Further Results on Stretch Formulations of Simple Shear and Pure Torsion for Incompressible Isotropic Hyperelastic Materials

In a recent paper by Vitral (2023), the author described new results on the Poynting effect in simple shear and pure torsion that can be derived from stretch formulations for incompressible isotropic hyperelastic materials. The particular example of a strain-energy given in terms of the Bell strains was used to illustrate the results. The Bell strain is a linear function of the stretch tensor and the quadratic model used by Vitral (2023) is called the quadratic-Biot material, which is composed of both even and odd powers of stretches. In this paper, we make use of an alternative strain-energy that is a linear function of the stretch invariants to obtain similar results, some of which differ qualitatively from those obtained in Vitral (2023). The material model used here is called the generalized Varga model, a classical strain-energy that has been previously used in several applications of nonlinear elasticity. While the analysis of simple shear and pure torsion are well known, it turns out that stretch formulations provide useful alternative outcomes for these problems that are different from the classical formulations that use invariants of the Cauchy-Green tensors. In particular, it is found that for both problems, a transition in the Poynting effect from the classical to a reverse Poynting effect can occur depending on the ratio of the two material constants appearing in the strain-energy.