Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Stress Tensor and Gradient of Hydrostatic Pressure in the Contact Plane of Axisymmetric Bodies Under Normal and Tangential Loading

Version 1 : Received: 8 March 2020 / Approved: 10 March 2020 / Online: 10 March 2020 (03:22:49 CET)

A peer-reviewed article of this Preprint also exists.

Willert, E.; Forsbach, F.; Popov, V.L. Stress Tensor and Gradient of Hydrostatic Pressure in the Contact Plane of Axisymmetric Bodies under Normal and Tangential Loading. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 2020, 100, doi:10.1002/zamm.201900223. Willert, E.; Forsbach, F.; Popov, V.L. Stress Tensor and Gradient of Hydrostatic Pressure in the Contact Plane of Axisymmetric Bodies under Normal and Tangential Loading. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 2020, 100, doi:10.1002/zamm.201900223.

## Abstract

The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one-dimensional integrals.

## Keywords

stress state; pressure gradient; normal contact; tangential contact; friction; axial symmetry; method of dimensionality reduction

## Subject

Engineering, Mechanical Engineering