**4. Conclusions**

The cord-rubber tire composite plies, as opposed to typical composite materials, have specific characteristics resulting from the method of tire forming. Variable cord density and its angle must be taken into account in tire computational models. This causes a grea<sup>t</sup> difficulty in deformation analysis of such objects, as it requires a correct description of variations in these parameters along the tire profile and creating user subroutines, which execute the description within the computer code.

The textile cord, which is the most commonly used in the construction of pneumatic bias tires, features non-linear stress–strain characteristics. Thus, in the analysis of a tire, it is necessary to use tangential modulus varying together with the deformation. Moreover, due to the negative thermal expansion coefficient of such a cord, a tire removed from a vulcanization mold changes its shape under the influence of cord shrinkage forces. It is necessary to take the thermal shrinkage into account, as this has a considerable influence on force values in body ply cord when the tire is inflated. The low influence of the shrinkage on the final axial displacement of a point located on tire sidewall and a 15% influence on the displacement of the point placed at crown were observed.

The finite element model makes it possible to predict many tire parameters and greatly extends the possibilities of the classic netting model, taking into account not only the cord plies but also the rubber. Moreover, due to the consideration for the contact between the tire beads and the rim, it is possible to perform a realistic simulation of tire mounting on the rim. The model credibility may be evidenced by the fact that, in the case of an actual bias tire simulation, the overall sizes of an inflated tire obtained with the use of the model were practically consistent with the sizes on an actual tire.

The model enables, for example, determination of such a vulcanization mold shape, thus the ready tire after inflating attains the required sizes. The selection of mold shape is made in a virtual space at the design stage and thus at the stage of low costs. This does not require, as was the case with the previously utilized trial and error method, a time-consuming mold preparation to manufacture prototype tires. From the tire designer's point of view, the model provides considerable support in the difficult design work, making it possible to obtain valuable results, e.g., inflated tire profile, forces in tire load-bearing members and, thus, an evaluation of its strength. It may serve as a virtual prototyping tool.

The presented method for determination of tire apparent lateral stiffness may be used in a comparative analysis of different variants of the same tire model but with various design parameters (e.g., number of plies, *epdm*, cord angle, etc.).

It was shown that, when textile cord specific characteristics were taken into account in the previously created radial tire model, the modified and extended model was effective in bias tire deformation analysis.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
