Numerical Methods in Contact Mechanics

Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems.
This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software.
Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided.

Contents:

1. Introduction to Computational Contact.
2. Geometry in Contact Mechanics.
3. Contact Detection.
4. Formulation of Contact Problems.
5. Numerical Procedures.
6. Numerical Examples.


About the Authors

Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricit? de France.

The book covers all basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes both for sequential and parallel computer architectures. The book is self-consistent and is intended for people working on implementation and improvement of contact algorithms in a finite element software. The book contains numerous examples and figures to make the material accessible for a broad audience.The book combines extended introductory parts with new developments, so it is accessible for freshmen in computational contact and is of interest for established researchers. Using a new tensor algebra, we introduce some original notions in contact kinematics and extend the classical formulation of contact elements. We discuss robust and efficient contact detection algorithms both for sequential and parallel computer architectures. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are given. Many validation problems and tests are presented.