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--- doc:user:elements:volumes:continuousdamage [2014/09/30 16:04] – joris
+++ doc:user:elements:volumes:continuousdamage [2021/04/09 11:33] – [LinGeersContinuousDamage] tanaka
@@ Line 9: / Line 9: @@
 === Description ===
+Lemaitre & Chaboche damage model [[doc:user:elements:volumes:continuousdamage#References|[1,2]]].
 $$
-\dot D = \left(\dfrac{\bar \sigma^2 R_\nu}{2ES\left(1-D\right)^2}\right)^s \dot \varepsilon^{pl} \mbox{ si } \varepsilon^{pl} > \varepsilon^{pl}_D
+\dot D = \left(\dfrac{\bar \sigma^2 R_\nu}{2ES\left(1-D\right)^2}\right)^s \dot \varepsilon^{pl} \mbox{, if } \varepsilon^{pl} > \varepsilon^{pl}_D \mbox{, and } \eta > \eta_D
 $$
@@ Line 19: / Line 20: @@
 $$
-where $ p $ is the pressure and $ \bar \sigma $ is Von Mises stress.
+where $ p $ is the pressure, $ \bar \sigma $ is Von Mises stress and $\eta$ is the stress triaxiality ratio.
 === Parameters ===
@@ Line 29: / Line 30: @@
 | Coefficient $ S $                                  |      ''LEMAITRE_BIG_S''      |     ''TO/TM''      |
 | Plastic strain threshold $ \varepsilon^{pl}_D $    |  ''LEMAITRE_EPL_THRESHOLD''  |     ''TO/TM''      |
+| Triaxiality threshold $ \eta_D $    |  ''LEMAITRE_TRIAX_THRESHOLD''  |     ''TO/TM''      |
 ===== BoneRemodContinousDamage =====
@@ Line 152: / Line 153: @@
 $$
-\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
 $$
@@ Line 194: / Line 195: @@
 $$
-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
 $$
@@ Line 212: / Line 213: @@
 ^   Name     ^     Metafor Code     ^  Dependency ^
 | $ \beta $  |  ''GEERS_BETA''  |     ''TO/TM''      |
@@ Line 239: / Line 239: @@
 \dot{\kappa} = C\left<1+A\dfrac{p}{\bar\sigma}\right> \left(\varepsilon^{pl}\right)^B \dot\varepsilon^{pl}
 $$
-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 MacCaulay symbols( $\langle \alpha\rangle = \alpha $ if $ \alpha \ge 0 $ and $ 0 $ otherwise)
 $$
@@ Line 250: / Line 250: @@
 | $ C $  |   ''GEERS_C''   |     ''TO/TM''      |
+===== References =====
+[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]
+[4]