# An Initial Case Study of the Computational Modeling of Cord-Rubber Segments
## 3 Results and Discussion
### Homogenized and Microstructural Model of Cord-Rubber Segment  
In Figure 13, the difference between the elemental triads is shown, i.e., the orientation of the elemental coordinate system in the homogenized and microstructural model. The composite part of the homogenized model is modeled as one part by an anisotropic hyperelastic model where the rubber matrix is described by a stiffness parameter (shear modulus) and the cord is characterized by tensile modulus and the cord direction. The direction of the cord is represented by the vector referring to the elemental coordinate system (green arrow). To correctly define the direction of the cord, the elemental coordinate system in the elements in the curved part of the composite had to be rotated to the cord direction. In the microstructural model, the cords are represented by linear isotropic material without rotating the elemental coordinate system (Figure 13, bottom side).  
The axial stiffness results of the cord-rubber segment represented by force vs. axial displacement curves are shown in Figure 14. The blue line represents the stiffness curve obtained on the uniaxial tension test machine, where the tension test was performed on a prototype cord-rubber segment (see Section 2.2). The tension test was performed until the first cords of the cord-rubber segment started to break, which was attained at a displacement of approximately 19 mm. The results from the computational modeling are shown only up to the displacement of 2 mm, which was determined from the previous multibody simulation of the whole flexible coupling to obtain the real operational deformations.  
Figure 12: The axial deformation of the cord–rubber segments over time.  
Figure 13: Elemental triads (elemental coordinate system) in the homogenized and microstructural model.  
The stiffness obtained from the technical experiment reaches approximately 5 kN/mm at a displacement of 2 mm. The resulting stiffness curve from the simulation shows that the homogenized and microstructural models can simulate the stiffness obtained from the experiment with an error of 10%. The slightly overestimated stiffness in the case of the microstructural model could be explained by the fact that the linear isotropic material model used in the microstructural model does not respect the direction of the cord in the curved part of the composite, thus adding additional stiffness in the axial direction of the cord-rubber segment.  
The equivalent (von Mises) stress distribution in the cord for the homogenized and microstructural models is shown in Figure 15. The stress distribution shows increasing stress in the lower cord layers (only valid in the straight part of the composite), hence, the inability of both the homogenized and microstructural models to simulate the real-world conditions where a step is applied during the manufacturing process with the aim of all layers being loaded in such a way that ensures the highest utilization of the strength potential in the cord-rubber segment. This is the reason another approach was considered--to concentrate on the composite part of the segment-- that involved slicing the cord bundle, modeling the whole cords, including the influence of manufacturing technology and using contacts instead of using the approach of adding all the components into one part, thus creating the mesh connections, which are the equivalent of bonded contacts.  
Figure 14: Force–axial displacement curves of the cord–rubber segment; experiment, homogenized model, microstructural model (The arrows represent the loading direction of the cord–rubber segment).  
Figure 15: The equivalent (von Mises) stress distribution in the cord: homogenized model (**up**), microstructural model (**down**).