Table of Contents
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 Hyperelastic materials.
Examples are found in Commit 2006-09-19, corrected in Commit 2006-09-28.