Cable isogeometric analysis with bending, torsion, and contact with Coulomb friction

We present a cable isogeometric analysis method based on the Kirchhoff–Love beam theory coupled with Coulomb friction. In simulation of cable entanglement, twist plays a key role. Isogeometric rotation-free bending-stabilized cable formulations are attractive in that they can incorporate bending effects without introducing additional rotational degrees of freedom. However, since the cross-sectional orientation is entirely determined by the centerline geometry, such formulations inherently lack torsional degrees of freedom. As a result, they are unable to represent twisting behavior and cannot properly account for cross-sectional orientation, and that limits their applicability to problems involving pre-bent configurations or geometries with non-axisymmetric cross sections. This limitation is particularly significant in the presence of frictional contact, where tangential forces acting on the cable surface naturally induce torsional effects. Therefore, a formulation that can account for torsion is essential for accurately capturing the resulting mechanical response. One possible approach in incorporating torsional effects is to employ beam models with rotational degrees of freedom, such as the Kirchhoff–Love beam model, which has been widely used in classical finite element formulations. Isogeometric implementations of such beam models have also been proposed in the literature. In this work, rather than introducing additional complexity into the beam formulation itself, we revisit the classical Kirchhoff–Love theory and provide a concise and consistent formulation within the isogeometric framework. Our focus is on the coupling with Coulomb friction, enabling an accurate representation of contact behavior with torsional effects. We present test computations with contact between a rigid body and an inclined rigid plane and between a flexible cable and an inclined rigid cable. In both problems, the tests cover the frictionless, stick, and slip cases. The results show the accuracy and robustness of the cable isogeometric analysis method presented.