Model reduction for nonlinear structural problems with multiple contact interfaces

Despite continuous progress in computational contact mechanics, simulating a complex structure with multiple frictional interfaces still requires a large computational cost due to multiple sources of nonlinearity: contact and friction status change, frictional dissipation, large sliding and finite deformations. This may induce limitations for industrial cases involving architectured materials such as spiral strand wire ropes with many wires in contact, often used in offshore engineering, which motivated this work.Among the alternative computational strategies to reduce calculation costs, an appealing one is to project the full-order problem on a reduced-order basis of the original problem through various model reduction techniques. However, their application to frictional problems remains an open question, especially for cases involving wide propagation of sliding/adhesion fronts.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 and naturally leads to a mixed domain decomposition method. 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 crucial point of the thesis is that the reduced model has to represent very faithfully the critical information located on the frictional interfaces between the wires, crucial for their fatigue life evaluation. The objective is to look for maximum reduction performances and convergence speed, while guaranteeing at the same time an accurate evaluation of the interface quantities. For this purpose, convergence criteria for the nonlinear solution method must assure a good convergence for local contact quantities. Moreover, a proper updating of the LATIN search directions can significantly increase the convergence speed. Finally, for highly irregular problems such as frictional contact problems, controlling the quality and size of progressively built PGD basis along the LATIN iterations is crucial for the efficiency of the method.