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doc:user:elements:volumes:isohard [2014/09/30 13:45] jorisdoc:user:elements:volumes:isohard [2020/07/08 10:15] – [Python] papeleux
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 |Initial yield stress $\sigma^{el}$  |  ''IH_SIGEL''  |  ''TM/TO''         | |Initial yield stress $\sigma^{el}$  |  ''IH_SIGEL''  |  ''TM/TO''         |
 |Plastic Modulus $h $                |    ''IH_H''    |  ''TM/TO''          |Plastic Modulus $h $                |    ''IH_H''    |  ''TM/TO''         
 +
 +**NB**: the plastic modulus is defined as $h = \frac{E E_T}{E - E_T} $, where $E$ is the Young's modulus and $E_T$ the tangent modulus.
  
 ===== SaturatedIsotropicHardening ===== ===== SaturatedIsotropicHardening =====
Line 54: Line 56:
 |Initial yield stress $\sigma^{el}$  |  ''IH_SIGEL''  |  ''TM/TO''         | |Initial yield stress $\sigma^{el}$  |  ''IH_SIGEL''  |  ''TM/TO''         |
 |$Q_1$                      |   ''IH_Q1''    |  ''TM/TO''          |$Q_1$                      |   ''IH_Q1''    |  ''TM/TO''         
-|$\xi_1$                    |   ''IH_KS1''    ''TM/TO''         +|$\xi_1$                    |   ''IH_KSI1''    ''TM/TO''         
 |$Q_2$                      |   ''IH_Q2''    |  ''TM/TO''          |$Q_2$                      |   ''IH_Q2''    |  ''TM/TO''         
-|$\xi_2$                    |   ''IH_KS2''    ''TM/TO''         +|$\xi_2$                    |   ''IH_KSI2''    ''TM/TO''         
  
 ===== RambergOsgoodIsotropicHardening ===== ===== RambergOsgoodIsotropicHardening =====
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 === Description === === Description ===
  
-Krupkowsky isotropic hardening+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}
 $$ $$
  
 === Parameters === === Parameters ===
  
-^          Name                                        ^  Metafor Code  ^ Dependency         ^ +^          Name                                                   ^  Metafor Code  ^ Dependency         ^ 
-|Initial equivalent plastic strain |  ''IH_EVPL0''  |  ''TM/TO''         | +| Initial equivalent plastic strain $\bar{\varepsilon}^{vp}_{0}$  |  ''IH_EVPL0''  |  ''TM/TO''         | 
-|$K $                                      |    ''IH_K''    |  ''TM/TO''         |  +strength coefficient  $K$                                       |    ''IH_K''    |  ''TM/TO''         |  
-|$n $                                      |    ''IH_N''    |  ''TM/TO''         +strain hardening exponent $n$                                   |    ''IH_N''    |  ''TM/TO''         
  
 ===== Nl8pIsotropicHardening ===== ===== Nl8pIsotropicHardening =====
Line 115: Line 117:
  
 $$ $$
-\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} &=\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} \, \\ +$$ 
-            & & \, P_1\left(1+P_6\,\bar{\varepsilon}^{vp}\right)^{P_7} \, \, P_8\,\bar{\varepsilon}^{vp+$$ 
-\end{eqnarray*}++ P_1\left(1+P_6\bar{\varepsilon}^{vp}\right)^{P_7} +  P_8\bar{\varepsilon}^{vp}
 $$ $$
  
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 ^          Name                                        ^  Metafor Code  ^ Dependency         ^ ^          Name                                        ^  Metafor Code  ^ Dependency         ^
-|Initial yield stress $\sigma^{el}$    ''IH_SIGEL''  |  ''GD''         |+|Initial yield stress $\sigma^{el}$    ''IH_SIGEL''  |  ''IF_EPL''         |
  
-[[doc:user:general:fonctions]] must be associated to ''IH_SIGEL'' (depending on generalized displacements ''GD'').+An [[doc:user:general:fonctions]] must be associated to ''IH_SIGEL'' (depending on ''Field(IF_EPL)'').
  
  
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 |$\Theta_{0}$  |   ''KM_THETA0''      ''TM/TO''            |$\Theta_{0}$  |   ''KM_THETA0''      ''TM/TO''           
 |$\Theta_{IV}$ |   ''KM_THETA4''      ''TM/TO''           | |$\Theta_{IV}$ |   ''KM_THETA4''      ''TM/TO''           |
 +
 +===== 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 (__init__),
 +  * a destructor (__del__) that must never be called, 
 +  * computeSvm  (epl, pLaw)
 +  * computeH (epl, pLaw)
 +  * computePotential (epl, pLaw) for hyperElastics models
 +See the example below of a Linear Isotropic Hardening : 
 +<code>
 +
 +class MyIsoH(PythonIsotropicHardening):
 +    def __init__(self, _no, _svm0, _h):
 +        print("MyIsoH : __init__")
 +        PythonIsotropicHardening.__init__(self,_no)
 +        self.svm0 = _svm0
 +        self.h    = _h
 +        print("no = ", _no)
 +        print("self.svm0 = ", self.svm0)
 +        print("self.h = ", self.h)
 +        print("MyIsoH : __init__ finished")
 +        print("computeSvm(0.0) = " , self.computeSvm(0.0, None))
 +    def __del__(self):
 +        print("MyIsoH : __del__")
 +        print("callToDestructor of MyIsoH not allowed. Add MyIsoH.__disown__()")
 +        input('')
 +        exit(1)
 +    def computeSvm(self, epl, pLaw) :
 +        #print "MyIsoH compute SVM"
 +        return self.svm0+epl*self.h
 +    def computeH(self, epl, pLaw) :
 +        #print "MyIsoH compute H"
 +        return self.h
 +    def computePotential(self, epl, pLaw) :
 +        #print "MyIsoH compute Potential"
 +        return (self.svm0+self.h*epl*0.5)*epl
 +</code>
  
  
doc/user/elements/volumes/isohard.txt · Last modified: 2020/07/08 10:16 by papeleux

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