A new mechanical model of short wire ropes: Theory and experimental validation

A new mechanical formulation is presented for assembling the constitutive relationships of single- and multiple-strand wire ropes. The model aims to predict the lower and upper bounds of the bending stiffness associated to the limit behaviors of perfect stick and full slip between the constituting wires. The wire rope is described as a shear deformable beam for which the generalized constitutive equations, accounting for the wires’ geometry and material properties, are derived according to Saint-Venant's theory extended to curvilinear thin rods. The distinguished feature of wire ropes, i.e., the possibility of relative sliding between the wires, is accounted for by the introduction of eigenstrains in the wires’ strain measures. An experimental campaign is carried out on two series of short steel wire ropes subjected to quasi-static bending loops obtaining hysteresis cycles for different amplitudes and rope lengths. The model is validated by comparing theoretically predicted and experimentally measured stiffnesses obtained from the bending hysteresis cycles as well as from axial-torsional tests present in the literature.