Response of a wire rope strand to axial and torsional loads: Asymptotic modeling of the effect of interwire contact deformations

Abstract

a b s t r a c tThe refined discrete mathematical model of a simple helical wire rope strand is developed. The effect of the transverse contraction of the wire strand through Poisson's ratio and also through local contact deformations (wire flattening) has been studied in detail. In order to express the interwire contact deformation in terms of the parameters describing the strand deformation, we formulate a two-dimensional model interwire contact problem. The interwire contact interaction is treated as a frictionless unilateral plain strain problem. The nonlinear model interwire contact problem has been solved by the method of matched asymptotic expansions. The constitutive equations for a helical wire rope strand, which take into account both the Poisson's ratio effect and the effect of contact deformation, are obtained in a closed form.

Analytical and finite element modelling of the elastic–plastic behaviour of metallic strands under axial–torsional loads

“…The proposed analytical formulation has been also compared, in the elastic range of deformation, to a recent analytical model developed by Argatov [2]. The latter is …”

Helical Birods: An Elastic Model of Helically Wound Double-Stranded Rods

“…This also implies that we have restricted the cross-sections from deforming transversely, both assumptions are not always uniformly made in rope modelling (see e.g. [2]), and we briefly discuss the possibility of relaxing these assumptions in Section 3.4. That said, unless the rods are significantly prone to such transverse deformations, our assumption does not seem unreasonable and significantly simplifies the following kinematic description of the individual rods, particularly in the cases where the curve R adopts a non-trivial (straight) configuration.…”

“…This possibility and its affect on the pressure is considered by Argatov [2], who treats the local contact problem using matched asymptotic expansions and uses this result to modify the pressure obtained by solving the equilibrium equations of helical rope model composed of Kirchhoff rods.…”

“…In subsequent work [24,32,33], both contact forces and moments were considered, though once again the studies only modelled an isolated helical rod, rather than considering the whole system in a single model. A number of authors have proposed various extensions or variations on this model [2,16,20,37] but they rely on the same geometric assumptions of elliptic cross-sections, which is not in general correct even if the rope remains unbent (see e.g., [29]). Alternative models make ad hoc assumptions regarding the kinematics of the constituent rods [12,46], but none of these works correctly treat the contact problem.…”

Mechanical Modeling and Analysis of Braided Wire Rope

“…And the finite element simulation of the wire rope under tension condition was carried out. [3][4][5] However, the scholars have less research on the braided wire rope. Some scholars have made a preliminary study for braided wire rope from types, performance, structural characteristics and the problems existing in the processing and use, causes analysis of fracture, etc.…”