## 3 Internal Contact Pressure Model Validation
### Validation for Wire Bending Model  
During the vibration of cables, bending occurs, leading to compression between the various layers of wires. As the curvature of the cable increases during the bending process, this compressive effect gradually grows, influencing the contact pressure between the wires. The model for the bending of the 91-strand configuration involves extracting the contact stress between the wires after the overall curvature of the cable and subsequently comparing it with PIC model. Previous studies show that the interaction forces between the wires exhibit distinct layering characteristics during the process of bending contact [39]. As Figure 19 shows, under different curvatures, both the FEA and PIC reveal a layered pattern in the distribution of contact stress. The contact pressure within the same layer mainly depends on the axial tension in the cable and the curvature, which shows a distinct trend where higher tension and curvature lead to increased contact stress. In PIC model, the force distribution across the cable cross-section is allocated based on its position. As a result, the axial force difference among wires in the same layer is small, resulting in an approximately linear trend in the calculated results. Between different layers, the contact  
Figure 17: Distribution of contact stress caused by radial pressure between wires of different layers: (**a**) numbering of contact points, red asterisks are contact point on the diagonal; (**b**) comparison between FEA and PIC for layers 1 to 3; (**c**) comparison between FEA and PIC for layers 4 to 6. Load1–6, respectively represent external radial forces of 145 N/m, 125 N/m, 105 N/m, 85 N/m, 65 N/m, 45 N/m. stress increases towards the inner layers, aligning with the assumption of contact pressure accumulating layer by layer. It is noteworthy that wires at positions away from the neutral axis exhibit relatively lower contact stress both in PIC and FEA. This phenomenon may be attributed to the reduced constraint on the outer wires, which may result in inadequate contact between wires and a subsequent decrease in contact force. Additionally, the outer wires are farther from the central wire, resulting in lower axial forces and vertical pressures compared to the inner wires, thus decreasing the available contact pressure for transmission. Figure 19: Comparison of contact stress between wires in different layers: (**a**) \(\mathrm{T}=18,000\) N and strand curvature = 0.001; (**b**) \(\mathrm{T}=18,000\) N and strand curvature = 0.01. Figure 18: Distribution of contact stress caused by radial force in the circumferential wires of the same layer: (**a**) contact point number of each layer of wire; (**b**) PIC result of contact stress at circumferential contact points; (**c**) comparison between FEA and PIC for layers 0 to 2; (**d**) comparison between FEA and PIC for layers 3 to 5. Figure 20 illustrates the variation in contact stress and cable curvature under different axial tension levels and force fluctuation coefficients. At lower curvatures, the contact stress induced by bending is almost negligible. However, with an increasing curvature, the contact stress between the wires exhibits exponential growth. Previous studies indicate that the interlayer tangential force in cables also grows exponentially during bending [39]. When the interlayer tangential force surpasses the interlayer frictional force, slippage occurs within that layer. Research on slippage usually assumes equal interlayer frictional forces, but this assumption is inadequate for accurate predictions of wire slippage due to variations in the number of internal wires, friction coefficients, and contact pressure between wires across different layers. Near the neutral axis of the cable, the tangential force between wires is maximal. However, at the same time, the interlayer frictional resistance is also at its peak. Therefore, determining the slippage state requires a consideration of the specific conditions of the cable.