The HyperFunction class manages hyperelastic laws, when IsoViscoElasticFunction manages a combination of HyperFunctions to create a viscoelastic law.

Ogden hyperelastic law.

The deviatoric potential is computed based on a Cauchy tensor with a unit determinant:

$$U^{dev}= \sum_i^3 \sum_j^3 \frac{\mu_j}{a_j} \left(\lambda_i^{\frac{1}{2}a_j}-1\right)$$

where $\lambda_i$ are eigenvalues of Cauchy deviatoric matrix $\hat{C}$.

Hencky hyperelastic law.

The deviatoric potential is computed based on a Cauchy tensor with a unit determinant:

$$U^{dev}= \frac{1}{4} \mu \sum_i^3 \left(\ln\lambda_i\right)^2$$

where $\lambda_i$ are eigenvalues of Cauchy deviatoric matrix $\hat{C}$.

Generic viscoelastic law.

This law is used to combine to hyperelastic functions, one to model the elastic part (spring), the other one the viscous part (dashpot).

Hyperelastic laws are used with materials called FunctionBasedHyperPk2Material, when the viscoelastic law is used with VeIsoHyperPk2Material, see Hyperelastic materials.

Examples are found in Commit 2006-09-19, corrected in Commit 2006-09-28.