Polynomial (hyperelastic model)

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The polynomial hyperelastic material model [1] is a phenomenological model of rubber elasticity. In this model, the strain energy density function is of the form of a polynomial in the two invariants of the left Cauchy-Green deformation tensor.

The strain energy density function for the polynomial model is [1]

where are material constants and .

For compressible materials, a dependence of volume is added


In the limit where , the polynomial model reduces to the Neo-Hookean solid model. For a compressible Mooney-Rivlin material and we have


  1. ^ a b Rivlin, R. S. and Saunders, D. W., 1951, Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber. Phi. Trans. Royal Soc. London Series A, 243(865), pp. 251-288.

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