Modeling Payne effect with a framework of multiple natural configurations

• Published in: International journal of engineering science Vol. 157
• Main Authors: Narayan, S.P. Atul, Palade, Liviu Iulian
• Format: Journal Article
• Language: English
• Published: Elsevier 01.12.2020
• Subjects: Mathematics
• ISSN: 0020-7225
• DOI: 10.1016/j.ijengsci.2020.103396

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 ampli-tude, and by the bell-shaped curve of loss modulus with strain amplitude, the responsehas many other peculiar features. The manner of decrease in storage modulus with strainamplitude does not change when the frequency of the test is changed. Static strain offsetsdo not change the relationship between storage modulus and strain amplitude. In addi-tion, when tested at relatively large strain amplitude levels, the material behavior changesand requires a certain period of time before it returns to what was initially observed. Inthis study, a model is developed to describe Payne effect using a framework of multiplenatural configurations. Assuming appropriate functional forms for the Helmholtz potentialand the rate of dissipation, and maximizing the rate of dissipation over all allowable me-chanical processes, the constitutive equations were obtained. In a simple one-dimensionalsetup, the model was able to describe many aspects of Payne effect reasonably well, in-cluding the independence of the nature of modulus decrease on the frequency of loadingand static strain offsets.