Contact dynamics with large deformations
Projektleiter:  Prof. Dr. rer. nat. B.I. Wohlmuth 
Projektbearbeiter:  Dr. S. Hüeber 
Initial Situation
Contact problems with nonlinear material laws and Coulomb friction
play important role in
many engineering and technical applications.
The main key is the construction of efficient algorithms for this
highly nonlinear problem.
To simulate such type of problems,
nonconforming discretization techniques for the linear problem
statement based on the Lagrange multipliers with dual shape
functions were
developed within the leaked Collaborative Research Center 404
at the University of Stuttgart In the bygone years.
Optimal a priori error estimates were established
for the resulting weak variational formulations.
Furthermore, efficient algorithms to solve the arising nonlinear
algebaic system based on semismooth Newton methods were developed.
For the frictionless case these methods can be equivalently
interpreted as primaldual active set strategies.
The main focus was the handling of the frictional problem with
Coulomb's friction law in the threedimensional setting.
A semismooth Newton algorithm with a superlinear convergence
behavior was developed for this highly nonlinear situation.
Current Results
We extend the above mentioned algorithms to contact dynamics
in combination with nonlinear materials as neoHookean or more
general MooneyRivlin laws.
Since the contact constraints are
treated by a semismooth Newton method it is quite natural to handle
both nonlinearities, the contact and the material ones, in one iteration loop.
We show, that for the formulation of the Newton system with respect
to the new constrained basis, the same modifications
as in the linear case have to be applied
to the original system with respect to the standard basis.
Thus, existing finite element codes can be easily
generalized to our algorithms.
For the dynamical prozess focus on
energyconserving timediscretization algorithms.
We use the method by Gonzales as
an algorithmic energyconserving scheme.
This methods conserves not only the energy but also
the linear and the angular momentum.
To avoid spurious osciallations in the Lagrange multiplier
we use a sligthly modified mass matrix. This matrix can be
interpreted as lumped version of the original one
whereas the mass lumping is only applied at the
possible contact region.
Dynamical contact problem with neoHookean material and Coulomb friction

Dynamical contact problem with neoHookean material: without friction (left) and Coulomb friction (right)
