1. Introduction

The goal of this book is to describe the method of dimensionality reduction in contact mechanics and friction. Contacts between three-dimensional bodies arise in a wide variety of applications. Therefore, their simulation, both analytically and numerically, are of major importance. From a mathematical point of view, contacts are described using integral equations having mixed boundary conditions. Furthermore, the stress distribution, the displacements of the surface, and even the shape of the contact domain are generally not known in such problems. It is, therefore, astounding that a large number of classical contact problems can be mapped to one-dimensional models of contacts with a properly defined linearly elastic foundation (Winkler foundation). This means that the results of the one-dimensional model correspond exactly to those of a three-dimensional model. According to this mapping concept, solving contact-mechanical problems is trivialized is such a way as to require no special knowledge other than the fundamentals of algebra and calculus.