doc:user:elements:volumes:isohard
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doc:user:elements:volumes:isohard [2013/07/11 14:44] – created joris | doc:user:elements:volumes:isohard [2020/07/08 10:16] (current) – [Python] papeleux | ||
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- | ====== | + | ====== |
- | La classe | + | The '' |
- | Lois implémentées dans Metafor. | + | |
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=== Description === | === Description === | ||
- | Ecrouissage isotrope linéaire | + | Linear isotropic hardening |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
- | |Limite élastique initiale | + | |Initial yield stress |
- | |Taux d' | + | |Plastic Modulus |
+ | |||
+ | **NB**: the plastic modulus is defined as $h = \frac{E E_T}{E - E_T} $, where $E$ is the Young' | ||
===== SaturatedIsotropicHardening ===== | ===== SaturatedIsotropicHardening ===== | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope à saturation | + | Saturated isotropic hardening |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
- | |Limite élastique initiale | + | |Initial yield stress |
- | |$Q $ | '' | + | |$Q $ | '' |
- | |$\xi$ | + | |$\xi$ |
===== DoubleSaturatedIsotropicHardening ===== | ===== DoubleSaturatedIsotropicHardening ===== | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope à double saturation | + | Double saturated isotropic hardening |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
- | |Limite élastique initiale | + | |Initial yield stress |
|$Q_1$ | |$Q_1$ | ||
- | |$\xi_1$ | + | |$\xi_1$ |
|$Q_2$ | |$Q_2$ | ||
- | |$\xi_2$ | + | |$\xi_2$ |
===== RambergOsgoodIsotropicHardening ===== | ===== RambergOsgoodIsotropicHardening ===== | ||
=== Description === | === Description === | ||
- | + | Ramberg-Osgood | |
- | Ecrouissage isotrope de Ramberg-Osgood | + | |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
- | |Limite élastique initiale | + | |Initial yield stress |
|$A $ | '' | |$A $ | '' | ||
|$n $ | '' | |$n $ | '' | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope de Swift (une forme plus commune de Ramberg - Osgood) | + | Swift isotropic hardening |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
- | |Limite élastique initiale | + | |Initial yield stress |
|$B $ | '' | |$B $ | '' | ||
|$n $ | '' | |$n $ | '' | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope de Krupkowsky | + | Krupkowski isotropic hardening |
$$ | $$ | ||
- | \sigma_{vm} = K \left(\bar{\varepsilon}^{vp}_ {0} + \bar{\varepsilon}^{vp}\right)^{n} | + | \sigma_{vm} = K \left(\bar{\varepsilon}^{vp}_{0} + \bar{\varepsilon}^{vp}\right)^{n} |
$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
- | |Defo Plastique équivalente initiale | + | | Initial equivalent plastic strain $\bar{\varepsilon}^{vp}_{0}$ |
- | |$K $ | '' | + | | strength coefficient |
- | |$n $ | '' | + | | strain hardening exponent |
===== Nl8pIsotropicHardening ===== | ===== Nl8pIsotropicHardening ===== | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope non linéaire | + | Nonlinear isotropic hardening with 8 parameters. First one implemented, |
- | Loi historique de Metafor (permet de faire quasi ce qu'on veut). | + | |
$$ | $$ | ||
- | \begin {eqnarray*} | + | \sigma_{vm} = \left(P_2-P_1\right) \left(1-\exp\left(-P_3\bar{\varepsilon}^{vp}\right)\right) + P_4\left(\bar{\varepsilon}^{vp}\right)^{P_5} |
- | \sigma_{vm} | + | $$ |
- | & & + \, P_1\left(1+P_6\,\bar{\varepsilon}^{vp}\right)^{P_7} | + | $$ |
- | \end{eqnarray*} | + | + P_1\left(1+P_6\bar{\varepsilon}^{vp}\right)^{P_7} + P_8\bar{\varepsilon}^{vp} |
$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ Nom ^ | + | ^ |
|$P_1$ | '' | |$P_1$ | '' | ||
|$P_2$ | '' | |$P_2$ | '' | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope linéaire par morceau. | + | Piecewise linear isotropic hardening. A function is associated to the yield stress. |
- | Associe une fonction quelconque à la limite élastique (par exemple pour faire du linéaire par morceau). | + | |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
- | |Limite élastique initiale | + | |Initial yield stress |
- | Une fonction d' | + | An [[doc: |
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=== Description === | === Description === | ||
- | |||
- | Ecrouissage isotrope de type puissance. | ||
$$ | $$ | ||
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$$ | $$ | ||
- | L' | + | This law is integrated with an iterative method. |
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
|$P_1$ | |$P_1$ | ||
|$P_2$ | |$P_2$ | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope de type " | + | " |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
|$P_1$ | |$P_1$ | ||
|$P_2$ | |$P_2$ | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope de type " | + | " |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ | + | ^ |
|$M_1$ | |$M_1$ | ||
|$M_2$ | |$M_2$ | ||
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=== Description === | === Description === | ||
- | Ecrouissage isotrope de type " | + | " |
$$ | $$ | ||
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$$ | $$ | ||
- | avec la contrainte limite de transition | + | where the transition |
$$ | $$ | ||
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$$ | $$ | ||
- | et la défo plastique de transition correspondante : | + | and the corresponding yield strain as |
$$ | $$ | ||
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$$ | $$ | ||
- | === Paramètres | + | === Parameters |
- | ^ Nom ^ | + | ^ |
|$\sigma_0$ | |$\sigma_0$ | ||
|$\beta$ | |$\beta$ | ||
|$\Theta_{0}$ | |$\Theta_{0}$ | ||
|$\Theta_{IV}$ | '' | |$\Theta_{IV}$ | '' | ||
+ | |||
+ | ===== Python ===== | ||
+ | |||
+ | User defined Isotropic Hardening by a pythonDirector : | ||
+ | |||
+ | Python Director allows user to define their own Isotropic Hardening law. Five functions has to be defined in the Python Class : | ||
+ | * a constructor (< | ||
+ | * a destructor (< | ||
+ | * computeSvm | ||
+ | * computeH (epl, pLaw) | ||
+ | * computePotential (epl, pLaw) for hyperElastics models | ||
+ | See the example below of a Linear Isotropic Hardening : | ||
+ | < | ||
+ | |||
+ | class MyIsoH(PythonIsotropicHardening): | ||
+ | def __init__(self, | ||
+ | print(" | ||
+ | PythonIsotropicHardening.__init__(self, | ||
+ | self.svm0 = _svm0 | ||
+ | self.h | ||
+ | print(" | ||
+ | print(" | ||
+ | print(" | ||
+ | print(" | ||
+ | print(" | ||
+ | def __del__(self): | ||
+ | print(" | ||
+ | print(" | ||
+ | input('' | ||
+ | exit(1) | ||
+ | def computeSvm(self, | ||
+ | #print " | ||
+ | return self.svm0+epl*self.h | ||
+ | def computeH(self, | ||
+ | #print " | ||
+ | return self.h | ||
+ | def computePotential(self, | ||
+ | #print " | ||
+ | return (self.svm0+self.h*epl*0.5)*epl | ||
+ | </ | ||
doc/user/elements/volumes/isohard.txt · Last modified: 2020/07/08 10:16 by papeleux