Contact determination methods for nonsmooth time-stepping schemes

Xavier Merlhiot
Nonsmooth time-stepping schemes (see in [1] and [5] for recent surveys) are known to be powerful numerical tools for multibody dynamics with intermittent contacts modeled by nonsmooth laws. In order to form effective numerical methods, these schemes need to be coupled with contact determination algorithms, also referred to as collision detection methods. Many works on this second topic have been carried out by the computer graphics and robotics communities over the past two decades (see [3] and [6] for overviews). This talk adopts the point of view of computational mechanics to give an introduction to geometric contact determination methods and to their combination with nonsmooth time-stepping schemes, which may raise robustness or stability issues in many situations. Emphasis will be put on the numerical qualification of the contact constraints, as illustrated by the combination of the popular NSCD method [2] with the contact determination method introduced in [4]. Through application examples, the talk will also discuss the possible tradeoffs between efficiency and robustness for the complete coupled methods, and numerical strategies for interactive simulation contexts.

Lecture slides

[1] V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems, ser. Lecture Notes in Applied and Computational Mechanics. Springer, 2008, vol. 35.
[2] M. Jean, The Non-Smooth Contact Dynamics method, Computer Methods in Applied Mechanics and Engineering, vol. 177, pp. 235-257, 1999.
[3] S. Kockara,T. Halic, K. Iqbal, C. Bayrak and R. Rowe; Collision detection: A survey, Systems, Man and Cybernetics, 2007. ISIC. IEEE International Conference on, pp.4046-4051, 2007.
[4] X. Merlhiot, A robust, efficient and time-stepping compatible collision detection method for non-smooth contact between rigid bodies of arbitrary shape, in Proceedings of the Multibody Dynamics 2007 ECCOMAS Thematic Conference, 2007.
[5] C. Studer, Numerics of Unilateral Contacts and Friction, ser. Lecture Notes in Applied and Computational Mechanics. Springer, 2009, vol. 47.
[6] M. Teschner et al. Collision detection for deformable objects, Computer Graphics Forum, vol. 24, no. 1, pp. 61-81, 2005.