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--- doc:user:elements:volumes:hyper_viscoelastic [2013/07/11 15:20] – created joris
+++ doc:user:elements:volumes:hyper_viscoelastic [2025/09/29 14:34] (current) – [IsoViscoElasticFunction] vanhulle
@@ Line 1: / Line 1: @@
+====== 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 two 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]].