METHOD OF DIMENSIONALITY REDUCTION IN CONTACT MECHANICS AND FRICTION: A USERS HANDBOOK. I. AXIALLY-SYMMETRIC CONTACTS

Abstract 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 completed, 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 their simplicity, all the results are exact. The present paper is a short practical guide to the MDR. 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