Shillor M., Sofonea M., Telega J.J. Models and Analysis of Quasistatic Contact. Variational Methods

Springer-Verlag Berlin Heidelberg, 2004. — 263 p. — (Lecture Notes in Physics 655). — ISBN: 978-3-540-44643-9 (eBook), 978-3-642-06178-3 (Softcover), 978-3-540-22915-5 (Hardcover).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 presentsmany 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 tocurrent 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.Evolution Equations, Contact and Friction.
Additional E.ects Involved in Contact.
Thermodynamic Derivation.
A Detailed Representative Problem.
Mathematical Preliminaries.
Elastic Contact.
Viscoelastic Contact.
Viscoplastic Contact.
Slip or Temperature Dependent Frictional Contact.
Contact with Wear or Adhesion.
Contact with Damage.
Dynamic, One-Dimensional and Miscellaneous Problems.
Conclusions, Remarks and Future Directions.