Finite Element Beam Models for Rope Applications and Cord Manufacturing

Steel ropes are widely used to hoist weights in suspension bridges, elevators, underground mining, and many other applications. However, their design in practice still relies heavily on experimental tests, which take a significant amount of cost and time for sample preparation and test implementation. Meanwhile, a comparable product, steel cords, which reinforce vehicle tires, also require plenty of ``trial and error" in designing the manufacturing process to meet the quality criteria. To the author's best knowledge, no software tool based on physical modelling of mechanical deformation has been applied in either rope product or cord process design. Aiming to close the gap, this thesis has been dedicated to developing finite element models for modelling the mechanical deformations of steel ropes and cords, two important product categories for the industrial partner Bekaert (www.bekaert.com). Since steel wires, as the primary constituents of ropes and cords, are highly slender entities, a 1D beam can represent each wire. This adoption of the beam model is expected to provide computational efficiency in the numerical prediction of ropes and cords with sufficient accuracy. Different beam models and their finite element formulations exist in the literature. This thesis has adopted and extended prior work about efficient and robust finite element formulations based on the geometrically exact Kirchhoff-Love beam theories with the frictionless beam-to-beam contact interactions to incorporate the elastoplastic deformations. Also, an extra extension allows the modelling of the frictional contact interactions of beam-to-beam and beam-to-surface. While the first type of contact forms the fundamental phenomenon occurring among wires in both products, the second must be included when considering the motion of ropes and cords when they are guided by the surfaces of mechanical parts, such as the pulleys for hanging ropes and those used in the manufacturing of cords. The elastoplastic behaviour of steel wires with arbitrarily curved initial configurations can be modelled, considering their axial stretching, spatial bending, and torsion under large rotations. Combining the frictional contact interactions of beam-to-beam and beam-to-surface under finite sliding, the mechanical behaviours of ropes and cords can be modelled. These finite element formulations have been implemented into an in-house program with more than twenty thousand lines, which has been applied to simulate the mechanical behaviours of ropes and cords. For ropes, the focus has been on modelling a stranded rope under tensile and torsional loads, where the load sharing between the core and out strands is an essential factor for endurance consideration. Efforts have been spent on simulating several important manufacturing steps for steel cords, and their applicability has been assessed.