Comparison of a natural configuration approach and a structural parameter approach to model the Payne effect
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O R I G I NA L PA P E R
S. P. Atul Narayan
· Liviu Iulian Palade
Comparison of a natural configuration approach and a structural parameter approach to model the Payne effect
Received: 2 April 2020 / Revised: 16 June 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract 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. 1 Introduction The addition of fillers to elastomers has been a common practice for several decades. The introduction of fillers in elastomers has been known to enhance material properties like strength, stiffness, durability, etc. But, in addition to these improvements, the fillers make the mechanical behavior of the elastomer highly complex and nonlinear. Because of the importance of filled elastomers and their widespread industrial applications, the nonlinear inelastic behavior of filled elastomers has been the subject of several experimental investigations. Moreover, numerous models have been developed to capture and predict its behavior in different loading conditions. Experimental investigations of the mechanical behavior of filler-reinforced elastomers have been extensive. One of the nonlinear responses observed in such experiments is the “stress-softening” of filled elastomers, otherwise known as the “Mullins effect” [8,22]. When filler-reinforced elastomers are subjected to a particular S. P. Atul Narayan (B) Department of Civil Engineering, Indian Institute of Technology Madras, Chennai 600036, India E-ma
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