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Trace: • Kinematic hardening • Réunion 7 Décembre 2015 • Continuous isotropic damage • Initial conditions
doc:user:elements:volumes:continuousdamage

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doc:user:elements:volumes:continuousdamage [2015/07/17 01:51] – canalesdoc:user:elements:volumes:continuousdamage [2021/04/09 11:35] (current) – [LinGeersContinuousDamage] tanaka
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 === Description === === Description ===
  
 +Lemaitre & Chaboche damage model [[doc:user:elements:volumes:continuousdamage#References|[1,2]]].
 $$ $$
-\dot D = \left(\dfrac{\bar \sigma^2 R_\nu}{2ES\left(1-D\right)^2}\right)^s \dot \varepsilon^{pl} \mbox{ si } \varepsilon^{pl} > \varepsilon^{pl}_D+\dot D = \left(\dfrac{\bar \sigma^2 R_\nu}{2ES\left(1-D\right)^2}\right)^s \dot \varepsilon^{pl} \mbox{, if } \varepsilon^{pl} > \varepsilon^{pl}_D \mbox{, and } \eta > \eta_D
 $$ $$
  
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 $$ $$
  
-where $ p $ is the pressure and $ \bar \sigma $ is Von Mises stress.+where $ p $ is the pressure, $ \bar \sigma $ is Von Mises stress and $\eta$ is the stress triaxiality ratio.
  
 === Parameters === === Parameters ===
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 | Coefficient $ S $                                  |      ''LEMAITRE_BIG_S''      |     ''TO/TM''      | | Coefficient $ S $                                  |      ''LEMAITRE_BIG_S''      |     ''TO/TM''      |
 | Plastic strain threshold $ \varepsilon^{pl}_D $    |  ''LEMAITRE_EPL_THRESHOLD''  |     ''TO/TM''      | | Plastic strain threshold $ \varepsilon^{pl}_D $    |  ''LEMAITRE_EPL_THRESHOLD''  |     ''TO/TM''      |
 +| Triaxiality threshold $ \eta_D $    |  ''LEMAITRE_TRIAX_THRESHOLD''  |     ''TO/TM''      |
 ===== BoneRemodContinousDamage ===== ===== BoneRemodContinousDamage =====
  
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 $$ $$
-\dot D = D_C\dfrac{\dot \varepsilon^{pl}}{\varepsilon^{pl}_f-\varepsilon^{pl}_D} \mbox{ si } \varepsilon^{pl} > \varepsilon^{pl}_D+\dot D = D_C\dfrac{\dot \varepsilon^{pl}}{\varepsilon^{pl}_f-\varepsilon^{pl}_D} \mbox{ if } \varepsilon^{pl} > \varepsilon^{pl}_D
 $$ $$
  
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 $$ $$
-D = 1 - \left(\dfrac{\kappa_i}{\kappa}\right)^{n_1} \left(\dfrac{\kappa-\kappa_i}{\kappa_c-\kappa_i}\right)^{n_2} \mbox{ si } \kappa_i\leq\kappa\leq\kappa_c+D = 1 - \left(\dfrac{\kappa_i}{\kappa}\right)^{n_1} \left(\dfrac{\kappa-\kappa_i}{\kappa_c-\kappa_i}\right)^{n_2} \mbox{ if } \kappa_i\leq\kappa\leq\kappa_c
 $$ $$
  
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 ^   Name     ^     Metafor Code     ^  Dependency ^  ^   Name     ^     Metafor Code     ^  Dependency ^ 
 | $ \beta $  |  ''GEERS_BETA''  |     ''TO/TM''      | | $ \beta $  |  ''GEERS_BETA''  |     ''TO/TM''      |
- 
  
  
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 \dot{\kappa} = C\left<1+A\dfrac{p}{\bar\sigma}\right> \left(\varepsilon^{pl}\right)^B \dot\varepsilon^{pl} \dot{\kappa} = C\left<1+A\dfrac{p}{\bar\sigma}\right> \left(\varepsilon^{pl}\right)^B \dot\varepsilon^{pl}
 $$ $$
-where $p$ is the pressure, and $ \overline{\sigma} $ the Von Mises stress. $\langle .\rangle$ are MacCaulay symbols( $\langle \alpha\rangle = \alpha $ if $ \alpha \ge 0 $ and $ 0 $ sinon)+where $p$ is the pressure, and $ \overline{\sigma} $ the Von Mises stress. $\langle .\rangle$ are Macaulay symbols( $\langle \alpha\rangle = \alpha $ if $ \alpha \ge 0 $ and $ 0 $ otherwise)
  
 $$ $$
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 | $ C $  |   ''GEERS_C''   |     ''TO/TM''      | | $ C $  |   ''GEERS_C''   |     ''TO/TM''      |
  
-==== References ==== +===== References ===== 
-[1] + 
-[2]+[1] Lemaitre J. A continuous damage mechanics model for ductile fracture. Journal of Engineering Materials and 
 +Technology 1985;107:9–83. 
 + 
 +[2] Chaboche JL. Description thermodynamique et phénoménologique de la viscoélasticité cyclique avec endommagement. 
 +PhD Thesis, Université Pierre et Marie Curie, Paris VI, 1978. 
 [3] [3]
 +
 [4] [4]
doc/user/elements/volumes/continuousdamage.1437090666.txt.gz · Last modified: (external edit)
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