Réduction de modèle pour un problème non-linéaire avec interfaces multiples : application à la modélisation de câbles d'ancrage

The employment of high fidelity simulators in industrial application still remain nowadays limited by their computational cost, in particular for the optimization of structure design and reliability assessment. To overcome this situation, several reduced order modeling (ROM) techniques have been developed. They aim to project the partial differential equation of the problem onto a reduced basis, reducing the computational cost by several order of magnitudes, all the more that dimensions in space, time or other parameters increase. 
This thesis will study the application of different ROM approaches to a non-linear problem with multiple interfaces, focusing on the study case of a steel wire rope in tension and bending. This problem requires to simulate the complicated evolution of contact and friction conditions among the rope wires. A finite element model of this study case was developed in [1.], to simulate efficiently the loading on a part of a mooring line of a floating wind turbine for a given sea state. A dedicated contact and friction model, assuming small sliding and finite rotations of beams representing the rope wires, succeeds to capture the wire mechanics with a reduced computational cost when compared to a large sliding algorithm. 
Considering first a small set of tension and bending, associated to a collection of several sea states, this thesis will try to gain more CPU cost reduction with different techniques: 
-    an “a posteriori” ROM determining the reduced basis in a preliminary learning stage with a greedy algorithm, 
-    and an “a priori” Proper Generalized Decomposition determining the reduced basis during the non-linear solver iterations. 
A key constraint of the reduction will be to keep enough critical information localized on the interfaces. Indeed, apart from particular environmental condition like corrosion, steel wire rope fatigue is largely determined by fretting fatigue resulting from friction variation among contacting wires. Considering the multi-scale spatial characteristics of the problem, with structure global modes and interface local modes, a domain decomposition method framework will be examined to improve performance. A starting point could be the non-intrusive implementation of the LATIN solver in Code_Aster of [2.]. 
A demonstration of the reduction will be finally illustrated by extending the dimension to sea loading parameters, to improve the fatigue life assessment of a floating wind turbine mooring system. 
[1.]    Bussolati, F. (2019). « Modèle multi-échelle de la fatigue des lignes d'ancrage câblées pour l'éolien offshore flottant». Thèse de doctorat,. ENS Paris-Saclay. 
[2.]    P. Oumaziz (2018). « Une méthode de décomposition de domaine mixte non-intrusive pour le calcul parallèle d’assemblages ». Thèse de doctorat, Université Paris-Saclay.  
 

Keywords: Base réduite, éléments finis, contact, frottement, non-linéaire