A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material

Nonlinear finite element analysis is widely used for structural optimization of the design and the reliability analysis of complex elastomeric components. However, high-precision numerical results cannot be achieved without reliable strain energy functions (SEFs) of the rubber or rubber nanocomposite material. Although hyperelastic constitutive models have been studied for nearly 80 years, selecting one that accurately describes rubber's mechanical response is still a challenge. This work reviews 85 isotropic SEFs based on both the phenomenological theory and the micromechanical network theory proposed from the 1940s to 2019. A fitting algorithm which can realize the automatic fitting optimization and determination of the parameters of all SEFs reviewed is developed. The ability of each SEF to reproduce the experimental data of both the unfilled and highly filled rubber nanocomposite is quantitatively assessed based on a new proposed evaluation index. The top 30 SEFs for the unfilled rubber and the top 14 SEFs for the highly filled rubber nanocomposite are presented in the ranking lists. Finally, some suggestions on how to select an appropriate hyperelastic constitutive model are given, and the perspective on the future progress of constitutive models is summarized.