# An Initial Case Study of the Computational Modeling of Cord-Rubber Segments
## 1 Introduction  
Elastomers are widely used materials for manufacturing across different fields. The area of use depends on the type of loading, with the advantage of these materials being in compression loading. In several cases, these structures are also loaded by bending or tension modes. Many elastomers are too weak to be used without reinforcement as load-bearing elements of those structures. That is why some reinforcing element is added to the rubber matrix for many elastomer products, such as tires [1, 2], hoses [3] and conveyor belts [4]. There are two main principles of reinforcement: either the rubber matrix is mixed with reinforcing fillers or the matrix is reinforced with bundles of fibers (cords). The primary function of reinforcing fibers is to improve the mechanical properties of the rubber compound. This reinforced material, consisting of a rubber matrix and reinforcing fibers woven into cords, is called a cord-rubber composite. It is advantageous to use computational modeling to assess the stress-strain behavior of a component of such material combination already in the design phase, thereby reducing the time and financial costs associated with prototype testing. Several authors [4, 5, 6, 7, 8] addressed this issue in the research literature across different applications. There are variouscomputational approaches to modeling cord-rubber composites' stress-strain behavior. These can be divided into three primary groups depending on the level of simplification: the macro-scale approach, micro-scale approach and multi-level approach combining both groups. Most of the studies in the literature use a macro-scale approach, where the properties of cord and rubber are homogenized and the cord-rubber composite is modeled with orthotropic or anisotropic constitutive models. [PERSON] [9] proposed an anisotropic hyperelastic constitutive model for numerical simulations of cylindrical pneumatic springs, which are used to reduce the transmission of vibrations to the driver's seat. A material model of the rubber-cord composite, which is part of the conveyor belt, was calibrated by [PERSON] [4]. The Bergstrom-Boyce, nonlinear finite model, which can simulate time-dependent phenomena and hysteresis, was used for rubber. The rubber-cord layers were tested only in tension and approximated by an orthotropic material model. [PERSON] [5] developed an anisotropic constitutive model for cord-rubber composites with rubber-cord interaction. The total deformation energy is divided into three parts, representing the deformation energy in the rubber, the cord and the interaction between the rubber and the cord. [PERSON] [3] studied offshore composite rubber hoses under internal pressure, focusing on stress and radial displacement. [PERSON] [6] developed a method to describe the effective mechanical properties of a cord-rubber composite in the form of a quadratic relationship between the Green strain tensor and the second Piola-Kirchhoff stress tensor. [PERSON] [10] addressed challenges in assuming small deformations in car tire cord-rubber layers by introducing a phenomenological approach to modeling them as an equivalent homogeneous anisotropic hyperelastic material. [PERSON] [11] formulated an anisotropic visco-hyperelastic constitutive model for cord-rubber composites that decomposed the unit-volume strain energy function into four components. The micro-scale approach was explored by [PERSON] [2], who studied tire reinforcement material modeling, examining standard models like linear, Yeoh and Marlow. [PERSON] [7] investigated the mechanical behavior of a railway cord-rubber composite air brake tube under uniaxial tension through microscale modeling. Standard cords, consisting of only one material, sometimes cannot meet the requirements placed on the components. Because of this, fibers from different materials are combined, resulting in a so-called hybrid cord. [PERSON] [12,13] presented the hybrid cord's finite element models, including its geometry and fiber structure.