doc:user:elements:volumes:continuousanisodamage
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doc:user:elements:volumes:continuousanisodamage [2013/11/11 22:06] – [BoneRemodContinuousAnisoDamage] marlene | doc:user:elements:volumes:continuousanisodamage [2014/09/30 17:16] – [Continuous orthotropic damage] joris | ||
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- | | + | |
- | La classe | + | The '' |
- | Lois implémentées dans Metafor | + | Laws implemented in Metafor |
===== AnisoDamageDummy ===== | ===== AnisoDamageDummy ===== | ||
- | Une loi bidon qui teste toutes les possibilités de variation de la variable | + | A dummy testing all possible variations of the damage |
===== LemaitreChabocheContinuousAnisoDamage ===== | ===== LemaitreChabocheContinuousAnisoDamage ===== | ||
- | Extension anisotrope de la [[doc: | + | Anisotropic extension of [[doc: |
- | === Description | + | === Description |
+ | |||
+ | The damage tensor is denoted $D$ | ||
$$ | $$ | ||
- | \dot D = \left(\dfrac{\tilde\sigma_{eq}^2 R_\nu}{2ES}\right)^s |D^{pl}| \mbox{ | + | \dot D = \left(\dfrac{\tilde\sigma_{eq}^2 R_\nu}{2ES}\right)^s |D^{pl}| \mbox{ |
$$ | $$ | ||
- | où $|D^{pl}|$ | + | where $|D^{pl}|$ |
- | La fonction de triaxialité est définie par: | + | The triaxiality function is defined as : |
$$ | $$ | ||
Line 26: | Line 28: | ||
$$ | $$ | ||
- | avec $ E $ le module de Young du matériau, $ \nu $ le coefficient du matériau, | + | where $ p $ is the pressure and $ \sigma_{eq} $ Von Mises stress. |
- | === Paramètres | + | === Parameters |
- | + | ^ | |
- | ^ | + | | Young Modulus |
- | | Module de Young $ E $ | '' | + | | Poisson |
- | | Coefficient de Poisson $\nu$ | + | | Exponent |
- | | Exposant | + | |
| Coefficient $ S $ | '' | | Coefficient $ S $ | '' | ||
- | | Déformation plastique seuil $ \varepsilon^{pl}_D $ | '' | + | | Plastic strain threshold |
===== BoneRemodContinuousAnisoDamage ===== | ===== BoneRemodContinuousAnisoDamage ===== | ||
- | Il s'agit d'une loi d' | + | This law is used for bone remodeling |
=== Description === | === Description === | ||
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$$ | $$ | ||
- | où | + | where |
+ | |||
+ | $S_v(d_h)$ is the surface per unit volume available for remodeling (polynomial of degree 5 in $d$), and $d_h$ is the average damage ($d_h = d_{ii}/3$) | ||
- | $S_v(d_h)$ est la surface disponible par unité de volume pour du remodelage (polynôme 5ème puissance de l' | ||
- | $$ | ||
\begin{align*} | \begin{align*} | ||
- | \dot r &= c_f(H, \rho_0)g_f\; | + | \dot r &= c_f(H, \rho_0)g_f\; |
- | \dot r &= -c_r(H, \rho_0)g_r\; | + | \dot r &= -c_r(H, \rho_0)g_r\; |
\end{align*} | \end{align*} | ||
- | $$ | ||
- | avec | ||
- | $$ | + | with |
+ | |||
\begin{align*} | \begin{align*} | ||
g_f &= N^{1/ | g_f &= N^{1/ | ||
g_r &= -N^{1/ | g_r &= -N^{1/ | ||
\end{align*} | \end{align*} | ||
- | $$ | ||
- | $ u $ est une mesure de l' | ||
- | === Paramètres === | + | $ u $ is a measure of the elastic strain energy. - [[http:// |
- | ^ | + | === Parameters === |
- | | Coefficient $ N $ | + | ^ |
- | | Pourcentage de surface | + | | Coefficient $ N $ | '' |
- | | Energie de déformation élastique de référence | + | | Percentage of available |
- | | Demi-largeur de la zone morte $ \omega $ | '' | + | | Reference elastic strain energy |
- | | Vitesse de remodelage en formation | + | | Half width of the dead zone $ \omega $ |
- | | Vitesse de remodelage en résorption | + | | Remodeling speed $ c_f $ |
- | | Densité du matériau non endommagé | + | | Remodeling speed $ c_r $ |
- | | "poids" | + | | Density of undamaged material |
+ | | "weight" | ||
==== AlvBoneRemodContinuousAnisoDamage ==== | ==== AlvBoneRemodContinuousAnisoDamage ==== | ||
- | + | This law is defined for the remodeling of the alveolar bone. Damage evolution also depends on pressure. | |
- | Il s'agit d'une loi d' | + | cfr [[http:// |
doc/user/elements/volumes/continuousanisodamage.txt · Last modified: 2016/03/30 15:23 by 127.0.0.1