doc:user:elements:volumes:iso_hypo_materials
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doc:user:elements:volumes:iso_hypo_materials [2015/06/26 18:35] – [KevinVoigtViscoElastHypoMaterial] papeleux | doc:user:elements:volumes:iso_hypo_materials [2022/07/14 11:04] – papeleux | ||
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| Young' | | Young' | ||
| Poisson Ratio | '' | | Poisson Ratio | '' | ||
+ | | Material Stiffness (0 : Ana - 1 : Num) | '' | ||
+ | | (only if element Stiffness == STIFF_ANALYTIC) | ||
| Objectivity Method \\ (Jaumann = 0, GreenNaghdi = 1) | '' | | Objectivity Method \\ (Jaumann = 0, GreenNaghdi = 1) | '' | ||
| Orthotropic axis | | Orthotropic axis | ||
Line 54: | Line 56: | ||
=== Description === | === Description === | ||
- | Kelvin-Voigt viscoelastic law | + | The Kelvin-Voigt viscoelastic law result in adding a viscous effect on the elastic material. |
+ | The similar spring/ | ||
+ | {{ : | ||
+ | |||
+ | The effect of viscosity is only impacting deviatoric stresses | ||
+ | (all computations done on a finite time step $\Delta t$) | ||
+ | |||
+ | $$ | ||
+ | \begin{cases} | ||
+ | p^{1} = p^{0} + 3K {\Delta\epsilon}_{ii} \\ | ||
+ | s^{1}_{ij} | ||
+ | \end{cases} | ||
+ | $$ | ||
+ | |||
+ | |||
+ | where $K$ and $G$ are compressibility and shear modulus. | ||
+ | |||
+ | |||
+ | === Parameters === | ||
+ | |||
+ | ^ | ||
+ | | Density | ||
+ | | Young' | ||
+ | | Poisson Ratio | ||
+ | | 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 === | === Parameters === | ||
+ | |||
^ | ^ | ||
- | | Density | + | | Density |
- | | Young' | + | | Young' |
- | | Poisson Ratio | + | | Poisson Ratio |
- | | Viscosity | + | | 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 ===== | ||
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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 '' | ||
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| Initial damage | | Initial damage | ||
| Integration method | | Integration method | ||
+ | | Micro-Crack Closure Effect parameter (=1.0 by default) | ||
===== ContinuousAnisoDamageEvpIsoHHypoMaterial ===== | ===== ContinuousAnisoDamageEvpIsoHHypoMaterial ===== |
doc/user/elements/volumes/iso_hypo_materials.txt · Last modified: 2022/07/14 12:41 by papeleux