Three-dimensional beam-to-beam frictional contact with small-sliding and finite rotations

Abstract Stranded cables, composed of multiple twisted wires, exhibit high tensile strength and flexibility, making them essential in numerous industrial applications, such as mooring lines for offshore structures, overhead conductors, and cable-stayed bridges. The complex interactions between individual wire strands - primarily fretting-induced frictional contact and fatigue - pose significant challenges for numerical modeling. In this context, point-wise contact interactions between wires of different layers are often critical. This study presents a new beam-to-beam small-sliding point-wise contact element tailored for modeling stranded cables under small relative sliding conditions. Unlike traditional contact formulations, the proposed approach eliminates the need for repetitive, computationally expensive contact searches by assuming small sliding amplitudes between beams, which allows for predefined node pairing. The method, implemented within a large rotation wireframe finite element framework, offers enhanced computational efficiency and maintains robustness through a smooth evolution of the contact normal, thanks to nodal cross-sectional rotations. Numerical examples demonstrate the model’s effectiveness in handling arbitrary small sliding cases.