Expressions were obtained for the Young's modulus, E, and the shear modulus, G, of an elastic material, resulting from a small extension, twist, or shear, respectively, superposed on a finite uniaxial stretch. The expressions are given in terms of the stretch ratio, λ, and the partial derivatives of the strain-energy function with respect to λ. The predictions of the theory arising from several proposed forms of the strain-energy function are calculated and compared. If the small deformation is imposed after the stress resulting from the finite stretch in a viscoelastic material has relaxed, substitution of the time- or frequency-dependent viscoelastic functions for the elastic constants describes viscoelastic behavior in the small deformation when the finite stretch is within the region in which strain and time effects can be factored.
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Peng et al. (1971) studied this question.