Polynomial hyperelastic model

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

For compressible materials, a dependence of volume is added where In the limit where

, the polynomial model reduces to the Neo-Hookean solid model.

For a compressible Mooney-Rivlin material