Comparison of a natural configuration approach and a structural parameter approach to model the Payne effect

The Payne effect, the nonlinear mechanical behavior of filled elastomers in oscillatory loading conditions, has received considerable attention in the literature. This is because of the extensive use of these materials in different industrial applications. While experimental investigations of the Payne effect have been comprehensive, the models developed to describe the behavior and predict the response in different loading conditions have not been adequate. Most models fall short of capturing some of the characteristic features of the Payne effect. Those models that do describe all aspects of the Payne effect employ a considerably large number of model parameters. In this study, two different models are developed to describe the Payne effect, using two different approaches. One was developed using a framework of multiple natural configurations. The other was developed using internal variables called structure parameters, like those used to characterize thixotropy of fluids. Both models use a relatively small number of model parameters. However, both models were able to capture to a reasonable extent the different features of the Payne effect. This includes the variation of the apparent storage and loss moduli with strain amplitude and frequency, the lack of effect of static strain offsets on the stress response to the oscillatory part of the strain loading and the nonlinear dependence of the response of the material on the loading history. Both models were found to describe experimental observations of the variation of the apparent storage modulus and the apparent loss modulus with strain amplitude and frequency.