Method of Dimensionality Reduction in Contact Mechanics and Friction: A User’s Handbook. Iii. Viscoelastic Contacts

Abstract

Until recently the analysis of contacts in tribological systems usually required the solution of complicated boundary value problems of three-dimensional elasticity and was thus mathematically and numerically costly. With the development of the so-called Method of Dimensionality Reduction (MDR) large groups of contact problems have been, by sets of specific rules, exactly led back to the elementary systems whose study requires only simple algebraic operations and elementary calculus. The mapping rules for axisymmetric contact problems of elastic bodies have been presented and illustrated in the previously published parts of The User's Manual, I and II, in Facta Universitatis series Mechanical Engineering [5, 9]. The present paper is dedicated to axisymmetric contacts of viscoelastic materials. All the mapping rules of the method are given and illustrated by examples.

Wear Analysis of a Heterogeneous Annular Cylinder

“…The method of dimensionality reduction gives an exact solution of axially-symmetric contact problems [9,14], including the case of this annular cylinder with rings. In this study it will be used to quickly determine the stress distribution of a contact.…”

A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials

“…In a recent paper Argatov (2015) discusses the advantages and disadvantages of MDR. A summary of all the mapping rules of MDR related to the solution of axisymmetric contact problems can be found in a paper by Popov and Heß (2014) .…”

Simulation of Frictional Dissipation Under Biaxial Tangential Loading With the Method of Dimensionality Reduction

“…In the case of uni-axial in-plane loading, the contact problem can be reduced to a contact of a rigid plane profile with a series of independent springs. This method is known as the method of dimensionality reduction [5,6,11]. It replaces a contact between two continuum bodies with an ensemble of independent one-spring problems and thus reduces the general contact problem to the above one-spring problem (see Fig.…”

“…According to the MDR rules, the distribution of normal pressure p in the threedimensional problem may be calculated using the following integral transformation [11]:…”