Finite Element Analysis of Nonsmooth Contact

1:30 PM-2:30 PM

*Room: Ballrooms I, II & III*

*Chair: Jerrold Marsden, California Institute of Technology*

The objective of this presentation is to describe the development of robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. These algorithms have many applications, for example to granular flows and to brittle solids undergoing fragmentation. Dynamic fragmentation often results in the formation of large numbers of fragments which undergo complex collision sequences before they eventually scatter. A robust and systematic procedure is therefore required in order to ascertain the precise sequence of collisions undergone by the bodies. The speaker will refer to contact processes such as described, involving the simultaneous interaction between many angular bodies, as nonsmooth contact.

A suitable mathematical framework for dealing with this class of
problems is furnished by nonsmooth analysis. However, it should be
noted that the admissible sets which arise in contact problems are
generally *nonconvex*, which precludes the direct application
of convex analysis. The speaker will discuss some algorithms in
simulations of fracture and fragmentation, and demonstrate their good performance.

**Michael Ortiz**

*Graduate Aeronautical Laboratories*

*California Institute of Technology*

*MMD, 2/9/99*