Stretch formulations and the Poynting effect in nonlinear elasticity

The second invariant of the left Cauchy–Green deformation tensor B (or right C) has been argued to play a fundamental role in nonlinear elasticity. Generalized neo-Hookean materials, which depend only on first invariant, lead universal relations that conflict with experimental data, fail display important mechanical behaviors (such as Poynting effect simple shear), and may not provide satisfactory link mesoscale. However, term is higher order strain contribution energy, us reflect what incomplete about materials. Instead usual elastic formulation, we investigate this matter from perspective stretch V=B Bell EBell=V−I formulations. Invariants these tensors offer different interpretation than those are linked classes main example adopt general isotropic energy quadratic strains, quadratic-Biot material. Despite being like neo-Hookean, material presents both classic reverse shear, whose direction switches function constant conjugate EBell. Its normal stress also local maximum amount transition observed Mooney–Rivlin solid. Moreover, even Varga model, linear poses question why true for model Green–Lagrange strains. Pure torsion solid cylinder discussed, particularly how behavior resultant axial force contrasts between