# An Initial Case Study of the Computational Modeling of Cord-Rubber Segments
## 4 Conclusions  
This paper composed a multi-scale computational model of cord-rubber segments of a flexible coupling in railway vehicles. The cord-rubber composite was modeled using various approaches, including homogenized anisotropic hyperelastic and microstructural models. The behavior of the cord bundle was investigated on a model without rubber. The sensitivity study of different numbers of cords and different cross-sections of cords was performed. The main conclusions are summarized as follows:  
1. The multibody simulation model of the cord-rubber coupling allows for a complex analysis of loading and behavior under varying stiffness characteristics of the cord-rubber segment. The model provides valuable insights into force effects during opera  
Figure 23: The torque and force reactions experienced by the cord–rubber coupling input flange. Figure 22: Reacting forces for individual segments. tion, such as the maximum transmitted torque, forces and axial deformation of the segment. Additionally, the model addresses practical considerations by minimizing force effects to simplify the assembly and exchange of individual segments. 2. Compared with the experimental data from the tension test, the homogenized and microstructural models of the cord-rubber segment can simulate the deformation response and overall stiffness relatively accurately when loaded in tension. The homogenized model is numerically more efficient than the microstructural model, which is caused by the low number of meshing elements needed to discretize the composite part of the segment in the case of the homogenized model. Both models fall short in simulating the segment's manufacturing technology influence. 3. The limitations of the homogenized model in realistically representing segment deformation were addressed by introducing a model with a cord bundle as a bulk material, achieved by slicing the geometry and allowing individual cord layers to slide over each other with frictional contacts. This also allowed us to include the influence of manufacturing technology in the computational model. However, because of the bulk material, the model shows a relatively large stiffness in shear loading modes, which does not agree with the stiffness in shear of the real cord-rubber segments. 4. The model with cord bundles modeled as individual cords overcomes all the limitations present in the previous models. Modeling individual cords with circular cross-sections allows for the creation of a cord bundle where no rubber will be present in the spaces between the individual cords, which will mean high stiffness in tension similar to other models but reduced stiffness in other loading modes (shear and torsion) where the stiffness is, to a large extent, determined by the shear modulus of the rubber. It is essential to preserve this flexibility in the coupling from the point of view of allowing for misalignment in the vehicle's drivetrain components. The model also enables the sliding of the cords over each other and moves cords from the upper layers between the cords in the lower layers, realistically representing the real-life deformation of the cord-rubber segment. Another critical factor is the inclusion of the manufacturing technology influence into the model, which is needed to provide a stress distribution over the cords that utilizes the whole strength potential of the cord-rubber segment. All these advantages of the model are at the cost of increased numerical demands of the model caused by a considerable number of elements needed to create the finite element mesh. 5. The importance of using the multi-scale model consists of determining deformations experienced by the cord-rubber segment with the multibody model of the cord-rubber coupling. The results are then used as boundary conditions in the homogenized and microstructural models of the cord-rubber segment.