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 $I_{1},I_{2}$ of the left Cauchy-Green deformation tensor.

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

W=\sum _{i=0}^{m}\sum _{j=0}^{n}C_{ij}(I_{1}-3)^{i}(I_{2}-3)^{j}

where $C_{ij}$ are material constants.

In the limit where $n=0$ , the polynomial model reduces to the Neo-Hookean solid model.

References

^ ^a ^b Rivlin, R. S. and Saunders, D. W., 1951, Large elastic deformations of isotropic materials VIII. Experiments on the deformation of rubber. Phi. Trans. Royal Soc. London Series A, 328, pp. 565-584.