## 3 Internal Contact Pressure Model Validation
### Validation for Sheathing Compression  
Externally enveloped with HDPE sheathing, parallel wire cables are subjected to a radial compression effect caused by the thermal expansion and contraction of the extrusion-molded polyethylene sheath during manufacturing process. Consequently, this compression exerts pressure on the internal wires, leading to their extruded contact and the generation of contact pressure.  
The radial compression model for the 91 wires simulates the internal wire-to-wire extrusion caused by the compression of the HDPE sheath on the cables, resulting in the generation of contact pressure. Under the influence of this radial pressure, contact pressure is generated both between different layers of wires, as Figure 15(a) shows, and within the same layer of wires, as Figure 15(b) shows. The two types of contact pressure are compared with the finite element model.  
Figure 15(b,c) illustrates the distribution of contact pressure among wires under varying loads for dint layers. Both PIC and FEA exhibit a discernible trend: a diminishing tendency of contact pressure towards the inner layers. The Boussinesq distribution is assumed in the theoretical analysis for the distribution of contact pressure. However, FEA and experimental results deviate from this pattern, possibly attributed to manufacturing errors in the wires during experiments [31]. It is possible that significant disparities in the radius and surface conditions of different wires may lead to an irregular stress distribution. At the same contact position, the greater the external radial force, the greater the contact stress, which is expected. However, in the finite element model, the stress at contact points around the central wire shows a different trend from that of the outer layer wires, which may come from the different distribution of force chains under different loads. Under low loads, there is less deformation induced by wire contact, and internal stresses within the cable mainly transmit along the diagonal of the cross-section. However, under higher loads, significant deformations in internal wires may change the force chain, resulting in certain wires  
Figure 16: Distribution of contact stress caused by radial pressure: (**a**) the contact points on the blue line are between different layers of wire; (**b**) the contact points on the red line are between the same layer of wire.  
dispersed among the force chains bearing only a fraction of the load [40]. Consequently, the stress distribution changes. On the whole, the PIC model aligns commendably with the actual stress levels between wires. It stands as a convenient method to predict the distribution of internal contact stress in cables, offering preliminary analytical data for experiment and engineering applications.  
For the case between the same layer of wire, because the distance between the contact point of the same layer and the central wire is the same, the wire bundle is divided into six layers according to the different distance from the central wire. The comparison of FEA and PIC for contact pressures in each layer is as follows.  
As Figure 18 shows, the 0 th layer comprises six contact points surrounding the central wire, which exhibit nearly identical contact pressure. However, for layers 1 to 5, there is considerable fluctuation in the contact pressure for the wires within the same layer. This variability arises from the different directions of contact forces among these wires, causing an unstable transmission of force within the same layer. Therefore, the contact pressure between wires in the same layer experiences a greater amplitude of variation compared to wires in different layers. However, there is a clear trend indicating that the contact pressure decreases towards the inner layers. The average contact pressure for the wires within the same layer in FEA aligns closely with the PIC model. This makes the theoretically derived contact pressure an intuitive reference for measuring the pressure levels within the wires.