Mathematical model of the viscoelastic behavior of rubber under cyclic loading

One of the urgent problems of the mechanics of car tires is the calculation of energy dissipation in a rolling tire under cyclic deformation. It forms the basis for determining the rolling resistance and heat buildup. The accuracy and reliability of the calculated predictions in this area depends on the adequate description of the physical properties of tire materials. This paper presents a mathematical model of the viscoelastic behavior of a tread rubber under uniaxial cyclic compression. The model is based on the concept of the rheological behavior of inelastic elastomers developed by Bergstrom and Boyce, the MIT experts. It is described in detail how to set up the model and determine the numerical values of its parameters for two tread rubbers of summer automobile tires. This procedure is used to process the results of cyclic pulse compression tests of rubber samples. The model parameters are determined by minimizing the deviation of the calculated values from the experimental ones obtained by the Nelder-Mead method. It is shown that the calculation model makes it possible to describe the hysteresis losses in rubber with sufficient accuracy. The article is intended for professionals dealing with applied calculations of polymeric materials.

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