Restricting the hyperelastic models for elastomers based on some thermodynamical, mechanical, and empirical criteria

The stress-strain relation for rubber-like or elastomeric polymers is derivable from a strain energy function within the context of hyperelasticity. In the mechanical characterization of elastomers, a certain functional form of the strain energy function is considered in a hyperelastic constitutive model that is fitted to some experimental stress- strain data via regression analysis. This allows the experimenters to identify the parameters in the strain energy function. Unfortunately, most researchers performed a blind fit to the experimental data without restricting the strain energy function, which could lead to non-sensical prediction of the material behavior in complex deformations. The current study presents some thermodynamical, mechanical, and empirical criteria that restrict the hyperelastic models, thus enabling the experimenters to find physically plausible material parameters. As an application of the criteria, the Yeoh model was restricted, and some specific constitutive inequalities were derived.