  The paper presents a new reduction method designed for dynamic contact
problems. Recently, we have proposed an efficient reduction scheme for the
node-to-node formulation, that leads to Linear Complementarity Problems (LCP).
Here, we enhance the underlying contact problem to a node-to-segment
formulation. Due to the application of the dual approach, a Nonlinear
Complementarity Problem (NCP) is obtained, where the node-to-segment condition
is described by a quadratic inequality and is approximated by a sequence of
LCPs in each time step. These steps are performed in a reduced approximation
space, while the contact treatment itself can be achieved by the Craig-Bampton
method, which preserves the Lagrange multipliers and the nodal displacements at
the contact zone. We think, that if the contact area is small compared to the
overall structure, the reduction scheme performs very efficiently, since the
contact shape is entirely recovered. The performance of the resulting reduction
method is assessed on two 2D computational examples
