doc:user:elements:volumes:iso_hypo_materials
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doc:user:elements:volumes:iso_hypo_materials [2015/07/14 14:40] – [KelvinVoigtViscoElastHypoMaterial] papeleux | doc:user:elements:volumes:iso_hypo_materials [2022/07/14 12:39] – papeleux | ||
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Line 17: | Line 17: | ||
| Young' | | Young' | ||
| Poisson Ratio | '' | | Poisson Ratio | '' | ||
+ | | Material Stiffness | ||
| Objectivity Method \\ (Jaumann = 0, GreenNaghdi = 1) | '' | | Objectivity Method \\ (Jaumann = 0, GreenNaghdi = 1) | '' | ||
| Orthotropic axis | | Orthotropic axis | ||
Line 37: | Line 38: | ||
| Young' | | Young' | ||
| Poisson ratio | '' | | Poisson ratio | '' | ||
+ | | Material Stiffness | ||
| Objectivity method \\ (Jaumann = 0, GreenNaghdi = 1) | | Objectivity method \\ (Jaumann = 0, GreenNaghdi = 1) | ||
| Orthotropic axis | '' | | Orthotropic axis | '' | ||
Line 64: | Line 66: | ||
\begin{cases} | \begin{cases} | ||
p^{1} = p^{0} + 3K {\Delta\epsilon}_{ii} \\ | p^{1} = p^{0} + 3K {\Delta\epsilon}_{ii} \\ | ||
- | s^{1}_{ij} | + | s^{1}_{ij} |
\end{cases} | \end{cases} | ||
$$ | $$ | ||
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| Viscosity coefficient | | Viscosity coefficient | ||
+ | |||
+ | ===== GeneralizedMaxwellViscoElastHypoMaterial===== | ||
+ | |||
+ | === Description === | ||
+ | |||
+ | The GeneralizedMaxwell viscoelastic model result in adding of up to now, maximum 2 visco-elastic Maxwell branches to the elastic material. The similar spring/ | ||
+ | {{ : | ||
+ | |||
+ | Defining Maxwell viscous parameters from materials data (for each Maxwell branch): | ||
+ | |||
+ | $$ | ||
+ | \begin{cases} | ||
+ | \Gamma_{i} &= \frac{\mu_{i}} | ||
+ | \tau_{i} | ||
+ | \end{cases} | ||
+ | $$ | ||
+ | |||
+ | The stresses in each Maxwell branch consist in 2 effects : | ||
+ | - the relaxation of previous time step stresses in this Maxwell branch | ||
+ | - the stress modification due to strain increment ${\Delta\epsilon}_{ij}$ | ||
+ | |||
+ | |||
+ | $$ | ||
+ | \begin{cases} | ||
+ | p^{1} &= p^{0} + 3K {\Delta\epsilon}_{ii} \\ | ||
+ | \underline{s}^{1} | ||
+ | \end{cases} | ||
+ | $$ | ||
+ | Stresses in each branch are computed using : | ||
+ | $$ | ||
+ | \begin{cases} | ||
+ | \underline{s}_{E}^{1} | ||
+ | \underline{s}^{1}_{M1} &= e^{(\frac{-\Delta t}{\tau_{1}})} \underline{s}^{0}_{M1} + \Gamma_{1} (1-e^{\frac{-\Delta t}{\tau_{1}}}) \frac{\tau_{1}}{\Delta t} 2G {\Delta\hat{\underline{\epsilon}}} \\ | ||
+ | \underline{s}^{1}_{M2} &= e^{(\frac{-\Delta t}{\tau_{2}})} \underline{s}^{0}_{M2} + \Gamma_{2} (1-e^{\frac{-\Delta t}{\tau_{2}}}) \frac{\tau_{2}}{\Delta t} 2G {\Delta\hat{\underline{\epsilon}}} \\ | ||
+ | \end{cases} | ||
+ | $$ | ||
+ | |||
+ | where $K$ and $G$ are compressibility and shear modulus, ${\Delta\underline{\epsilon}}$ is the stain increment during the time step $\Delta t$. | ||
+ | these equations shown clearly the necessity to track history of the total stresses but also to each Maxwell branch stresses $\underline{s}^{1}_{M1}$ and $\underline{s}^{1}_{M2}$. | ||
+ | |||
+ | |||
+ | === Parameters === | ||
+ | |||
+ | |||
+ | ^ | ||
+ | | Density | ||
+ | | Young' | ||
+ | | Poisson Ratio | ||
+ | | Material Stiffness | ||
+ | | Number of Maxwell branches 1 (default) or 2 | ||
+ | | Maxwel 1 Stiffness | ||
+ | | Maxwel 1 Viscosity | ||
+ | | Maxwel 2 Stiffness | ||
+ | | Maxwel 2 Viscosity | ||
+ | |||
+ | model implemented based on {{: | ||
+ | Rothert H. Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Computational Mechanics 1997; | ||
===== EvpIsoHHypoMaterial ===== | ===== EvpIsoHHypoMaterial ===== | ||
Line 102: | Line 161: | ||
| Young' | | Young' | ||
| Poisson Ratio | | Poisson Ratio | ||
+ | | Material Stiffness | ||
| Thermal Expansion | | Thermal Expansion | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
Line 147: | Line 207: | ||
| Young' | | Young' | ||
| Poisson Ratio | '' | | Poisson Ratio | '' | ||
+ | | Material Stiffness | ||
| Thermal expansion | | Thermal expansion | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
Line 180: | Line 241: | ||
| Young' | | Young' | ||
| Poisson Ratio | '' | | Poisson Ratio | '' | ||
+ | | Material Stiffness | ||
| Thermal expansion | | Thermal expansion | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
Line 213: | Line 275: | ||
| Young' | | Young' | ||
| Poisson Ratio | '' | | Poisson Ratio | '' | ||
+ | | Material Stiffness | ||
| Thermal Expansion | | Thermal Expansion | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
Line 252: | Line 315: | ||
| Young' | | Young' | ||
| Poisson Ratio | '' | | Poisson Ratio | '' | ||
+ | | Material Stiffness | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | '' | | Number of the material law which defines the yield stress $\sigma_{yield}$ | '' | ||
| Number of the damage evolution law | '' | | Number of the damage evolution law | '' | ||
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$$ | $$ | ||
- | f=\dfrac{\overline{\sigma}}{1-D}-\sigma_{yield}=0 | + | f=\dfrac{\overline{\sigma}}{1-h\cdot |
$$ | $$ | ||
- | where $ \overline{\sigma} $ is the equivalent stress computed as a function of [[doc: | + | where $ \overline{\sigma} $ is the equivalent stress computed as a function of [[doc: |
+ | $$ | ||
+ | h = \left\{ | ||
+ | | ||
+ | \text{DAMAGE_MCCE} & | ||
+ | 1.0 & | ||
+ | | ||
+ | | ||
+ | $$ | ||
The evolution law coupled with plasticity can be integrated three ways depending on the parameter '' | The evolution law coupled with plasticity can be integrated three ways depending on the parameter '' | ||
Line 311: | Line 383: | ||
| Young' | | Young' | ||
| Poisson Ratio | | Poisson Ratio | ||
+ | | Material Stiffness | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | '' | | Number of the material law which defines the yield stress $\sigma_{yield}$ | '' | ||
| Number of the damage evolution law | '' | | Number of the damage evolution law | '' | ||
| Initial damage | | Initial damage | ||
| Integration method | | Integration method | ||
+ | | Micro-Crack Closure Effect parameter (=1.0 by default) | ||
===== ContinuousAnisoDamageEvpIsoHHypoMaterial ===== | ===== ContinuousAnisoDamageEvpIsoHHypoMaterial ===== | ||
Line 345: | Line 419: | ||
| Young' | | Young' | ||
| Poisson Ratio | | Poisson Ratio | ||
+ | | Material Stiffness | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
| Number of the damage evolution law | '' | | Number of the damage evolution law | '' | ||
Line 371: | Line 446: | ||
| Young' | | Young' | ||
| Poisson Ratio | | Poisson Ratio | ||
+ | | Material Stiffness | ||
| Number of the material law which defines the yield stress $\sigma_{yield}$ | | Number of the material law which defines the yield stress $\sigma_{yield}$ | ||
| Number of the damage evolution law | '' | | Number of the damage evolution law | '' |
doc/user/elements/volumes/iso_hypo_materials.txt · Last modified: 2022/07/14 12:41 by papeleux