## 1 Introduction
[18; 19] predicted the response of wire ropes with different shapes and structures by ABAQUS and analyzed the stress and deformation of these different wire ropes. [PERSON] et al. [20; 21] analyzed the stress and strain distribution of four types of wire rope with different lay directions under axial tensile force and compared the simulation result with the experimental result to verify the effectiveness of the finite element model. [PERSON] and [PERSON] [22] simulated the deflection experiment with a wire rope, and the error of the simulation result was 11.16% compared with the actual experimental result. [PERSON] et al. [23] proposed a fine modeling method for locking coil wire ropes, studying the stress distribution pattern of the wire during the tensioning process. The theoretical and simulation results showed that the stress of the central wire was greater than the stress of the external wire, and the failure usually occurred near the end of the wire. [PERSON] et al. [24] conducted tensile experiments to determine the strain-stress curve of the wire rope and studied the stress and strain evolution of the wire rope in the elastic state by finite element analysis. [PERSON] et al. [25] predicted the stress response of a 6 \(\times\) 19 + IWS wire rope in the linear region by finite element analysis and established a life model of crack extension based on elastic fracture mechanics. [PERSON] [26; 27] established a 1/6 pitch finite element model of a 6 \(\times\) 6 + IWS wire rope, compared the contact stress of a 1 \(\times\) 7 + IWS wire rope under different broken wire conditions, and found that wires around the broken wire will bear a greater load. With the increase in the number of broken wires, the bearing capacity of the wire rope is rapidly weakened. [PERSON] et al. [28] proposed an accurate and efficient finite element model for the mechanical analysis of wire ropes and studied the axial mechanical properties of a 6 \(\times\) 36 SW + IWR wire rope using experimental, theoretical, and numerical methods. At present, studies on the mechanical characteristics of wire rope based on analytical analysis and numerical simulation have obtained certain results. However, the related studies based on analytical analysis often focus on dealing with wire ropes with simple structures. The vast majority of the numerical studies are based on the FEM (finite element method) and focus on simple wire ropes such as single-helix wire ropes, because the convergence of the FEM could be very difficult due to the complex geometry of wire ropes and complex contact conditions under loading. Overall, there are few studies on wire ropes with complex double-helix structures, such as the 6 \(\times\) K31 WS + FC wire rope. In addition, most of the above studies failed to establish a finite element model of the wire rope with a full pitch, so the simulation results are not convincible enough to reflect the actual mechanical response of the wire rope under loading. Furthermore, current research on the broken wires of wire ropes only focuses on explaining the patterns of broken wire in experiments or actual working conditions, and the influences of broken wires on the mechanical characteristics of wire ropes have not been fully analyzed. Thus, the main objectives of this paper are to propose a comprehensive framework for analyzing the mechanical characteristics of wire ropes with complex structures with high efficiency and accuracy, and quantitatively study the influence of broken wires on the mechanical response of a 6 \(\times\) K31 WS + FC wire rope in detail. This work will provide a practical method for the performance evaluation of wire ropes under broken wire conditions, and partly fills the gap in the relevant research. This article is arranged as follows: In Section 2, a precise geometric model of a 6 \(\times\) K31 WS + FC wire rope is proposed. In Section 3, a finite element model of the wire rope is established and the mechanical response of the wire rope under axial strain has been obtained.