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


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

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

The horizontal displacement imposed on the upper facet varies between :math:`0` and :math:`-1\mathit{mm}` in :math:`100` 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.


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

The solutions are calculated at point :math:`C` for orthotropic material and compared to code_aster modeling with isotropic material. They are given in terms of stress :math:`{\mathrm{\sigma }}_{\mathit{xy}}`, total volume deformation :math:`{\mathrm{\epsilon }}_{v}` and isotropic work-hardening coefficients :math:`\left({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m}\right)` and deviatory :math:`\left({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m}\right)`, and summarized in the following tables:

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

.. csv-table::

    ":math:`t` "," TYPE "," ISOTROPE ", "Tolerance (%)"
    "10.0", "'AUTRE_ASTER'", "-9.905E+03", "0.1"


:math:`{\mathrm{\epsilon }}_{V}=\text{trace}\left(\mathrm{\epsilon }\right)`

.. csv-table::

    ":math:`t` "," TYPE "," ISOTROPE ", "Tolerance (%)"
    "10.0", "'AUTRE_ASTER'", "-6.604E-05", "0.1"


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

.. csv-table::

    ":math:`t` "," TYPE "," ISOTROPE ", "Tolerance (%)"
    "10.0", "'AUTRE_ASTER'", "1.69732E-02", "0.1"


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

.. csv-table::

    ":math:`t` "," TYPE "," ISOTROPE ", "Tolerance (%)"
    "10.0", "'AUTRE_ASTER'", "1.43123E-01", "0.1"


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

.. csv-table::

    ":math:`t` "," TYPE "," ISOTROPE ", "Tolerance (%)"
    "10.0", "'AUTRE_ASTER'", "1.00107E-01", "0.1"