  In this work, we present a model order reduction technique for nonlinear
structures assembled from components.The reduced order model is constructed by
reducing the substructures with proper orthogonal decomposition and connecting
them by a mortar-tied contact formulation. The snapshots for the substructure
projection matrices are computed on the substructure level by the proper
orthogonal decomposition (POD) method. The snapshots are computed using a
random sampling procedure based on a parametrization of boundary conditions. To
reduce the computational effort of the snapshot computation full-order
simulations of the substructures are only computed when the error of the
reduced solution is above a threshold. In numerical examples, we show the
accuracy and efficiency of the method for nonlinear problems involving material
and geometric nonlinearity as well as non-matching meshes. We are able to
predict solutions of systems that we did not compute in our snapshots.
