文档介绍：T. Belytschko, Contact-Impact, December 16, 1998 1
CHAPTER 10
CONTACT-IMPACT
by Ted Belytschko
Northwestern University
Copyright 1996
INTRODUCTION
This Chapter introduces the treatment of problems with contact and impact.
Many problems in the simulation of prototype tests and manufacturing processes involve
contact and impact. For example, in the simulation of a drop test on a product, the
various parts must be separated by so-called sliding interfaces which can model contact,
sliding and separation. In the simulation of manufacturing processes, sliding interfaces
are also important: the modeling of the surfaces between the die and workpiece in sheet
metal forming, the modeling of the tool-workpiece interface in machining, the modeling
of extrusion are some examples of where sliding interfaces are needed. In
crashworthiness simulation of automobiles, ponents, including the engine,
wheels, radiator, etc. can contact during the crash and their surfaces automatically must
be treated as sliding interfaces. The treatment of impact always requires a subsequent
treatment of contact, since bodies which impact will stay in contact until rarefaction
waves result in release.
In this Chapter, the governing equations and finite element procedures for
problems with contact-impact are introduced for Lagrangian meshes; the modeling of
contact with Eulerian meshes introduces difficulties which have not been resolved yet.
The governing equations for bodies in contact are identical to the equations introduced
previously, except that it is necessary to add the ic and kinematic conditions on the
contact interface. The key condition is the condition of rability: namely, the
condition that two bodies cannot rate. The general condition of rability
cannot be expressed as a useful equation, so several approaches to developing specialized
forms of these conditions have evolved. We will consider two of these forms: a rate form
which is useful for explicit dyn