The context of this paper concerns the simulation of the complex evolution of contact and friction con- ditions between the wires of mooring line ropes for floating offshore wind turbines to accurately predict their fatigue life. In order to deal with the strong non-linearity of the problem and the high compu- tational times required, the non-linear LATIN solver and model-order reduction based on the Proper Generalized Decomposition (PGD) are proposed to solve the problem. In this context a one-dimensional benchmark problem, representative of the problem at hand, is analyzed within the LATIN-PGD frame- work: first different convergence indicators for the LATIN solver are proposed in order to check and assure convergence of local contact interface quantities, crucial for fatigue life determination. Then the reducibility of the problem is investigated, focusing on efficiently sorting and controlling the reduced basis size and quality throughout the iterations of the non-linear solver.