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