Non-Hookean elasticity with arbitrary Poisson's ratios

In a previous paper \cite{Itskov-MoSM} we presented a hyperelastic isotropic material model whose stress-strain response is nonlinear even at infinitesimal deformations and cannot thus be linearized. As a result values of Poisson's ratio greater than one half were obtained. In this contribution, we further propose an isotropic strain energy function which is always positive-definite and depending on material constants delivers arbitrary values of Poisson's ratio (except of $-1$) in agreement with the laws of thermodynamics. The model response appears stable and plausible in various deformation states.