Zero-Dimensional Model for Dynamic Behavior of Engineered Rubber in Automotive Applications

This paper presents a zero-dimensional model for the simulation of the mechanical behavior of automotive engineered rubber components, such as flexible couplings. The objective is to develop a real-time-capable model, able to simulate the behavior of a driveline containing elastomer components: the engineered rubber model has to correlate stretch to stress, the mechanical behavior being represented by means of a hysteresis cycle. The study presents the implementation of Maxwell and Voigt models, showing their limits in the representation of the material behavior: elastomers present a nonlinear response in the relationship stress-strain. A combination of Maxwell and Voigt models, with stiffness and damping variable according to the stress and strain rate, to represent nonlinear material responses, is coupled to a relaxation model, in order to represent the Mullins effect (the rubber mechanical behavior also depends on load history). Experimental tests have been carried out with different pre-load settings, stress amplitudes and stress frequencies. Tests results have been used to calibrate the parameters defining the simulation model, comparing the model outputs to experimental data: an optimization algorithm has been applied, with the aim of minimizing the results discrepancy with respect to experimental results. The optimization tool has been also used to reduce the number of parameters defining the model, in order to simplify the required computational power, avoiding at the same time over-parametrization. In the second section of the paper, the model is used for the simulation of a different rubber component, whose behavior is identified using quasi-static load ramps, frequency and amplitude sweeps, steps and random cycles. An alternative model formulation, minimizing the degrees of freedom is then applied to the new dataset. The model parameters are separately optimized using different tests, in order to capture the specific mechanical behavior. Finally, the identified parameters are used to simulate the elastomer response in random tests, comparing the results to experimental data, to evaluate the simulation quality in terms of RMSE.