Abstract
For a wide class of “typical tribological systems,” there are a number of properties that allow for the significant simplification of contact problems and, in this way, make fast calculations of multi-scalar systems possible. These simplified properties, which are used by the method of dimensionality reduction, include (1) the ability to separate the elastic and inertial properties in three-dimensional systems and (2) the close analogy between three-dimensional contacts and certain one-dimensional problems. The first of these will be discussed in this chapter, while further chapters are dedicated to the second one.
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Notes
- 1.
Definition of the material parameter E see next chapter.
References
H. Hertz, Über die Berührung fester elastischer Körper. J. für die reine und angewandte Mathematik 92, 156–171 (1881)
V.L. Popov, Contact Mechanics and Friction. Physical Principles and Applications (Springer-Verlag 2010), p. 362
L.D. Landau, E.M. Lifschitz, Elastizitätstheorie, (Lehrbuch der Theoretischen Physik, Band VII). 7., überarb. Auflage, Akademie Verlag (Berlin 1991), §§ 8, 9
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Popov, V.L., Heß, M. (2015). Separation of the Elastic and Inertial Properties in Three-Dimensional Systems. In: Method of Dimensionality Reduction in Contact Mechanics and Friction. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53876-6_2
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DOI: https://doi.org/10.1007/978-3-642-53876-6_2
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