Modeling Payne effect with a framework of multiple natural configurations

Abstract

Payne effect is the complex nonlinear response of filled elastomers to oscillatory loading. Although usually characterized by the decrease in the storage modulus with strain amplitude, and by the bell-shaped curve of loss modulus with strain amplitude, the response has many other peculiar features. The manner of decrease in storage modulus with strain amplitude does not change when the frequency of the test is changed. Static strain offsets do not change the relationship between storage modulus and strain amplitude. In addition, when tested at relatively large strain amplitude levels, the material behavior changes and requires a certain period of time before it returns to what was initially observed. In this study, a model is developed to describe Payne effect using a framework of multiple natural configurations. Assuming appropriate functional forms for the Helmholtz potential and the rate of dissipation, and maximizing the rate of dissipation over all allowable mechanical processes, the constitutive equations were obtained. In a simple one-dimensional setup, the model was able to describe many aspects of Payne effect reasonably well, including the independence of the nature of modulus decrease on the frequency of loading and static strain offsets.