A new I₁-based hyperelastic model for rubber elastic materials

In this Note, we propose a new hyperelastic model for rubber elastic solids applicable over the entire range of deformations. The underlying stored-energy function is a linear combination of the I₁-based strain invariants φ (I₁ ; α) = (I₁^α - 3^α) / (α 3^{α - 1}), where α is a real number. The predictive capabilities of the model are illustrated via comparisons with experimental data available from the literature for a variety of rubbery solids. In addition, the key theoretical and practical strengths of the proposed stored-energy function are discussed.