Method of Dimensionality Reduction in Contact Mechanics: User’s Manual

Valentin L. Popov · Markus Hess · Emanuel Willert

ago 2018 · Technische Universität Berlin, Department of System Dynamics and Friction Physics

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The present book is a collection of open-access papers describing the foundations and applications of the Method of Dimensionality Reduction (MDR), first published in the Journal “Facta Universitatis. Series Mechanical Enginerring” in the years 2014-2018.

The Method of Dimensionality Reduction (MDR) is a method of calculation and simulation of contacts of elastic and viscoelastic bodies. It consists essentially of two simple steps: (a) substitution of the three-dimensional continuum by a uniquely defined one-dimensional linearly elastic or viscoelastic foundation (Winkler foundation) and (b) transformation of the three-dimensional profile of the contacting bodies by means of the MDR-transformation. As soon as these two steps are done, the contact problem can be considered to be solved. For axial symmetric contacts, only a small calculation by hand is required which does not exceed elementary calculus and will not be a barrier for any practically-oriented engineer. Alternatively, the MDR can be implemented numerically, which is almost trivial due to the independence of the foundation elements. In spite of its simplicity, all results are exact. The present book brings together papers covering the most important aspects of the MDR and providing a practical guide for its use.

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Prof. Dr. rer. nat. Valentin L. Popov studied physics (1976-1982) and obtained his doctorate in 1985 from the Moscow State Lomonosov University. He worked at the Institute of Strength Physics of the Russian Academy of Sciences. After a guest-professorship in the field of theoretical physics at the University of Paderborn (Germany) from 1999 to 2002, he has headed since 2002 the department of System Dynamics and the Physics of Friction in the Institute of Mechanics at the Berlin University of Technology.

Dr. Markus Heß studied Engineering Science at TU Berlin. He obtained his doctorate in 2011 and in the same year received the research award from the Tribology Society for his dissertation.  From 2011 to 2015 he headed the physics department of the preparatory college of the TU Berlin and since 2015 he has been working as an assistant professor in the department of System Dynamics and Friction Physics.

M.Sc. Emanuel Willert studied Engineering Science at the TU Berlin and the Polytechnical University Tomsk. Since 2015 he has been active as a research assistant in the department of System Dynamics and Friction Physics. He is co-author of “Handbuch der Kontaktmechanik” – Springer, 2018.