A New Stored Energy Function for Rubber Like Materials for Low Strains

Abstract

Stored Energy function plays an important role in the numerical analysis of rubber products. Though elastomers are capable of stretching more than 500%, many applications like tires, require accurate representation of their stored energy at relatively low strains of 50%. In the present work the existing stored energy functions are evaluated for such strains (< 50%). This has been carried out by conducting uniaxial tension, uniaxial compression experiments. NeoHookean, Mooney-Rivlin, Ogden, Yeoh, Arruda-Boyce and Vander Waals models are evaluated for these strains by using the uniaxial tension and compression data. A new stored energy function is proposed for small strains which is a logarithmic function of first and second invariants. The new stored function is compared with the existing models. The comparison is carried out by calculating the R² values for the uniaxial tension and compression. It seems that the proposed stored energy function gives better prediction in tension and compression for less than 50% strains.

Keywords:

• hyperelastic materials
• finite element method
• stored energy function
• rubber
• tire modeling
• finite strain elasticity

ACKNOWLEDGEMENT

The authors thank Hari Sankar Singhania Elastomer & Tyre Research Institute (HASETRI), India group for their constant support and encouragement throughout the research. Special thanks to Dilip Dhupia, who helped us while conducting the experiments.