Restricting the HyperelasticModels for Elastomers Basedon Some Thermodynamical,Mechanical, and Empirical Criteria

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Abstract
The stress–strain relation for rubber-like or elastomeric polymersis derivable from a strain energy function within the context of hyperelasticity.In the mechanical characterization of elastomers, a certain functional form ofthe strain energy function is considered in a hyperelastic constitutive modelthat is fitted to some experimental stress–strain data via regression analysis. Thisallows the experimenters to identify the parameters in the strain energy function.Unfortunately, most researchers performed a blind fit to the experimental datawithout restricting the strain energy function, which could lead to non-sensicalprediction of the material behavior in complex deformations. The current studypresents some thermodynamical, mechanical, and empirical criteria that restrictthe hyperelastic models, thus enabling the experimenters to find physicallyplausible material parameters. As an application of the criteria, the Yeoh modelwas restricted, and some specific constitutive inequalities were derived.