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


Characteristics of modeling
-----------------------------------

The modeling is two-dimensional with plane deformations D_ PLAN and static non-linear.

The vertical displacement imposed on the upper facet varies between :math:`0` and :math:`-\mathrm{0.2m}` in :math:`280` time steps between :math:`t=0.` and :math:`t=10`. The automatic subdivision of the time step is activated to manage situations of non-convergence of local integration.

The calculation option INDL_ELGA, which allows the directions of the Rice tensor to be calculated, is also activated. The results provided by this option are tested in non-regression mode.

The calculation option PDIL_ELGA, which allows you to calculate the values of the parameter A1_ LC2, is also activated. The results provided by this option are tested in non-regression mode.


Tested sizes and results
------------------------------

The solutions are calculated at point :math:`C` and compared to references GEFDYN. They are given in terms of stress :math:`{\sigma }_{\mathrm{yy}}`, total volume deformation :math:`{\varepsilon }_{v}` and isotropic work-hardening coefficients :math:`({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m})` and deviatory :math:`({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m})`, and summarized in the following tables:

:math:`{\sigma }_{\mathrm{yy}}(\mathrm{kPa})`

.. csv-table::

    ":math:`{\varepsilon }_{\mathrm{zz}}` "," TYPE "," GEFDYN ", "Tolerance (%)"
    "-1% ", "'SOURCE_EXTERNE'", "-243.1", "1.0"
    "-2% ", "'SOURCE_EXTERNE'", "-287.8", "1.0"
    "-5% ", "'SOURCE_EXTERNE'", "-345.1", "1.0"
    "-10% ", "'SOURCE_EXTERNE'", "-372.9", "1.0"
    "-20% ", "'SOURCE_EXTERNE'", "-377.2", "1.0"


:math:`{\varepsilon }_{V}=\text{trace}(\varepsilon )`

.. csv-table::

    ":math:`{\varepsilon }_{\mathrm{zz}}` "," TYPE "," GEFDYN ", "Tolerance (%)"
    "-1% ", "'SOURCE_EXTERNE'", "-4.07E-3", "1.0"
    "-2% ", "'SOURCE_EXTERNE'", "-6.04E-3", "1.0"
    "-5% ", "'SOURCE_EXTERNE'", "-8.18E-3", "2.0"
    "-10% ", "'SOURCE_EXTERNE'", "-7.19E-3", "6.0"
    "-20% ", "'SOURCE_EXTERNE'", "-1.87E-3", "4.0"


:math:`({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m})` (Map :math:`\mathrm{YZ}`)

.. csv-table::

    ":math:`{\varepsilon }_{\mathrm{zz}}` "," TYPE "," GEFDYN ", "Tolerance (%)"
    "-1% ", "'SOURCE_EXTERNE'", "0.398", "2.0"
    "-2% ", "'SOURCE_EXTERNE'", "0.455", "1.0"
    "-5% ", "'SOURCE_EXTERNE'", "0.517", "2.0"
    "-10% ", "'SOURCE_EXTERNE'", "0.553", "6.0"
    "-20% ", "'SOURCE_EXTERNE'", "0.582", "1.0"


:math:`({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m})` (Map :math:`\mathrm{XY}`)

.. csv-table::

    ":math:`{\varepsilon }_{\mathrm{zz}}` "," TYPE "," GEFDYN ", "Tolerance (%)"
    "-1% ", "'SOURCE_EXTERNE'", "0.643", "2.0"
    "-2% ", "'SOURCE_EXTERNE'", "0.755", "1.0"
    "-5% ", "'SOURCE_EXTERNE'", "0.870", "1.0"
    "-10% ", "'SOURCE_EXTERNE'", "0.926", "1.0"
    "-20% ", "'SOURCE_EXTERNE'", "0.961", "1.0"


:math:`({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m})`

.. csv-table::

    ":math:`{\varepsilon }_{\mathrm{zz}}` "," TYPE "," GEFDYN ", "Tolerance (%)"
    "-1% ", "'SOURCE_EXTERNE'", "0.146", "1.0"
    "-2% ", "'SOURCE_EXTERNE'", "0.155", "1.0"
    "-5% ", "'SOURCE_EXTERNE'", "0.166", "1.0"
    "-10% ", "'SOURCE_EXTERNE'", "0.181", "2.0"
    "-20% ", "'SOURCE_EXTERNE'", "0.214", "1.0"



Comments
------------

The comparison between *Code_Aster* and GEFDYN solutions is particularly good, with generally less than :math:`1\text{\%}` errors. Relative errors greater than :math:`1\text{\%}` appear for lower levels of tested values.