On the benefits of a multiscale domain decomposition method to model-order reduction for frictional contact problems

In this paper, the efficiency of a multiscale strategy based on a domain decomposition method (DDM) for model-order reduction of time-dependent frictional contact problems is presented. The proposed strategy relies on the LArge Time INcrement (LATIN) nonlinear solver combined with model reduction based on the Proper Generalized Decomposition (PGD). The LATIN presents a robust treatment of contact conditions, sharing similarities with augmented Lagrangian approaches, and naturally leads to a mixed DDM. In addition, the global space-time formulation of the method allows PGD-based model reduction to be used during computations, creating and enriching on-the-fly reduced bases per substructure to better track sliding fronts and propagative phenomena. The introduction of a multiscale strategy in the LATIN framework is consistent with the physics of contact problems, in which phenomena with different wavelengths interact: local solutions at contact interfaces presents high gradient effects with a short wavelength compared to the characteristic length of the structure. By taking advantage of this, the coarse scale problem of the strategy enables to capture efficiently the behavior of the problem at the structural level, focusing then on capturing the local contact variations at the contact interfaces. The most important features of the approach are shown comprehensively on a simple one-dimensional frictional contact problem. Then, its robustness and effectiveness are tested on a two-dimensional multibody frictional contact problem with more complex loadings. Guidelines are also given for choosing the parameters of the strategy, in particular those driving the construction of the reduced basis.