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doc:user:elements:volumes:iso_hypo_materials [2015/07/14 16:14] – [GeneralizedMaxwellViscoElastHypoMaterial] papeleuxdoc:user:elements:volumes:iso_hypo_materials [2022/07/14 11:04] – papeleux
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 | Young's modulus                                    |  ''ELASTIC_MODULUS''  |              | | Young's modulus                                    |  ''ELASTIC_MODULUS''  |              |
 | Poisson Ratio                                      |   ''POISSON_RATIO''   |              | | Poisson Ratio                                      |   ''POISSON_RATIO''   |              |
 +| Material Stiffness (0 : Ana - 1 : Num)             | ''MATERIALSTIFFMETHOD''  |      -       |
 +|     (only if element Stiffness == STIFF_ANALYTIC)  |                       |       -      |
 | Objectivity Method \\ (Jaumann = 0, GreenNaghdi = 1) |    ''OBJECTIVITY''    |      -       | | Objectivity Method \\ (Jaumann = 0, GreenNaghdi = 1) |    ''OBJECTIVITY''    |      -       |
 | Orthotropic axis                                   |    ''ORTHO_AX1_X''    |      -       | | Orthotropic axis                                   |    ''ORTHO_AX1_X''    |      -       |
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 \begin{cases} \begin{cases}
 p^{1}  = p^{0} + 3K {\Delta\epsilon}_{ii} \\ p^{1}  = p^{0} + 3K {\Delta\epsilon}_{ii} \\
-s^{1}_{ij}  = s^{0}_{ij} + 2G {\Delta\epsilon}_{ij} + \eta \frac{{\Delta\epsilon}_{ij}}{\Delta t}+s^{1}_{ij}  = s^{0}_{ij} + 2G {\Delta\hat{\epsilon}}_{ij} + \eta \frac{{\Delta\hat{\epsilon}}_{ij}}{\Delta t}
 \end{cases} \end{cases}
 $$ $$
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 The GeneralizedMaxwell viscoelastic model result in adding of up to now, maximum 2 visco-elastic Maxwell branches to the elastic material. The similar spring/damper model is shown at the figure below The GeneralizedMaxwell viscoelastic model result in adding of up to now, maximum 2 visco-elastic Maxwell branches to the elastic material. The similar spring/damper model is shown at the figure below
-{{ :doc:user:elements:volumes:generalizedmaxwell.png?200 |}}+{{ :doc:user:elements:volumes:generalizedmaxwell.png?400 |}}
  
 Defining Maxwell viscous parameters from materials data (for each Maxwell branch):  Defining Maxwell viscous parameters from materials data (for each Maxwell branch): 
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 \begin{cases} \begin{cases}
 p^{1}      &= p^{0} + 3K {\Delta\epsilon}_{ii} \\ p^{1}      &= p^{0} + 3K {\Delta\epsilon}_{ii} \\
-\underline{s}^{1}  &= s^{0}_{ij} + 2G {\Delta\underline{\epsilon}} +\underline{s}^{1}_{M1} + \underline{s}^{1}_{M2}+\underline{s}^{1}  &= \underline{s}_{E}^{1} + \underline{s}^{1}_{M1} + \underline{s}^{1}_{M2}
 \end{cases} \end{cases}
 $$ $$
 +Stresses in each branch are computed using : 
 $$ $$
 \begin{cases} \begin{cases}
-\underline{s}^{1}_{M1} &= e^{(\frac{-\Delta t}{\tau_{1}})} \underline{s}^{0}_{M1} + \Gamma_{1} (1-e^{\frac{-\Delta t}{\tau_{1}}}) \frac{\tau_{1}}{\Delta t} 2G {\Delta\underline{\epsilon}} \\ +\underline{s}_{E}^{1}  &= \underline{s}_{E}^{0} + 2G {\Delta\hat{\underline{\epsilon}}} \\ 
-\underline{s}^{1}_{M2} &= e^{(\frac{-\Delta t}{\tau_{2}})} \underline{s}^{0}_{M2} + \Gamma_{2} (1-e^{\frac{-\Delta t}{\tau_{2}}}) \frac{\tau_{2}}{\Delta t} 2G {\Delta\underline{\epsilon}} \\+\underline{s}^{1}_{M1} &= e^{(\frac{-\Delta t}{\tau_{1}})} \underline{s}^{0}_{M1} + \Gamma_{1} (1-e^{\frac{-\Delta t}{\tau_{1}}}) \frac{\tau_{1}}{\Delta t} 2G {\Delta\hat{\underline{\epsilon}}} \\ 
 +\underline{s}^{1}_{M2} &= e^{(\frac{-\Delta t}{\tau_{2}})} \underline{s}^{0}_{M2} + \Gamma_{2} (1-e^{\frac{-\Delta t}{\tau_{2}}}) \frac{\tau_{2}}{\Delta t} 2G {\Delta\hat{\underline{\epsilon}}} \\
 \end{cases} \end{cases}
 $$ $$
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 | Maxwel 2 Viscosity                                |   ''VISCO_ETA2''      |      -       | | Maxwel 2 Viscosity                                |   ''VISCO_ETA2''      |      -       |
  
-model implemented based on +model implemented based on {{:doc:user:references:materials:1997_formulation_and_implementation_of_three-dimensional_viscoelasticity_at_small_and_finite_strains_kaliske_rothert.pdf|Kaliske M, 
-"Kaliske & Rothert +Rothert H. Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Computational Mechanics 1997;19:228-239.}}
-Formulation and Implementation of three-dimensional viscoelasticity at small and finite strains +
-Computational mechanics 19(1997) 228-239"+
 ===== EvpIsoHHypoMaterial ===== ===== EvpIsoHHypoMaterial =====
  
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 $$ $$
-f=\dfrac{\overline{\sigma}}{1-D}-\sigma_{yield}=0+f=\dfrac{\overline{\sigma}}{1-h\cdot D}-\sigma_{yield}=0
 $$ $$
  
-where $ \overline{\sigma} $ is the equivalent stress computed as a function of [[doc:user:elements:volumes:plasticity_criterion#vonmisesplasticcriterion|Von Mises plasticy criterion]], $ \sigma_{yield} $ is the yield stress, $ D $ is the damage variable updated as a function of the [[doc:user:elements:volumes:continuousdamage|damage evolution law]].+where $ \overline{\sigma} $ is the equivalent stress computed as a function of [[doc:user:elements:volumes:plasticity_criterion#vonmisesplasticcriterion|Von Mises plasticy criterion]], $ \sigma_{yield} $ is the yield stress, $ D $ is the damage variable updated as a function of the [[doc:user:elements:volumes:continuousdamage|damage evolution law]]. Moreover, $h$ is the Micro-Crack Closure Effect parameter that makes the distinction of the weakening effect of damage under compressive and tensile stress states, which is defined as: 
 +$$ 
 + h = \left\{ 
 + \begin{array}{ll} 
 +  \text{DAMAGE_MCCE} &\mbox{, if } \dfrac{p}{J_2}< 0.0\\ 
 +  1.0 &\mbox{, if } \dfrac{p}{J_2}\geq 0.0\\ 
 + \end{array} 
 + \right. 
 +$$
  
 The evolution law coupled with plasticity can be integrated three ways depending on the parameter ''TYPE_INTEG'': The evolution law coupled with plasticity can be integrated three ways depending on the parameter ''TYPE_INTEG'':
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 | Initial damage                         |     ''DAMAGE_INIT''     |    -     | | Initial damage                         |     ''DAMAGE_INIT''     |    -     |
 | Integration method                         |     ''TYPE_INTEG''      |    -     | | Integration method                         |     ''TYPE_INTEG''      |    -     |
 +| Micro-Crack Closure Effect parameter (=1.0 by default)   |    ''DAMAGE_MCCE''     | |
  
 ===== ContinuousAnisoDamageEvpIsoHHypoMaterial ===== ===== ContinuousAnisoDamageEvpIsoHHypoMaterial =====
doc/user/elements/volumes/iso_hypo_materials.txt · Last modified: 2022/07/14 12:41 by papeleux
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