A Model for Hyper-Elastic Material Behavior Under Thermal Aging With an Application to Natural Rubber

Numerous hyper-elastic theoretical material models have been proposed over the past 60 years to capture the stress-strain behavior of large deformation incompressible isotropic materials. Among them, however, only few models have considered the thermal aging effect on model parameters. Having a simple, closed-form equation that includes the effect of aging temperature and time in describing the stress-strain behavior could facilitate fatigue analysis and life time prediction of rubber-like materials. In this vein, this paper defines a new and simple Weight Function Based (WFB) model that describes hyper-elastic materials’ behavior as a function of aging time and temperature variations. More than 130 natural rubber specimens were thermally aged in an oven and tested under uni-axial loading to observe their stress-strain behavior at various temperatures and aging times. The temperature ranged from 76.7 °C to 115.5 °C, and the aging time from zero to 600 hours. The proposed WFB model is based on the Yeoh model and basic continuum mechanics assumptions, and it was applied to the tested natural rubber materials. Moreover, it was verified against Treloar’s historic tensile test data for uni-axial tension of vulcanized natural rubber material, and also compared to the Ogden and the Yeoh models. A non-linear least square optimization tool in Matlab was used to determine all hyper-elastic material model parameters and all other fitting purposes. The proposed model has better accuracy in fitting Treloar’s data compared to the Ogden and the Yeoh models using the same fitting tool under the same initial numerical conditions.