Polynomial (hyperelastic model)

The polynomial hyperelastic material model 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 formula_1 of the left Cauchy-Green deformation tensor.
The strain energy density function for the polynomial model is 
where formula_3 are material constants and formula_4.
For compressible materials, a dependence of volume is added
where
In the limit where formula_7, the polynomial model reduces to the Neo-Hookean solid model. For a compressible Mooney-Rivlin material formula_8 and we have