Different phenomenological, empirical, and micromechanical constitutive models have been proposed to describe the behavior of incompressible isotropic hyper-elastic materials. Among these models, very few have accounted for the thermal aging effect on the model constants and parameters. This article introduces a new empirical constitutive hyper-elastic model for thermally aged hyper-elastic materials. The model named “the weight function based (WFB) model” considers the effect of aging temperature and time on its parameters. The WFB model formulation can facilitate fatigue analysis and lifetime prediction of rubber-like materials under aging conditions. The WFB model in this article defines all rubber-like material properties, such as fracture stretch, strength, and stiffness, by predicting the full stress–strain curve at any aging time and temperature. The WFB model was tested on natural rubber for uniaxial and biaxial loading conditions. More than 100 specimens were aged and tested uniaxially under various temperatures and aging times to extract the stress–strain behavior. The temperatures used in the test ranged from 76.7°C to 115.5°C, and the aging time ranged from 0 to 600 hours (hrs). A classical bulge test experiment was generated to extract the biaxial natural rubber material behavior. An ABAQUS finite element analysis model was created to simulate and verify the generated biaxial stress–strain curve. The proposed model represents the aging effect on the tested natural rubber under uniaxial and biaxial loading conditions with an acceptable error margin of less than 10% compared to experimental data.
A 12 year EDF study of concrete creep under uniaxial and biaxial loading
