Reconciling the fundamental phenomenological expression of the strain energy of rubber with established experimental facts

The fundamental Rivlin expression of the strain energy function of rubber materials is readjusted and expanded to an optimal and efficient number of terms, and then stress–stretch behavior relations are derived to provide an accurate prediction of different modes of deformation. An analysis of the effect of deformation on simple and shear reduced stresses has permitted strain invariants I1 and I2 to be taken into consideration when the strain energy function is modeled and has permitted their effects to be highlighted over the entire range of states of strain. With the proposed model, the fit of the experimental data has been shown to provide an accurate response and predictive description in simple extension, biaxial extension, and pure shear.