Work - conjugacy of stress and strain tensors and its role in 3D hyperelastic isotropic material formulation

In accordance with the framework of hyperelastic isotropic material description it appears possible to replace work-conjugate stress and strain quantities by alternative pairs of work-conjugate stress and strain quantities while other things left unaltered, i.e. based on a retained architecture of the strain energy density function. This replacement results in formally representing different kinds of material response behavior. This may be recognized from the various comparable forms of resulting uniaxial force versus axial stretch behavior in the representative 3D principal axes system. Clarifying and achieving comprehensive understanding of these observations is the main purpose of this paper.