On Applications of Semi-Analytical Methods of Contact Mechanics

Vladislav V Aleshin

doi:10.3389/fmech.2020.00030

Abstract

This paper is concerned with possible applications of semi-analytical methods of frictional contact mechanics. The semi-analytical solutions, such as the Method of Memory Diagrams, enables to write the load-displacement relationship for contact of two axisymmetric bodies with friction as an analytical expression with parameters calculated via a numerical procedure. As a result, a complex history-dependent solution is obtained for an arbitrary loading history in a computationally efficient way. This fact allows one to calculate hysteretic responses to extremely complex loading histories such as random vibrations. Another case when complex loading histories appear is a harmonic excitation of a dynamic contact system in which inertia is taken into account. The both examples are considered here. The random excitation case can be used as a basis for modeling for wear in frictional contacts while the second one may be extended to describe coupled dynamic contact systems, stick-slip phenomena, or friction-induced instabilities.

Highlights

This paper concerns the use of one semi-analytical method of frictional contact mechanics
To other semi-analytical methods in contact mechanics, the Memory Diagrams (MMD) can be regarded as a direct generalization of the classical Cattaneo-Mindlin (Cattaneo, 1938; Mindlin and Deresiewicz, 1953) solution developed for elastic spheres in contact loaded by a subsequent application of constant normal and tangential forces
Semi-analytical methods in frictional contact mechanics enable the efficient calculation of a hysteric tangential forcedisplacement relationship of an axisymmetric contact system for an arbitrary loading history

Summary

INTRODUCTION

This paper concerns the use of one semi-analytical method of frictional contact mechanics. To other semi-analytical methods in contact mechanics, the MMD can be regarded as a direct generalization of the classical Cattaneo-Mindlin (Cattaneo, 1938; Mindlin and Deresiewicz, 1953) solution developed for elastic spheres in contact loaded by a subsequent application of constant normal and tangential forces. As it was shown, the contact zone consists of stick and slip areas that represent a central circle, and outer annulus, respectively. For equal bodies with the elastic constants E and ν having the contact geometry as in Figure 1 (contact forces N and T, and displacements a and b, contact zone radius c, and stick zone radius s) the solution has the following form:

METHOD OF THE MEMORY DIAGRAMS

CONCLUSIONS AND PERSPECTIVES