Differences

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--- doc:user:elements:volumes:hyper_dev_potential [2025/11/14 15:13] – [BonetBurtonHyperPotential] vanhulle
+++ doc:user:elements:volumes:hyper_dev_potential [2025/11/14 15:33] (current) – [Anisotropic Elastic Potentials] vanhulle
@@ Line 78: / Line 78: @@
 W_{dev} = \sum^n_{i=1} W_{dev}^{(i)} \left(\bar{I}_1, \bar{I}_2, \bar{I}_3, \bar{I}_4^{(i)}, \bar{I}_5^{(i)} \right) = \sum^n_{i=1} W_{dev}^{(i)} \left(\bar{I}_1, \bar{I}_2, J, \bar{I}_4^{(i)}, \bar{I}_5^{(i)} \right)
 $$
+At the moment, a maximum of 3 separate principal directions can be given to the material law.
 === Reminders ===
@@ Line 122: / Line 123: @@
 | Holzapfel-Gasser-Ogden coefficient ($k_2$)  |  ''HYPER_HGO_K2''  |  ''TO/TM''  |
 | Fiber dispersion fraction ($d$)  |  ''HYPER_HGO_DISP''  |  ''TO/TM''  |
+| Direction of the first principal (fiber) direction ($a^1_x$) |  ''HYPER_FIB1_X''  |  -  |
+| Direction of the first principal (fiber) direction ($a^1_y$) |  ''HYPER_FIB1_Y''  |  -  |
+| Direction of the first principal (fiber) direction ($a^1_z$) |  ''HYPER_FIB1_Z''  |  -  |
+| Direction of the second principal (fiber) direction ($a^2_x$) |  ''HYPER_FIB2_X''  |  -  |
+| Direction of the second principal (fiber) direction ($a^2_y$) |  ''HYPER_FIB2_Y''  |  -  |
+| Direction of the second principal (fiber) direction ($a^2_z$) |  ''HYPER_FIB2_Z''  |  -  |
+| Direction of the third principal (fiber) direction ($a^3_x$) |  ''HYPER_FIB3_X''  |  -  |
+| Direction of the third principal (fiber) direction ($a^3_y$) |  ''HYPER_FIB3_Y''  |  -  |
+| Direction of the third principal (fiber) direction ($a^3_z$) |  ''HYPER_FIB3_Z''  |  -  |
@@ Line 149: / Line 159: @@
 | Bonet-Burton coefficient ($\gamma$)  |  ''HYPER_BB_GAMMA''  |  ''TO/TM''  |
 | Use the alternative Bonet-Burton law with $\beta~\text{ln}J$ \\ boolean: ''true'' (default) |  ''HYPER_BB_USE_LNJ''  |  ''TO/TM''  |
+| Direction of the first principal (fiber) direction ($a^1_x$) |  ''HYPER_FIB1_X''  |  -  |
+| Direction of the first principal (fiber) direction ($a^1_y$) |  ''HYPER_FIB1_Y''  |  -  |
+| Direction of the first principal (fiber) direction ($a^1_z$) |  ''HYPER_FIB1_Z''  |  -  |
+| Direction of the second principal (fiber) direction ($a^2_x$) |  ''HYPER_FIB2_X''  |  -  |
+| Direction of the second principal (fiber) direction ($a^2_y$) |  ''HYPER_FIB2_Y''  |  -  |
+| Direction of the second principal (fiber) direction ($a^2_z$) |  ''HYPER_FIB2_Z''  |  -  |
+| Direction of the third principal (fiber) direction ($a^3_x$) |  ''HYPER_FIB3_X''  |  -  |
+| Direction of the third principal (fiber) direction ($a^3_y$) |  ''HYPER_FIB3_Y''  |  -  |
+| Direction of the third principal (fiber) direction ($a^3_z$) |  ''HYPER_FIB3_Z''  |  -  |
+====== Rheological Laws ======
+{{:doc:user:ico-worker.png?25|Under construction}} Other laws will follow with the addition of visco-elasticity.
+===== CombinedElasticPotential =====
+=== Description ===
+The ''CombinedElasticPotential'' material law allows to combine two deviatoric hyperelastic potentials together as
+$$
+\boldsymbol{\sigma}^e = \boldsymbol{\sigma}^e_1 + \boldsymbol{\sigma}^e_2
+$$
+This can be illustrated using the following analogous rheological element
+{{ :doc:user:references:materials:rheoelast.png?300 |}}
+The main purpose of this element is to create anisotropic hyperelastic materials, as they are often composed of an isotropic (generally a Neo-Hookean) matrix component and an anisotropic fibrous component (see [[doc:user:elements:volumes:hyper_functionbased|anisotropic material examples]]). Nonetheless, this material law can also be used to add two or more deviatoric potentials, since ''CombinedElasticPotential'' can combine with itself.