A phenomenological expression of strain energy in large elastic deformations of isotropic materials

Abstract

A new model is constructed to validate a non-linear elastic response of rubber-like materials. The proposed model is phenomenological and is the combination of Rivlin expression truncated in invariant $\mathop I\nolimits_{1}$ with a term in $\mathop I\nolimits_{2}$ coming from the Hart-Smith model and which has been modified by Gornet et al. This model has five rheological parameters adjusted with a genetic algorithm. The genetic algorithm method is used in binary code and two sets of experimental data (Treloar data and Nunes and Moreira data) from the literature to compare the proposed model. With Treloar rubber data the simple tension suffices for the determination of the parameter values. Thus, the fit of experimental data is shown to provide an accurate response and predictive description in biaxial tension and pure shear with the same sets of material parameters. Unlike, with Moreira data, the proposed model has given direct material parameters in simple shear with good correlation. On the other hand, a comparison is made between the proposed model and the Beda model (2007), Gornet et al. model and hybrid integral approach (HIA) model. The proposed model is the most efficient among three other classical models because the proposed model emerges from very small relative errors with Treloar's experimental data: 0.42 ± 0.08 in simple tension, 0.44 ± 0.07 in biaxial tension and 0.42 ± 0.05 in pure shear. This model also incorporates all the criteria for model validation described in the literature.