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doc:user:elements:volumes:hyper_viscoelastic

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.

doc/user/elements/volumes/hyper_viscoelastic.txt · Last modified: 2016/03/30 15:23 (external edit)