This application-oriented book introduces readers to the associations and relationships between contact mechanics and friction, providing them with a deeper understanding of tribology. It addresses the related phenomena of contacts, adhesion, capillary forces, friction, lubrication, and wear from a consistent point of view. The author presents (1) methods for rough estimates of tribological quantities, (2) simple and general methods for analytical calculations, and (3) the crossover into numerical simulation methods, the goal being to convey a consistent view of tribological processes at various scales of magnitude (from nanotribology to earthquake research). The book also explores the system dynamic aspects of tribological systems, such as squeal and its suppression, as well as other types of instabilities and spatial patterns. It includes problems and worked-out solutions for the respective chapters, giving readers ample opportunity to apply the theory to practical situations and to deepen their understanding of the material discussed. The second edition has been extended with a more detailed exposition of elastohydrodynamic lubrication, an updated chapter on numerical simulation methods in contact mechanics, a new section on fretting in the chapter on wear, as well as numerous new exercises and examples, which help to make the book an excellent reference guide.

The English edition of “Contact Mechanics and Friction” lying before you is, for st the most part, the text of the 1 German edition (Springer Publishing, 2009). The book was expanded by the addition of a chapter on frictional problems in ear- quake research. Additionally, Chapter 15 was supplemented by a section on elasto-hydrodynamics. The problem sections of several chapters were enriched by the addition of new examples. This book would not have been possible without the active support of J. Gray, who translated it from the German edition. I would like to thank Prof. G. G. - charyan and Prof. S. Sobolev for discussions and critical comments on the chapter over earthquake dynamics. Dr. R. Heise made significant contributions to the - velopment and correction of new problems. I would like to convey my affecti- ate thanks to Dr. J. Starcevic for her complete support during the composition of this book. I want to thank Ms. Ch. Koll for her patience in creating figures and Dr. R. Heise, M. Popov, M. Heß, S. Kürscher, and B. Grzemba for their help in pro- reading. Berlin, November 2009 V.L. Popov Preface to the German Edition

This book describes for the first time a simulation method for the fast calculation of contact properties and friction between rough surfaces in a complete form. In contrast to existing simulation methods, the method of dimensionality reduction (MDR) is based on the exact mapping of various types of three-dimensional contact problems onto contacts of one-dimensional foundations. Within the confines of MDR, not only are three dimensional systems reduced to one-dimensional, but also the resulting degrees of freedom are independent from another. Therefore, MDR results in an enormous reduction of the development time for the numerical implementation of contact problems as well as the direct computation time and can ultimately assume a similar role in tribology as FEM has in structure mechanics or CFD methods, in hydrodynamics. Furthermore, it substantially simplifies analytical calculation and presents a sort of “pocket book edition” of the entirety contact mechanics. Measurements of the rheology of bodies in contact as well as their surface topography and adhesive properties are the inputs of the calculations. In particular, it is possible to capture the entire dynamics of a system – beginning with the macroscopic, dynamic contact calculation all the way down to the influence of roughness – in a single numerical simulation model. Accordingly, MDR allows for the unification of the methods of solving contact problems on different scales. The goals of this book are on the one hand, to prove the applicability and reliability of the method and on the other hand, to explain its extremely simple application to those interested.

Tribology is the science of friction, lubrication and wear of moving components. Results obtained from tribology are used to reduce energy losses in friction pro cesses, to reduce material losses due to wear, and to increase the service life of components. Contact Mechanics plays an important role in Tribology. Contact Mechanics studies the stress and strain states of bodies in contact; it is contact that leads to friction interaction and wear. This book investigates a variety of contact problems: discrete contact of rough surfaces, the effect of imperfect elasticity and mechanical inhomogeneity of contacting bodies, models of friction and wear, changes in contact characteristics during the wear process, etc. The results presented in this book were obtained during my work at the Insti tute for Problems in Mechanics of the Russian Academy of Sciences. The first steps of this research were carried out under the supervision of Professor L. A. Galin who taught me and showed me the beauty of scientific research and solutions. Some of the problems included in the book were investigated together with my col leagues Dr. M. N. Dobychin, Dr. O. G. Chekina, Dr. I. A. Soldatenkov, and Dr. E. V. Tor skaya from the Laboratory of Friction and Wear (IPM RAS) and Prof. F. Sadeghi from Purdue University (West Lafayette, USA). I would like to express my thanks to them. I am very grateful to Professor G. M. L.

This book describes the solution of contact problems with an emphasis on idealized (mainly linear) elastic problems that can be treated with elementary analytical methods. General physical and mathematical features of these solutions are highlighted. Topics covered include the contact of rough surfaces and problems involving adhesive (e.g. van der Waals) forces. The author is a well-known researcher in the subject with hands-on experience of the topics covered and a reputation for lucid explanations. The target readership for the book includes researchers who encounter contact problems but whose primary focus is not contact mechanics. Coverage is also suitable for a graduate course in contact mechanics and end-of-chapter problems are included.

This treatise is concerned with the stresses and deformation of solid bodies in contact with each other, along curved surfaces which touch initially at a point or along a line. Examples are a railway wheel and rail, or a pair of gear wheel teeth. Professor Johnson first reviews the development of the theory of contact stresses since the problem was originally addressed by H. Hertz in 1882. Next he discusses the influence of friction and the topographical roughness of surfaces, and this is incorporated into the theory of contact mechanics. An important feature is the treatment of bodies which deform plastically or viscoelastically. In addition to stationary contact, an appreciable section of the book is concerned with bodies which are in sliding or rolling contact, or which collide.

This proceedings volume contains 66 papers presented at the second "Contact Mechanics International Symposium" held in Carry-Le-Rouet. France. from September 19th to 23rd. 1994, attended by 110 participants from 17 countries. This symposium was the continuation of the first CMIS held in 1992 in Lausanne. of the Symposium Euromech 273 "Unilateral Contact and Dry Friction" held in 1990 in La Grande Motte. France. and of the series of "Meetings on Unilateral Problems in Structural Analysis" organized in Italy. every other year. during the eighties. The primary purpose of the symposium was to bring specialists of contact mechanics together in order to draw a representative picture of the state of the art and to identify new trends and new features in the field. In view of the contributions made. one may assert that the mechanics of contact and friction has now reached a stage where the foundations are clear both from the mathematical and from the computational standpoints. Some of the difficulties met may be identified by saying that frictional contact is governed by resistance laws that are non smooth and whose flow rule is not associated with the yield criterion through the traditional normality property.

This book provides an updated review on the development of scanning probe microscopy and related techniques, and the availability of computational techniques not even imaginable a few decades ago. The 36 chapters cover instrumental aspects, theoretical models and selected experimental results, thus offering a broad panoramic view on fundamental issues in nanotribology which are currently being investigated. Compared to the first edition, several topics have been added, including triboluminescence, graphene mechanics, friction and wear in liquid environments, capillary condensation, and multiscale friction modeling. Particular care has been taken to avoid overlaps and guarantee the independence of the chapters. In this way, our book aims to become a key reference on this subject for the next five to ten years to come.

Fundamentals of Friction, unlike many books on tribology, is devoted to one specific topic: friction. After introductory chapters on scientific and engineering perspectives, the next section contains the necessary background within the areas of contact mechanics, surfaces and adhesion. Then on to fracture, deformation and interface shear, from the macroscopic behavior of materials in frictional contact to microscopic models of uniform and granular interfaces. Lubrication by solids, liquids and gases is presented next, from classical flow properties to the reorganization of monolayers of molecules under normal and shear stresses. A section on new approaches at the nano- and atomic scales covers the physics and chemistry of interfaces, an array of visually exciting simulations, using molecular dynamics, of solids and liquids in sliding contact, and related AFM/STM studies. Following a section on machines and measurements, the final chapter discusses future issues in friction.

Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.