doc:user:elements:volumes:hyper_materials
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doc:user:elements:volumes:hyper_materials [2013/07/11 16:20] – joris | doc:user:elements:volumes:hyper_materials [2024/04/12 14:55] (current) – radermecker | ||
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- | ====== | + | ====== |
+ | |||
+ | ===== NeoHookeanHyperMaterial ===== | ||
+ | |||
+ | === Description === | ||
+ | |||
+ | Neo-Hookean hyperelastic law, using a '' | ||
+ | |||
+ | (Quasi-)incompressibility is treated by a volumetric/ | ||
+ | |||
+ | $$ | ||
+ | | ||
+ | $$ | ||
+ | |||
+ | |||
+ | |||
+ | $$ | ||
+ | U^{dev}=\dfrac{g_0}{2} \left[\text{tr}\right(\hat{\mathbf{C}}\left)-3\right] | ||
+ | $$ | ||
+ | |||
+ | === Parameters === | ||
+ | ^ | ||
+ | | Density | ||
+ | | NeoHookean coefficient ($C_1$) | ||
+ | | Initial bulk modulus ($k_0$) | ||
+ | |||
+ | ===== MooneyRivlinHyperMaterial ===== | ||
+ | |||
+ | === Description === | ||
+ | |||
+ | Mooney-Rivlin hyperelastic law, using a '' | ||
+ | |||
+ | (Quasi-)incompressibility is treated by a volumetric/ | ||
+ | |||
+ | $$ | ||
+ | | ||
+ | $$ | ||
+ | |||
+ | |||
+ | |||
+ | $$ | ||
+ | U^{dev}=\dfrac{g_0}{2} \left[\text{tr}\right(\hat{\mathbf{C}}\left)-3\right] | ||
+ | $$ | ||
+ | |||
+ | === Parameters === | ||
+ | ^ | ||
+ | | Density | ||
+ | | Mooney-Rivlin coefficient ($C_1$) | ||
+ | | Mooney-Rivlin coefficient ($C_2$) | ||
+ | | Initial bulk modulus ($k_0$) | ||
===== NeoHookeanHyperPk2Material ===== | ===== NeoHookeanHyperPk2Material ===== | ||
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=== Description === | === Description === | ||
- | Loi hyperélastique | + | Neo-Hookean hyperelastic law, using a '' |
- | Le potentiel volumique est calculé à partir de la compression moyenne de l' | + | The potential per unit volume is computed based on the average compressibility over the element, |
$$ | $$ | ||
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$$ | $$ | ||
- | Le potentiel déviatorique est calculé à partir du tenseur de Cauchy | + | The deviatoric potential is computed based on a Cauchy |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ Nom ^ Code Metafor | + | ^ Name |
- | | Densité | + | | Density |
- | | Module de compressibilité initial | + | | Initial bulk modulus |
- | | Module de cisaillement initial | + | | Initial shear modulus |
===== LogarihtmicHyperPk2Material ===== | ===== LogarihtmicHyperPk2Material ===== | ||
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=== Description === | === Description === | ||
- | Loi hyperélasyique Logarithmique utilisant un tenseur Pk2. | + | Logarithmic hyperelastic law, using a '' |
- | Le potentiel volumique est calculé à partir de la compression moyenne de l' | + | The potential per unit volume is computed based on the average compressibility of the element, |
$$ | $$ | ||
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$$ | $$ | ||
- | Le potentiel déviatorique est calculé à partir du tenseur de Cauchy | + | The deviatoric potential is computed based on a Cauchy |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ Nom ^ Code Metafor | + | ^ Name ^ Metafor |
- | | Densité | + | | Density |
- | | Module de compressibilité initial | + | | Initial bulk modulus |
- | | Module de cisaillement initial | + | | Initial shear modulus |
===== EvpIsoHLogarithmicHyperPk2Material ===== | ===== EvpIsoHLogarithmicHyperPk2Material ===== | ||
=== Description === | === Description === | ||
+ | Logarithmic hyperelastic law, using a '' | ||
- | Loi hyperélastique Logarithmique utilisant un tenseur '' | + | The potential per unit volume is computed based on the average compressibility of the element, |
- | + | ||
- | Le potentiel volumique est calculé à partir de la compression moyenne de l' | + | |
$$ | $$ | ||
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$$ | $$ | ||
- | Le potentiel déviatorique est calculé à partir du tenseur de Cauchy | + | The deviatoric potential is computed based on a Cauchy |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | + | ||
- | ^ | + | |
- | | Densité | + | |
- | | Module de compressibilité initial ($k_0$) | + | |
- | | Module de cisaillement initial ($g_0$) | + | |
- | | Numéro de la loi définissant la contrainte limite $\sigma_{yield}$ | '' | + | |
- | + | ||
+ | ^ | ||
+ | | Density | ||
+ | | Initial bulk modulus ($k_0$) | ||
+ | | Initial shear modulus ($g_0$) | ||
+ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | '' | ||
===== FunctionBasedHyperPk2Material ===== | ===== FunctionBasedHyperPk2Material ===== | ||
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=== Description === | === Description === | ||
- | Loi hyperélastique utilisant un tenseur | + | Hyperelastic law, using a '' |
- | Le potentiel volumique est calculé à partir de la compression moyenne de l' | + | The potential per unit volume is computed based on the average compressibility of the element, |
$$ | $$ | ||
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$$ | $$ | ||
- | Le potentiel déviatorique est calculé à partir d'une fonction utilisateur de type hyperélastique définie dans [[doc: | + | The deviatoric potential is computed based on a hyperelastic user function defined in [[doc: |
- | === Paramètres | + | === Parameters |
- | ^ Nom ^ Code Metafor | + | ^ Name |
- | | Densité | + | | Density |
- | | Module de compressibilité initial | + | | Initial bulk modulus |
- | | Numéro de la loi hyperélastique | + | | Number of the hyperelastic law |
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=== Description === | === Description === | ||
- | Loi viscoélastique à base hyperélastique utilisant un tenseur | + | Viscoelastic hyperelastic law, using a '' |
- | La loi comporte une branche principale | + | |
- | Chaque branche se comporte selon une loi viscoélastique entrée par l' | + | Each branch has its behavior corresponding to a viscoelastic law, supplied by the user. |
- | Le potentiel volumique est calculé à partir de la compression moyenne de l' | + | The potential per unit volume is computed based on the average compressibility of the element, |
$$ | $$ | ||
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$$ | $$ | ||
- | Le potentiel déviatorique est calculé à partir des lois visco-élastiques | + | The deviatoric potential is computed based on the viscoelastic laws : |
$$ | $$ | ||
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$$ | $$ | ||
- | Le potentiel de dissipation | + | The dissipation |
$$ | $$ | ||
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$$ | $$ | ||
- | avec | + | where |
$$ | $$ | ||
\Delta\hat{C} = {\hat{F}^n}^{-T} \hat{C}^{n+1} {\hat{F}^n}^{-1} | \Delta\hat{C} = {\hat{F}^n}^{-T} \hat{C}^{n+1} {\hat{F}^n}^{-1} | ||
$$ | $$ | ||
- | et | + | |
$$ | $$ | ||
\Delta C^{\text{vis}} = {{F^{\text{vis}}}^n}^{-T} {C^{\text{vis}}}^{n+1} {{F^{\text{vis}}}^n}^{-1} | \Delta C^{\text{vis}} = {{F^{\text{vis}}}^n}^{-T} {C^{\text{vis}}}^{n+1} {{F^{\text{vis}}}^n}^{-1} | ||
$$ | $$ | ||
- | Les potentiels | + | The potentials |
- | === Paramètres | + | === Parameters |
- | ^ Nom ^ | + | ^ Name ^ |
- | | Densité | + | | Density |
- | | Module de compressibilité initial | + | | Initial bulk modulus |
- | | Numéro de la loi viscoélastique principale | + | | Number of the main viscoelastic law |
- | | Numéro de la loi viscoélastique de Maxwell | + | | Number of the first Maxwell |
- | | Numéro de la loi viscoélastique de Maxwell | + | | Number of the second |
- | | Numéro de la loi viscoélastique de Maxwell | + | | Number of the third Maxwell |
doc/user/elements/volumes/hyper_materials.txt · Last modified: 2024/04/12 14:55 by radermecker