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doc:user:elements:volumes:hyper_materials

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doc:user:elements:volumes:hyper_materials [2024/04/12 14:51] radermeckerdoc:user:elements:volumes:hyper_materials [2024/04/12 14:55] radermecker
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 === Parameters === === Parameters ===
-^   Name                                                  ^     Metafor Code   +^   Name                                                  ^  Metafor Code  
-| Density                                                  ''MASS_DENSITY''  +| Density                                                 |''MASS_DENSITY''
-| NeoHookean coefficient ($C_1$)                              ''RUBBER_C1''    |  +| NeoHookean coefficient ($C_1$)                          | ''RUBBER_C1''  |  
-| Initial bulk modulus ($k_0$)                            |    ''RUBBER_PENAL''+| Initial bulk modulus ($k_0$)                            |''RUBBER_PENAL'' 
 + 
 +===== MooneyRivlinHyperMaterial ===== 
 + 
 +=== Description === 
 + 
 +Mooney-Rivlin hyperelastic law, using a ''Cauchy'' stress tensor $\boldsymbol{\sigma}$, stress in the current configuration. 
 + 
 +(Quasi-)incompressibility is treated by a volumetric/deviatoric multiplicative split of the deformation gradient, i.e.  $\bar{\mathbf{F}} = J^{-1/3}\mathbf{F}$. Hence the deviatoric potential is based on reduced invariants of $\bar{\mathbf{b}} =\bar{\mathbf{F}}\bar{\mathbf{F}}^T $. 
 + 
 +$$ 
 + W\left(I_1,I_2,J\right)  =  \bar{W}\left(\bar{I_1},\bar{I_2}\right) + K f\left(J\right) = C_1\left(\bar{I_1} - 3\right) + C_2\left(\bar{I_2} - 3\right)+ \frac{k_0}{2}\left[ \left(J-1\right)^2 + \ln^2 J\right] 
 +$$ 
 + 
 + 
 + 
 +$$ 
 +U^{dev}=\dfrac{g_0}{2} \left[\text{tr}\right(\hat{\mathbf{C}}\left)-3\right] 
 +$$ 
 + 
 +=== Parameters === 
 +^   Name                                                  ^  Metafor Code  ^ 
 +| Density                                                 |''MASS_DENSITY''
 +| Mooney-Rivlin coefficient ($C_1$)                          | ''RUBBER_C1''  |  
 +| Mooney-Rivlin coefficient ($C_2$)                          | ''RUBBER_C2''  |  
 +| Initial bulk modulus ($k_0$)                            |''RUBBER_PENAL''|  
  
 ===== NeoHookeanHyperPk2Material ===== ===== NeoHookeanHyperPk2Material =====
doc/user/elements/volumes/hyper_materials.txt · Last modified: 2024/05/02 11:15 by radermecker

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