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Erschienen in:
2015 | OriginalPaper | Buchkapitel
15. Coupling to the Microscale
verfasst von : Valentin L. Popov, Roman Pohrt, Markus Heß
Erschienen in: Method of Dimensionality Reduction in Contact Mechanics and Friction
Verlag: Springer Berlin Heidelberg
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Abstract
The application of the method of dimensionality reduction is, of course, limited to the spatial scales for which continuum mechanics can be used. Every practical application using the method will lose its validity even earlier, due to the finite spatial resolution of the surface topography. Therefore, it begs the question of whether the interactions on even smaller scales can be summarized into a microscopic “contact law” or “law of friction,” so that also the properties of the smallest possible scale can be taken into account in the simulation. In this chapter, we explain how the limitations of the finite spatial resolution can be eliminated by the introduction of a “microscopic” nonlinear stiffness.