  The paper proposes an approach for the efficient model order reduction of
dynamic contact problems in linear elasticity. Instead of the augmented
Lagrangian method that is widely used for mechanical contact problems, we
prefer here the Linear Complementarity Programming (LCP) method as basic
methodology. It has the advantage of resulting in the much smaller dual problem
that is associated with the governing variational principle and that turns out
to be beneficial for the model order reduction. Since the shape of the contact
zone depends strongly on the acting outer forces, the LCP for the Lagrange
multipliers has to be solved in each time step. The model order reduction
scheme, on the other hand, is applied to the large linear system for the
displacements and computed in advance by means of an Arnoldi process. In terms
of computational effort the reduction scheme is very appealing because the
contact constraints are fully satisfied while the reduction acts only on the
displacements. As an extension of our approach, we furthermore take up the idea
of the Craig-Bampton method in order to distinguish between interior nodes and
the nodes in the contact zone. A careful performance analysis closes the paper.
