# Metafor

ULiege - Aerospace & Mechanical Engineering

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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. 