A Small-Sliding Beam-to-Beam Contact Formulation For The Fatigue Estimate Of Spiral Strand Wire Ropes
Résumé
Fatigue life prediction of spiral strand wire ropes used for instance in mooring systems of floating off- shore wind turbines is a challenging issue. Accounting for dissipation mechanisms such as frictional phenomena among wires is a key factor but generally leads to costly simulations. A common modeling assumption consists in using beam finite elements to model each wire combined with a beam-to-beam contact formulation [1]. However, even though wire ropes may undergo large displacements/rotations, a finite-sliding tracking formulation is still time-consuming and often unnecessary.
In this work, a small-sliding tracking approach is chosen for the contact of non parallel beams with circular cross-section. In spiral strand wire ropes, such pointwise contacts occur between adjacent layers of wires with different lay angles. Contacting wires can undergo only relatively small sliding relative to each other, but large displacements/rotations of the beams are permitted. Initial contact locations in the undeformed model configuration can be easily determined by straightforward geometrical operations from the nominal geometry. Beam meshes can be defined accordingly in order to locate mesh nodes at these locations. Under small-sliding assumption, one assumes that beams remain locally straight in the potential contact’s vicinity. In this case, the contact normal can be defined from the cross product of beam tangent directors at the initial “master” contacting nodes and directly updated according to the rotation vectors at these master nodes. This results in a smooth variation of the contact normal which is crucial in the targeted applications.
This small-sliding contact formutation is implemented as a two-node user-element in commercial code Abaqus v6.14 [2]. Numerical benchmarks and a tension-bending test on a multilayer wire rope are presented in order to evaluate the accuracy and the efficiency of the approach.
REFERENCES
[1] Lalonde, S., Guilbault, R., and Le ́geron, F. Modeling multilayered wire strands, a strategy based on 3D finite element beam-to-beam contacts – Part I: Model formulation and validation. Int. J. of Mech. Sci. (2017), 126:281–296.
[2] Bussolati, F., Guidault, P.-A., Guiton, M.L.E., Allix, O., Wriggers, P. Robust contact and friction model for the fatigue estimate of a wire rope in the mooring line of a Floating Offshore Wind Turbine. Virtual Design and Validation, Lect. Notes Appl. Comp.Mech., Springer, (2020), 93:249–270.