Finite Element Solutions to the Bending Stiffness of a Single-Layered Helically Wound Cable With Internal Friction

This paper is focused on the bending stiffness of a cable consisting of a straight core wound around by a layer of helical wires, taking friction into account. Depending on the interaction between the cable components, the effective bending stiffness of the cable lies between an upper bound B_max and a lower bound B_min according to analytic models in literature. Two finite element models are created. The first aims to determine the maximum obtainable bending stiffness, whereby two contact types are tested: one bonding together all the touching surfaces and the other one only bonding together the wire–core contact surfaces. The numerical results show that B_max is achieved for the first contact type, while neglecting the wire–wire contact lowers the bending stiffness due to the rotation of wire cross sections. In the second model, the wires are allowed to slip, while the cable is subjected to tension and bending. The effects of the tension level, the friction coefficient, and the contact types are investigated. The numerical results are able to capture the increase of bending stiffness with increasing tension and decreasing curvature, consistent with experimental observations and analytic models. The initial bending stiffness is sensitive to the imperfect contact between the components and is lower than B_max. The final bending stiffness is higher than B_min because of the contribution of friction and it increases with the friction coefficient.