doc:user:elements:volumes:continuousanisodamage
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doc:user:elements:volumes:continuousanisodamage [2013/07/11 14:53] – created joris | doc:user:elements:volumes:continuousanisodamage [2016/03/30 15:23] (current) – external edit 127.0.0.1 | ||
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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 |
- | ===== BoneRemodContinuousAnisoDamage | + | ===== LemaitreChabocheContinuousAnisoDamage |
- | Il s'agit d'une loi d' | + | Anisotropic extension of [[doc: |
+ | === Description | ||
+ | |||
+ | The damage tensor is denoted $D$ | ||
+ | |||
+ | $$ | ||
+ | \dot D = \left(\dfrac{\tilde\sigma_{eq}^2 R_\nu}{2ES}\right)^s |D^{pl}| \mbox{ if } \varepsilon^{pl} > \varepsilon^{pl}_D | ||
+ | $$ | ||
+ | |||
+ | where $|D^{pl}|$ is a tensor with the same eigenvectors as $D^{pl}$, and eigenvalues equal to the absolute value of $D^{pl}$ eigenvalues. | ||
+ | The triaxiality function is defined as : | ||
+ | |||
+ | $$ | ||
+ | R_\nu = \dfrac{2}{3}\left(1+\nu\right) + 3\left(1-2\nu\right) \left(\dfrac{p}{\sigma_{eq}}\right)^2 | ||
+ | $$ | ||
+ | |||
+ | where $ p $ is the pressure and $ \sigma_{eq} $ Von Mises stress. | ||
+ | |||
+ | === Parameters === | ||
+ | ^ Name ^ Metafor Code ^ Dependency | ||
+ | | Young Modulus $ E $ | '' | ||
+ | | Poisson ratio $\nu$ | '' | ||
+ | | Exponent $ s $ | ||
+ | | Coefficient $ S $ | '' | ||
+ | | Plastic strain threshold $ \varepsilon^{pl}_D $ | '' | ||
+ | |||
+ | ===== BoneRemodContinuousAnisoDamage ===== | ||
+ | |||
+ | This law is used for bone remodeling (extracted from Doblaré' | ||
=== 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 | ||
- | $$ | + | with |
- | \begin{eqnarray*} | + | |
- | g_f &=& N^{1/ | + | |
- | g_r &=& \dfrac{1}{N^{1/ | + | |
- | \end{eqnarray*} | + | |
- | $$ | + | |
- | $ u $ est une mesure de l' | ||
- | === Paramètres === | + | \begin{align*} |
+ | g_f &= N^{1/ | ||
+ | g_r &= -N^{1/ | ||
+ | \end{align*} | ||
- | ^ Nom | ||
- | | Coefficient $ N $ | ||
- | | Pourcentage de surface disponible $ k $ | ||
- | | Energie de déformation élastique de référence $ \psi $ | '' | ||
- | | Demi-largeur de la zone morte $ \omega $ | '' | ||
- | | Vitesse de remodelage en formation $ c_f $ | ||
- | | Vitesse de remodelage en résorption $ c_r $ | ||
- | | Densité du matériau non endommagé | ||
- | | " | ||
+ | $ u $ is a measure of the elastic strain energy. - [[http:// | ||
+ | === Parameters === | ||
+ | ^ Name ^ Metafor Code ^ Dependency | ||
+ | | Coefficient $ N $ | '' | ||
+ | | Percentage of available surface $ k $ | '' | ||
+ | | Reference elastic strain energy $ \psi $ | ||
+ | | Half width of the dead zone $ \omega $ | ||
+ | | Remodeling speed $ c_f $ | ||
+ | | Remodeling speed $ c_r $ | ||
+ | | Density of undamaged material $ \rho_0 $ | ||
+ | | " | ||
- | ==== AlvBoneRemodContinuousAnisoDamage ==== | ||
- | Il s'agit d'une loi d' | + | |
+ | ==== AlvBoneRemodContinuousAnisoDamage ==== | ||
+ | This law is defined for the remodeling of the alveolar bone. Damage evolution also depends on pressure. | ||
+ | cfr [[http:// |
doc/user/elements/volumes/continuousanisodamage.1373547200.txt.gz · Last modified: 2016/03/30 15:22 (external edit)