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Method of dimensionality reduction in contact mechanics and friction

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Method of Dimensionality Reduction in Contact Mechanics and Friction

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.


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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.