La fonction principale des systèmes d'ancrage des éoliennes offshore flottantes est de limiter les mouvements du support. Les lignes d'ancrage qui les composent sont typiquement constituées de chaînes, de câbles aciers, de câbles synthétiques ou d'une combinaison de ces composants.Dans cette thèse, on se concentre sur les câbles en acier qui permettent de réduire le poids et d'augmenter la résistance en tension par rapport aux chaînes. Leur dimensionnement dépend des chargements en tension et flexion, liés aux mouvements du flotteur sous l'action de la mer et du vent.L'objectif de la thèse est le développement d'un nouveau modèle numérique pour prédire la durée de vie en fatigue des câbles d'ancrage d'une éolienne offshore flottante. Il doit notamment simuler les glissements relatifs entre les fils au cours d'une flexion du câble. Des résultats d'essais de tension-flexion de la littérature ont en effet montré que la première rupture est localisée près du plan neutre de flexion, où ces déplacements relatifs sont les plus grands. Cet effet majeur sur la durée de vie du câble n'est pas pris en compte par les lois de fatigue en tension-tension des normes de design offshore actuelles.Il faut aussi remarquer que l'utilisation d'un modèle détaillé de câble dans une démarche de dimensionnement à la fatigue représente un vrai défi. Le nombre élevé d'interactions de contact à modéliser, de l'ordre de plusieurs milliers par mètre de câble, et le grand nombre de cas de chargement rendent ce type de calculs très coûteux.Les chargements qui sont utilisés dans le modèle local de câble sont issus de calculs globaux réalisés à l'aide d'un logiciel multiphysique (Deeplines). Ce logiciel permet de simuler les conditions environnementales (vent, houle, courant) appliquées sur l'ensemble de la structure offshore.Nous montrons que le comportement non linéaire en flexion du câble, lié aux interactions de contact entre les fils, n'influence pas significativement les résultats du modèle global. Cette observation justifie une démarche de type descendante, les calculs globaux pouvant être réalisés en première étape. Les évolutions temporelles des tensions et courbures globales sont appliquées uniformément sur le fil central du modèle local du câble. La continuité du câble est représentée par des conditions de périodicité reliant les sections de bord à des points internes du modèle situés sur la même position circonférentielle. Les fils sont modélisés par des éléments poutres. On obtient les contraintes généralisées sur les fils, les forces de contact et les glissements relatifs. Des premières analyses ont montré que les déplacements relatifs entre les fils restent petits dans notre cadre d'application. Afin de réduire le coût calcul, nous avons développé un nouvel élément de contact entre poutres non parallèles, avec un appariement fixe de contact, dans l'hypothèse de petits glissements mais en grands déplacements et grandes rotations. Des tests numériques montrent l'amélioration obtenue, avec un résultat plus proche d'un modèle de référence qui considère un contact surfacique. De plus, le nouveau modèle réduit significativement le coût calcul et se montre plus robuste en convergence, ce qui s'avère crucial pour un calcul de fatigue. Les sorties du modèle local sont ensuite utilisées pour prédire un état de contrainte 3D, en exploitant des solutions analytiques de contact entre corps cylindriques. Finalement, un critère de fatigue multiaxial de la littérature est appliqué pour évaluer le risque en dommage. / The main function of mooring systems of floating offshore wind turbines is to ensure station keeping. The mooring lines can be composed of chains, wire ropes, synthetic ropes, or even a combination of them. In this thesis we focus on wire ropes, whose advantage over chain is to sustain high tension at a lower weight. Their design must consider the successive tension and bending loading induced by the floater movement for various wind and waves conditions.The thesis purpose is to develop a new numerical model, dedicated to the prediction of fatigue damage in mooring wire ropes of a floating wind turbine. In particular it has to simulate the relative movements between the wires when the rope is bent. Results from free-bending fatigue tests in the literature show the importance of these effects, since the first rupture is localized near the neutral plane, where fretting is more important. This phenomenon affecting the fatigue life is not considered by fatigue criteria of current offshore standards, which are related to tension-tension loading.It is worth noting that the use of a detailed model of wire rope in a fatigue design procedure represents a real challenge. The high number of contact interactions to be modeled, which are several thousands per meter of rope, and the large amount of loading cases make this type of computations extremely time-consuming.The loading used in the developed local model of wire rope is obtained from global computations performed with a dedicated multiphysics software (Deeplines). This software allows to simulate the environmental conditions (wind, waves, current) applied on the whole structural system.Some preliminary computations showed that the nonlinear bending behavior of the wire rope, linked to the wire contact interactions, does not significantly affect the output of the global model. This observation justifies the use of a top-down scheme, with a prior computation of the global scale.The global scale tension and curvature are then uniformly imposed on the central wire of the local model. The continuity of the rope is represented by periodic conditions which link the end sections to points within the model, at the same circumferential locations. The wires are modeled by beam elements. The outputs at the local scale are the stress resultants on the wires, and the contact forces and relative displacements at contact locations.Small sliding between the wires has been observed from first numerical analysis, for a representative loading case. Therefore, in order to reduce the computational cost of the wire rope model, a new node-to-node contact element has been developed, dedicated to the modeling of contact between non-parallel beams with circular cross section. It assumes fixed contact pairing and finite rotations. Numerical benchmarks and experimental tests on wire ropes show the improvement with results closer to a reference surface-to-surface model, when compared to standard algorithm for the simulation of contact between beams. Moreover, the new model reduces significantly the CPU cost and is also more robust, which is crucial for fatigue life estimates.The outputs of the local scale model are then used to obtain the complete 3D stress state by means of analytical solutions of contact between solids with cylindrical shape. Finally, a multiaxial fatigue criterion is applied in order to assess the safety of the system.

The primary aim of this research was to investigate the bending behaviour of helically wound steel cables of various types (i.e. normal spiral strands, sheathed spiral strands and locked coil cables) in the presence of friction and to propose more efficient computational models for their analysis under combined tension and bending. The proposed model fully takes into account interwire contact forces both in the radial direction (point contact between wires in different layers) and hoop direction (line contact within the wires in the same layer). Extensive theoretical parametric studies have been undertaken on a variety of cable constructions covering a wide range of geometrical and material parameters. Explicit formulations have been developed for the smooth transition of the bending stiffness from no-slip to full slip regimes, as a function of cable curvature. Based on these formulations, it is now possible to calculate the relative displacements of the wires, as well as the tensile, bending and hoop stresses in the individual wires of the cable. Furthermore, bending stiffness of the cable is shown to decrease by a factor of 2 to 16, depending upon the friction coefficient between wires and the type of cable construction. Wherever possible, the theoretical results have been compared with experimental results from the available literature and are found in very good agreement with them. A simple method for the determination of the bending stiffness of large diameter multi-layered cable has been developed. The simplified method is further shown to provide estimates of the bending stiffness which are very close to those calculated by the original theory, allowing hand calculations for an easier use in industry. The proposed formulations have been extended to cater for the effects of external hydrostatic pressure on sheathed spiral strands in deep water applications. These forces are shown to have a great influence on the pattern of interwire contact forces and hence the interlayer slippage between the wires in the strand. Numerical results have been obtained and analysed for three different 127 mm diameter strands with lay angles of 12°, 18° and 24° respectively, experiencing a wide range of external hydrostatic pressures of 0 to 2,000 metres. The significant increase in normal contact force between wires is shown to suppress the slippage of wires in the cable. However, the no-slip and full slip values of the effective bending stiffness of the cable is shown to be independent of the level of hydrostatic pressure. A theoretical model is also proposed for estimating wire kinematics, pattern of interwire slippage, contact forces as well as the flexural rigidity of locked coil cables with outer layers made of shaped wires. In order to validate this model, numerical results are reported for two different locked coil cables. It is shown that the shaped wires in the outer layers of locked coil cables play an important role in the distribution of contact forces, slip initiation and cable unwinding.