  To be feasible for computationally intensive applications such as parametric
studies, optimization and control design, large-scale finite element analysis
requires model order reduction. This is particularly true in nonlinear settings
that tend to dramatically increase computational complexity. Although
significant progress has been achieved in the development of computational
approaches for the reduction of nonlinear computational mechanics models,
addressing the issue of contact remains a major hurdle. To this effect, this
paper introduces a projection-based model reduction approach for both static
and dynamic contact problems. It features the application of a non-negative
matrix factorization scheme to the construction of a positive reduced-order
basis for the contact forces, and a greedy sampling algorithm coupled with an
error indicator for achieving robustness with respect to model parameter
variations. The proposed approach is successfully demonstrated for the
reduction of several two-dimensional, simple, but representative contact and
self contact computational models.
