Mechanical modeling of metallic strands subjected to tension, torsion and bending

Aim of the present work is to build a link between a structural theory for large-scale analyses of three-dimensional cable structures undergoing, in general, large displacements and rotations, and a refined mechanical description of metallic strands, fully accounting for their composite nature and hysteretic bending behavior. A new formulation for metallic strands is presented. The strand overall mechanical behavior is modeled according to the Euler-Bernoulli beam theory. A constitutive law relating the cross sectional generalized stresses and strains of the adopted structural model is obtained by summing over the individual contributions of wires. Each wire in the strand is individually modeled as a curved thin rod. Kinematic equations are proposed to relate the wire generalized strain variables to those of the strand cross section. The equilibrium of the individual wires is analyzed under the hypothesis of radial contact between adjacent layers taking, most notably, also into account the effects due to the residual radial contact forces induced by the strand manufacturing process. Deformations of contact surfaces are neglected and friction is accounted for, through the Amontons-Coulomb law, in the study of the stick-slip conditions. The proposed sectional model accounts for some distinctive characteristic aspects of wire ropes, such as the coupling between axial force and torque and the non-linear, and non-holonomic, relation between bending moment and curvature, which is a consequence of sliding of wires. The performance of the proposed formulation is assessed with reference to well-documented physical tests and established analytical formulations. Moreover, the role of the residual contact forces due to the stranding process, on the bending behavior of a typical multi-layer strand is assessed.