Basic ideas and applications of the method of reduction of dimensionality in contact mechanics

The method of reduction of dimensionality in contact mechanics is based on a mapping of some classes of three-dimensional contact problems onto one-dimensional contacts with elastic foundations. Recently, a rigorous mathematical proof of the method has been provided for contacts of arbitrary bodies of revolution with and without adhesion. The method of reduction of dimensionality has been further verified for randomly rough surfaces. The present paper gives an overview of the physical foundations of the method and of its applications to elastic and viscoelastic contacts with adhesion and friction. Both normal and tangential contact problems are discussed.