Valentin L. Popov, Emanuel Willert, Markus Heß

DOI Number
First page
Last page


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.


Contact, Friction, Viscoelasticity, Rheology, Method of Dimensionality Reduction

Full Text:



Popov, V.L., Heß, M., 2015, Method of dimensionality reduction in contact mechanics and friction, Springer, Berlin Heidelberg.

Argatov, I.I., Heß, M., Pohrt, R., Popov, V.L., 2016, The extension of the method of dimensionality reduction to non-compact and non-axisymmetric contacts, ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 96(10), pp. 1144-1155.

Willert, E., Popov, V.L., 2017, Exact one-dimensional mapping of axially symmetric elastic contacts with superimposed normal and torsional loading, ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 97(2), pp. 173-182.

Heß, M., 2016, A simple method for solving adhesive and non-adhesive axisymmetric contact problems of elastically graded materials, International Journal of Engineering Science, 104, pp. 20-33.

Heß, M., Popov, V.L., 2016, Method of Dimensionality Reduction in Contact Mechanics and Friction: A User’s Handbook. II. Power-Law Graded Materials, Facta Universitatis-Series Mechanical Engineering, 14(3), pp. 251-268.

Argatov, I.I., Popov, V.L., 2016, Rebound indentation problem for a viscoelastic half-space and axisymmetric indenter – Solution by the method of dimensionality reduction, ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 96(8), pp. 956-967.

Kürschner, S., Filippov, A.E., 2012, Normal contact between a rigid surface and a viscous body: Verification of the method of reduction of dimensionality for viscous media, Physical Mesomechanics, 15(5-6), pp. 270-274.

Willert, E., Popov, V.L., 2018, Short note: Method of Dimensionality Reduction for compressible viscoelastic media. I. Frictionless normal contact of a Kelvin-Voigt solid, ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 98(2), pp. 306-311.

Popov, V.L., Heß, M., 2014, Method of Dimensionality Reduction in Contact Mechanics and Friction: A Users Handbook. I. Axially-Symmetric Contacts, Facta Universitatis-Series Mechanical Engineering, 12(1), pp. 1-14.

Popov, V.L., 2017, Contact Mechanics and Friction. Physical Principles and Applications, 2nd Edition, Springer, Berlin Heidelberg.

Popov, V.L., Heß, M., Willert, E., 2018, Handbuch der Kontaktmechanik – Exakte Lösungen axialsymmetrischer Kontaktprobleme, Springer, Berlin Heidelberg.

Lee, E.H., Radok, J.R.M., 1960, The Contact Problem for Viscoelastic Bodies, Journal of Applied Mechanics, 27(3), pp. 438-444.

Willert, E., Kusche, S., Popov, V.L., 2017, The influence if viscoelasticity on velocity-dependent restitutions in the oblique impact of spheres, Facta Universitatis-Series Mechanical Engineering, 15(2), pp. 269-284.

Greenwood, J.A., 2010, Contact between an axisymmetric indenter and a viscoelastic half-space, International Journal of Mechanical Sciences, 52(6), pp. 829-835.



  • There are currently no refbacks.

ISSN: 0354-2025 (Print)

ISSN: 2335-0164 (Online)

COBISS.SR-ID 98732551

ZDB-ID: 2766459-4