Characterization of hyperelastic deformation behavior of rubber-like materials

Abstract

This paper proposes a new hyperelastic model for rubber-like materials applicable over the entire modes of the large deformations. The whole material parameters have been identified using the mathematical approach combined with the genetic algorithm for the best method for the structure of hyperelastic models applicable to incompressible rubber-like materials. The step-by-step method is used on the restricted form by gradually adding a term of the highest degree of the hyperelastic model when the deformation increases. This combination greatly minimizes the difference between experimental data and analytical solutions. It is about a method that is applied to nonlinear behaviors leading to an optimal solution. The power of the model is demonstrated via comparisons with different phenomenological hyperelastic models using the experimental data from the Treloar and Nunes works. According to the litterature, many authors have proposed a model based on both strain invariants but unable to reproduce the equibiaxial deformation mode. This work offers the constitutive hyperelastic model based on both strain invariants $$I_1$$ and $$I_2$$ with a minimal number of rheological parameters.