doc:user:elements:volumes:hyper_materials
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doc:user:elements:volumes:hyper_materials [2014/10/01 17:42] – joris | doc:user:elements:volumes:hyper_materials [2024/04/12 14:55] – radermecker | ||
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====== Hyperelastic materials ====== | ====== Hyperelastic materials ====== | ||
+ | |||
+ | ===== 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 ($k_0$) | ||
+ | |||
+ | ===== NeoHookeanHyperMaterial ===== | ||
+ | |||
+ | === 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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Neo-Hookean hyperelastic law, using a '' | Neo-Hookean hyperelastic law, using a '' | ||
- | The potential per unit volume is calculated | + | The potential per unit volume is computed |
$$ | $$ | ||
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$$ | $$ | ||
- | The deviatoric potential is calculated | + | The deviatoric potential is computed |
$$ | $$ | ||
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| Density | | Density | ||
| Initial bulk modulus ($k_0$) | | Initial bulk modulus ($k_0$) | ||
- | | Initial shear modulus ($g_0$) | + | | Initial shear modulus ($g_0$) |
===== LogarihtmicHyperPk2Material ===== | ===== LogarihtmicHyperPk2Material ===== | ||
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Logarithmic hyperelastic law, using a '' | Logarithmic hyperelastic law, using a '' | ||
- | The potential per unit volume is calculated | + | The potential per unit volume is computed |
$$ | $$ | ||
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$$ | $$ | ||
- | The deviatoric potential is calculated | + | The deviatoric potential is computed |
$$ | $$ | ||
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Logarithmic hyperelastic law, using a '' | Logarithmic hyperelastic law, using a '' | ||
- | The potential per unit volume is calculated | + | The potential per unit volume is computed |
$$ | $$ | ||
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$$ | $$ | ||
- | The deviatoric potential is calculated | + | The deviatoric potential is computed |
$$ | $$ | ||
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Hyperelastic law, using a '' | Hyperelastic law, using a '' | ||
- | The potential per unit volume is calculated | + | The potential per unit volume is computed |
$$ | $$ | ||
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$$ | $$ | ||
- | The deviatoric potential is calculated | + | The deviatoric potential is computed |
=== Parameters === | === Parameters === | ||
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Each branch has its behavior corresponding to a viscoelastic law, supplied by the user. | Each branch has its behavior corresponding to a viscoelastic law, supplied by the user. | ||
- | The potential per unit volume is calculated | + | The potential per unit volume is computed |
$$ | $$ | ||
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$$ | $$ | ||
- | The deviatoric potential is calculated | + | The deviatoric potential is computed |
$$ | $$ |
doc/user/elements/volumes/hyper_materials.txt · Last modified: 2024/05/02 11:15 by radermecker