Beam-to-beam Frictional Contact Formulation with Small Sliding for Overhead Conductors Undergoing Large Rotations

Spiral strand wire ropes exhibit high tensile strength and flexibility making them essential in many applications such as mooring lines for offshore structures or overhead conductors. Simulation demand for these structures is high, particularly to evaluate their lifespan, the main source of damage usually coming from a combination of fretting between wires and fatigue. As such simulations require extensive calculations to account for multiple loading states, speed and accuracy of frictional contact models are crucial. Full 3D models obtain results close to experimental data but at high numerical costs. Thus, a common way to reduce the CPU cost is to model each wire with beam finite elements and use beam-to-beam contact formulations allowing arbitrary large sliding. However, the need for a CPU-intensive contact search phase in each iteration makes them computationally expensive, and sometimes unnecessary, particularly when dealing with fretting interactions where the relative slip amplitudes are small. The proposed work is a continuation of previous works from the authors where a small-sliding beam-to-beam point-wise frictional contact element between non-collinear beams has been proposed and implemented as a user-element in Abaqus™. Due to their peculiar helical architecture, using the penalty method for normal contact can lead to significant interpenetration induced by significant tension-bending coupling. To improve accuracy and robustness, normal contact is treated here using Lagrange multipliers. The tangential behavior is handled with a regularized Coulomb’s law. Moreover, the formulation in a previous publication was written for an updated Lagrangian framework well-adapted to Abaqus™. This formulation easily handles very large rotations by evicting singularities but does not perfectly respect frame objectivity and path independence principles. Considering that the target applications do not involve very large rotations, the Eulerian framework has been chosen to better respect those fundamental principles. The current contact element is implemented in a Matlab™ home-made beam finite element code in large rotations based on Eulerian formulation.