Modeling A
==============


Characteristics of the mesh
----------------------------

Number of knots: 12.

3D modeling: 2 quadratic volume elements: HEXA8.


Tested features
-----------------------

Python commands are inserted directly into command file ASTER. These commands are used to write post-processing functions on the result fields, such as averages, the trace of a strain or stress tensor,... etc. The result fields are retrieved by the EXTR_COMP command.


Tested values
---------------

**First calculation:**

The Young's modulus in the :math:`X` direction in this case is the mean of the :math:`{\sigma }_{\mathit{xx}}` constraints:

:math:`{E}_{\mathit{xx}}^{\mathit{eff}}\mathrm{=}\mathrm{\langle }{\sigma }_{\mathit{xx}}\mathrm{\rangle }`

**Second calculation:**

The Young's modulus in the :math:`Y` direction in this case is the mean of the :math:`{\sigma }_{\mathit{yy}}` constraints:

:math:`{E}_{\mathit{yy}}^{\mathit{eff}}\mathrm{=}\mathrm{\langle }{\sigma }_{\mathit{yy}}\mathrm{\rangle }`


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", ":math:`\text{\%}` **difference**"
    ":math:`\mathrm{\langle }{\sigma }_{\mathit{xx}}\mathrm{\rangle }` ", "133333", "134134", "1.00"
    ":math:`\mathrm{\langle }{\sigma }_{\mathit{yy}}\mathrm{\rangle }` ", "150000", "150000", "0.00"