====== Viscoelastic laws ======

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

===== OgdenHyperFunction =====

=== Description ===

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} $.

=== Parameters ===
^   Name                                             ^     Metafor Code     ^  Dependency ^
| $ \mu_1 $                            |    ''OGDEN_MU1''     |  -  |
| $ \mu_2 $                            |    ''OGDEN_MU2''     |  -  |
| $ \mu_3 $                            |    ''OGDEN_MU3''     |  -  |
| $ a_1 $                            |    ''OGDEN_A1''     |  -  |
| $ a_2 $                            |    ''OGDEN_A2''     |  -  |
| $ a_3 $                            |    ''OGDEN_A3''     |  -  |

===== HenckyHyperFunction =====

=== Description ===

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} $.

=== Parameters ===
^   Name                               ^     Metafor Code     ^  Dependency ^
| $ \mu $                              |    ''HENCKY_MU''     |  -  |

===== IsoViscoElasticFunction =====

=== Description ===

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).


=== Parameters ===
^   Name                                             ^     Metafor Code     ^  Dependency ^
|  Number of the elastic law  |    ''VE_SPRING_LAW''     |  -  |
|  Number of the viscous law   |    ''VE_DASHPOT_LAW''    |  -  |


===== Applications =====

Hyperelastic laws are used with materials called ''FunctionBasedHyperPk2Material'', when the viscoelastic law is used with ''VeIsoHyperPk2Material'', see [[doc:user:elements:volumes:hyper_materials]].

Examples are found in [[commit:2006:09_19]], corrected in [[commit:2006:09_28]].