Numerics of Unilateral Contacts and Friction, 2009
Modeling and Numerical Time Integration in Non-Smooth Dynamics
Lecture Notes in Applied and Computational Mechanics Series, Vol. 47

Mechanics provides the link between mathematics and practical engineering app- cations. It is one of the oldest sciences, and many famous scientists have left and will leave their mark in this fascinating ?eld of research. Perhaps one of the most prominentscientists in mechanics was Sir Isaac Newton, who with his ?laws of - tion? initiated the description of mechanical systems by differential equations. And still today, more than 300 years after Newton, this mathematical concept is more actual than ever. The rising computer power and the development of numerical solvers for diff- ential equations allowed engineersall over the world to predict the behavior of their physical systems fast and easy in an numerical way. And the trend to computational simulation methods is still further increasing, not only in mechanics, but practically in all branches of science. Numerical simulation will probablynot solve the world?s engineering problems, but it will help for a better understanding of the mechanisms of our models.

Mathematical Preliminaries.- Non-Smooth Mechanics.- Inclusion Problems.- Time-Stepping.- Augmented Time-Stepping by Step Size Adjustment and Extrapolation.- The dynamY Software.- Summary.

Gives an excellent overview on well established methods in non-smooth mechanics Broad treatment of the subject including modeling, and evaluation of the contact problem, numerical time integration and implementation Closes a gap between highly specialized mathematical literature and engineering application