Strain-Energy Functions

Abstract

The isotropic elastic properties of a hyperelastic material model are described in terms of a strain-energy (stored-energy) function, typically as a function of the three invariants of each of the two Cauchy-Green deformation tensors, given in terms of the principal extension ratios, or stretches. A number of different strain-energy formulations exist, having properties and characteristics that make them appropriate for characterizing different hyperelastic material systems. The primary, and probably best known and most widely employed, strain-energy function formulation is the Mooney-Rivlin model, which reduces to the widely known neo-Hookean model. Other models which have been demonstrated to be quite appropriate and desirable for modeling rubberlike materials are the Ogden, Yeoh, Arruda-Boyce (statistically based), and Gent models. Flexible foams which exhibit finite elasticity characteristics can be modeled as hyperelastic material systems to a large extent. Strain-energy function models which are designated as foam models are the Blatz-Ko model and the Ogden-Storaker model. Soft tissues can also be modeled employing hyperelastic material models. Models designated as soft tissue models are the Fung model, the Holzapfel-Gasser-Ogden (HGO) model, and the Veronda-Westmann model.