Numerics of Unilateral Contacts and Friction : Modeling and Numerical Time Integration in Non-Smooth Dynamics

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.

This book is especially suited for people both in research and industry who are interested in the numerical simulation of mechanical systems with unilateral contacts and friction. Such systems can be found in various fields of technical application; consider for example contacts between wheels and ground in vehicle dynamics, walking machines, limit stops and friction in arbitrary kind of mechanisms or contacts between thousands of grains in granular mechanics. The book focuses mainly on rigid multibody systems dynamics with unilateral contacts and friction, however, the proposed non-smooth modeling approach is much more general and also well suited for non-rigid applications.

Four main topics are addressed:

• Non-smooth modeling of unilateral contacts and friction by set valued force laws,
• Mathematical evaluation of these laws using normal cone inclusions with associated projective equations,
• Numerical time-stepping integration methods for non-smooth systems,
• Implementation in a software code.

The book closes the gap between highly specialized mathematical literature and engineering application, gives an excellent overview on well established methods in non-smooth mechanics and opens new perspectives for the future development in this promising field of active research.