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doc:user:elements:volumes:continuousdamage

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doc:user:elements:volumes:continuousdamage [2015/07/17 01:54] – [LemaitreChabocheContinuousDamage] 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]]].+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 ˉσ is Von Mises stress.+where p is the pressure, ˉσ is Von Mises stress and η 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 εplD    |  ''LEMAITRE_EPL_THRESHOLD''  |     ''TO/TM''      | | Plastic strain threshold εplD    |  ''LEMAITRE_EPL_THRESHOLD''  |     ''TO/TM''      |
 +| Triaxiality threshold ηD    |  ''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 ^ 
 | β  |  ''GEERS_BETA''  |     ''TO/TM''      | | β  |  ''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 ¯σ the Von Mises stress. ⟨.⟩ are MacCaulay symbols( ⟨α⟩=α if α≥0 and 0 sinon)+where p is the pressure, and ¯σ the Von Mises stress. ⟨.⟩ are Macaulay symbols( ⟨α⟩=α if α≥0 and 0 otherwise)
  
 $$ $$
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 ===== References ===== ===== References =====
  
-[1]+[1] Lemaitre J. A continuous damage mechanics model for ductile fracture. Journal of Engineering Materials and 
 +Technology 1985;107:9–83.
  
-[2]+[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.1437090888.txt.gz · Last modified: 2016/03/30 15:22 (external edit)
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