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 of the left Cauchy-Green deformation tensor. The strain energy density function for the polynomial model is where are material constants and . 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 and we have