Modélisation B ============== Caractéristiques de la modélisation ----------------------------------- La modélisation est de type «point matériel» avec des relations linéaires sur les composantes du tenseur des déformations simulant l'incompressibilité, en quasi-statique non-linéaire. On considère ici la phase 2 du chargement, avec un état de contraintes initial hydrostatique :math:`{\sigma}_{xx}^{0}={\sigma}_{yy}^{0}={\sigma}_{zz}^{0}={\sigma}^{0}=-30\mathit{kPa}` Les données sont identiques à celles de la modélisation A. Caractéristiques du maillage ---------------------------- Pas d'élément fini Grandeurs testées et résultats ------------------------------ Les solutions sont calculées au point :math:`C` et comparées aux résultats obtenus avec GEFDYN (mêmes tests que la modélisation A). Elles sont données en termes de pression isotrope, de déformation volumique plastique :math:`{\varepsilon}_{v}^{p}` et de facteurs de mobilisation, et récapitulées dans les tableaux suivants: :math:`3\cdot P'={\sigma}_{ij}\cdot {\delta}_{ij}` :math:`(\mathrm{kPa})` +---------------------------------+----------------------------------+-------------------------------+----------------+ | |Code_Aster(:math:`\mathit{kPa}` ) |GEFDYN (:math:`\mathit{kPa}` ) |erreur relative | | .. image:: images/Object_87.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_87.svg: | | | | | | | | | | (:math:`\mathit{kPa}` ) | | | | +---------------------------------+----------------------------------+-------------------------------+----------------+ | -15 | -80.223 | -80.194 | 0.038% | +---------------------------------+----------------------------------+-------------------------------+----------------+ | 15 | -73.988 | -74.078 | -0.122% | +---------------------------------+----------------------------------+-------------------------------+----------------+ | -15 | -66.055 | -66.250 | -0.295% | +---------------------------------+----------------------------------+-------------------------------+----------------+ | 15 | -52.625 | -52.999 | -0.707% | +---------------------------------+----------------------------------+-------------------------------+----------------+ | -15 | -45.539 | -45.672 | -0.292% | +---------------------------------+----------------------------------+-------------------------------+----------------+ :math:`{\varepsilon}_{v}^{p}=\mathit{trace}({\varepsilon}^{p})` +---------------------------------+-----------+----------+----------------+ | |Code_Aster |GEFDYN |erreur relative | | .. image:: images/Object_89.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_89.svg: | | | | | | | | | | (:math:`\mathit{kPa}` ) | | | | +---------------------------------+-----------+----------+----------------+ | -15 | -2.62e-5 | -2.63e-5 | -0.225% | +---------------------------------+-----------+----------+----------------+ | |-2.80e-5 |-2.78e-5 |0.854% | | .. image:: images/Object_90.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_90.svg: | | | | | | | | | | | | | | +---------------------------------+-----------+----------+----------------+ | |-4.48e-5 |-4.43e-5 |1.076% | | .. image:: images/Object_91.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_91.svg: | | | | | | | | | | | | | | +---------------------------------+-----------+----------+----------------+ | |-7.11e-5 |-7.05e-5 |0.842% | | .. image:: images/Object_92.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_92.svg: | | | | | | | | | | | | | | +---------------------------------+-----------+----------+----------------+ | |-1.13e-4 |-1.11e-4 |1.412% | | .. image:: images/Object_93.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_93.svg: | | | | | | | | | | | | | | +---------------------------------+-----------+----------+----------------+ | |-1.85e-4 |-1.85e-4 |0.261% | | .. image:: images/Object_94.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_94.svg: | | | | | | | | | | | | | | +---------------------------------+-----------+----------+----------------+ :math:`({r}_{\mathit{iso}}^{c}+{r}_{\mathit{ela}}^{s})` +----------------------------------+-----------+--------+----------------+ | |Code_Aster |GEFDYN |erreur relative | | .. image:: images/Object_96.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_96.svg: | | | | | | | | | | (:math:`\mathit{kPa}` ) | | | | +----------------------------------+-----------+--------+----------------+ | |0.00140 |0.00138 |1.329% | | .. image:: images/Object_97.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_97.svg: | | | | | | | | | | | | | | +----------------------------------+-----------+--------+----------------+ | |0.00220 |0.00217 |1.406% | | .. image:: images/Object_98.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_98.svg: | | | | | | | | | | | | | | +----------------------------------+-----------+--------+----------------+ | |0.00341 |0.00337 |1.246% | | .. image:: images/Object_99.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_99.svg: | | | | | | | | | | | | | | +----------------------------------+-----------+--------+----------------+ | |0.00518 |0.00510 |1.663% | | .. image:: images/Object_100.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_100.svg: | | | | | | | | | | | | | | +----------------------------------+-----------+--------+----------------+ | |0.00195 |0.00189 |2.947% | | .. image:: images/Object_101.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_101.svg: | | | | | | | | | | | | | | +----------------------------------+-----------+--------+----------------+ :math:`({r}_{\mathit{dev}}^{m}+{r}_{\mathit{ela}}^{d})` +----------------------------------+-----------+-------+----------------+ | |Code_Aster |GEFDYN |erreur relative | | .. image:: images/Object_103.svg | | | | | :width: 91 | | | | | :height: 24 | | | | | | | | | | | | | | | .. _RefImage_Object_103.svg: | | | | | | | | | | (:math:`\mathit{kPa}` ) | | | | +----------------------------------+-----------+-------+----------------+ | 15 | 0.326 | 0.326 | -0.088% | +----------------------------------+-----------+-------+----------------+ | -15 | 0.395 | 0.394 | 0.172% | +----------------------------------+-----------+-------+----------------+ | 15 | 0.395 | 0.394 | 0.172% | +----------------------------------+-----------+-------+----------------+ | -15 | 0.579 | 0.578 | 0.255% | +----------------------------------+-----------+-------+----------------+