# An Initial Case Study of the Computational Modeling of Cord-Rubber Segments
## 3 Results and Discussion
### Model with Cord Bundle as a Bulk of the Material and as Individual Cords  
The difference in stiffness for segments with composite parts modeled as cord bundles sliced vertically, horizontally and both ways, with and without the manufacturing technology influence, is shown in Figures 16 and 17. Stiffness results in tension represented by the force-axial displacement curve of the segments, showing insignificant differences between the stiffnesses of the different variants of slicing the segment. In the cases without the influence of manufacturing technology, there is visible progressivity of the force-displacement curve when compared to the homogenized and microstructural models. Adding frictional contact between the cord bundle and the bushing likely explains this phenomenon. Stiffness results in shear (force-lateral displacement curves) show a significant influence of manufacturing technology on the overall shear stiffness. Another big difference is in the shear stiffness results between the variant with horizontal slices and the other two variants, where the stiffness reaches nearly double the value compared to the two different variants. This is explained by the large bending stiffness of the horizontal slices resulting from the large length in the bending direction when the cord bundle segment is loaded in shear. Figure 16: Force–axial displacement curves of the segment with cord bundle; vertical slice, horizontal slice, both slices (MT—model with the inclusion of the manufacturing technology influence; the arrows represent the loading direction of the cord–rubber segment). Figure 17: Force–lateral displacement curves for the segment with cord bundle: vertical slice, horizontal slice, both slices (MT—model with the inclusion of the manufacturing technology influence; the arrows represent the loading direction of the cord–rubber segment). As in the homogenized and microstructural model, the equivalent (von Mises) stress in cord bundles sliced vertically, horizontally and both ways has an increasing distribution in the direction of the first cord layers (see Figure 18). The stress values in vertically sliced and horizontally sliced bundles attain similar maximum values of 42.9 MPa and 42.1 MPa, respectively, comparable to the maximum value in the homogenized model. The smallest values are present in the model with bundles sliced both ways, caused by the regular rectangular pattern of the sliced cord bundle, hence, the uniform distribution of stresses. Among all these models, the biggest value of the stress can be seen in the case of the microstructural model, where the cords are embedded in the rubber matrix and are connected to the rubber parts of the segment by mesh connection. In the case of the first layers of cords, the space between the steel bushing and the cord is filled with a small amount of rubber, creating a stress concentration. The inability of the homogenized model to realistically model the deformation of the segment is eliminated in the model with a cord bundle of bulk material by slicing the geometry and allowing the individual cord layers to slide over each other. This is achieved with the help of using the frictional contacts between the individual layers. The sliding of the layers over others is most visible in the segment's shear deformation, which is displayed in Figure 19, where a top view of the total deformation in all three variants of bundle slicing is shown. Compared to the model with a sliced cord bundle, a higher level of accuracy and cord interaction can be achieved by individually modeling the cords. Figure 20 shows the cross-section view of the total deformation of individual cords loaded in tension, where the top part is the deformation in the middle of the segment and the bottom part is the  
Figure 19: Top view of the total deformation in shear of the segment with cord bundle as the bulk of material: (**a**) vertically sliced; (**b**) horizontally sliced; (**c**) both slices.