Homogenization of Rubber-Cord Layers at Moderately Large Deformations

The rubber-cord layers in passenger car tires are usually calculated assuming that deformations in them are small. However, rubber-cord layers can experience deformations of up to 15%. In calculations, the rubber-cordis usually replaced by an effective material. In this work, a phenomenological approach is used to construct a model of the effective material, where the inhomogeneous rubber-cord layer is replaced by an equivalent homogeneous anisotropic hyperelastic material. To describe the averaged properties of rubber-cord, the elastic potential of a transversely isotropic or orthotropic material can be used. However, in the case of a thin inhomogeneous layer, the traditional definition of averaging needs a modification. In this work, it is proposed to use the 3D averaged elastic properties of the layer surrounded by a homogeneous material. To determine constants of the elastic potential, nonlinear local problems on the periodicity cell has to be solved. In the case of a transversely isotropic potential, a set of local problems sufficient to determine the constants is proposed. It is shown that the procedure for determining the constants is stable relative to perturbations of the parameters of periodicity cell. To differentiate the potential, the symbolic calculations from the Octave package were used. The numerical calculations performed showed that the structure of the potential proposed and the scheme for determining material parameters are suitable.