings

The method applies to axis-symmetric shapes using MDR integral transformation.

It extends to arbitrary shapes through numerical or experimental solutions.

The approach accommodates combined normal and tangential dynamic loading.

Abstract

In the present paper we show that the normal contact problem between two elastic bodies in the halfspace approximation can always be transformed to an equivalent problem of the indentation of a profile into an elastic Winkler foundation. Once determined, the equivalent profile can be used also for tangential contact problems and arbitrary superimposed normal and tangential loading histories as well as for treating of contact problems with linearly viscoelastic bodies. In the case of axis-symmetric shapes, the equivalent profile is given by the MDR integral transformation. For all other shapes, the profile is deduced from the solution of the elastic contact normal problem, which can be obtained numerically or experimentally.