Control of non-linearity and shrinkage-expansion asymmetry in volumetric strain energy formulations of hyperelastic materials

Hyperelastic strain energy formulations feature deviatoric (shape changing) and volumetric (volume changing) contributions. Much attention has been given to the development of experimentally motivated constitutive formulations of the deviatoric contributions. However, fewer variations have been proposed for the volumetric contribution, and many are valid only for small volumetric distortions. This paper critically reviews common volumetric strain energy formulations and proposes two novel ones which are both valid for large strain volume changes, and uniquely allow for the separate control of the response for shrinkage (volume decrease) and expansion (volume increase).