The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.
Author(s): Meir Shillor, Mircea Sofonea, Józef Joachim Telega (auth.)
Series: Lecture notes in physics 655
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 2004
Language: English
Pages: 263
City: Berlin; New York
Tags: Mathematical Methods in Physics;Mathematical and Computational Physics;Mechanics;Physics and Applied Physics in Engineering;Continuum Mechanics and Mechanics of Materials
1 Introduction....Pages 1-6
2 Evolution Equations, Contact and Friction....Pages 9-29
3 Additional E.ects Involved in Contact....Pages 31-47
4 Thermodynamic Derivation....Pages 49-64
5 A Detailed Representative Problem....Pages 65-81
6 Mathematical Preliminaries....Pages 85-99
7 Elastic Contact....Pages 101-115
8 Viscoelastic Contact....Pages 117-134
9 Viscoplastic Contact....Pages 135-162
10 Slip or Temperature Dependent Frictional Contact....Pages 163-182
11 Contact with Wear or Adhesion....Pages 183-206
12 Contact with Damage....Pages 207-222
13 Dynamic, One-Dimensional and Miscellaneous Problems....Pages 225-234
14 Conclusions, Remarks and Future Directions....Pages 235-239
