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


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

**Modeling** :math:`\mathrm{2D}` **:** 1 quadrangle QUAD8


.. image:: images/Object_9.svg
    :width: 155
    :height: 213


.. _RefImage_Object_9.svg:

The imposed load is as follows:


* the nodes :math:`\mathit{N1}`, :math:`\mathrm{N5}` and :math:`\mathrm{N2}` are blocked in the direction :math:`y`,


* node :math:`\mathrm{N1}` is locked in the direction :math:`x`,


* the nodes :math:`\mathrm{N4}`, :math:`\mathrm{N7}` and :math:`\mathrm{N3}` are displaced by :math:`\mathrm{1.5mm}` in :math:`\mathrm{1.5s}` spread over 50 increments.


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

The values are calculated at Gauss points.

At calculation time :math:`t\mathrm{=}0.93s`, we find for both models:

For the local version of the Rousselier model:


.. csv-table::

    "**Identification**", "**Type**", "**Aster**"
    "At the Gauss point no. 1, "", ""
    ":math:`{\sigma }_{\mathit{yy}}` "," NON_REGRESSION ", "942.702065474503"
    ":math:`{\sigma }_{\mathit{zz}}` "," NON_REGRESSION ", "135,66771521734"
    ":math:`p` "," NON_REGRESSION ", "0.6298511315011"
    ":math:`f` "," NON_REGRESSION ", "0.22492981455403"


For the Rousselier model in a non-local version:


.. csv-table::

    "**Identification**", "**Type**", "**Aster**"
    "At the Gauss point no. 1, "", ""
    ":math:`{\sigma }_{\mathit{yy}}` "," NON_REGRESSION ", "942.7047955569"
    ":math:`{\sigma }_{\mathit{zz}}` "," NON_REGRESSION ", "135,66857672362"
    ":math:`p` "," NON_REGRESSION ", "0.62985864189150"
    ":math:`f` "," NON_REGRESSION ", "0.22492903398716"




At the final moment :math:`t\mathrm{=}1.5s`, we find for the gradient model:


.. csv-table::

    "**Identification**", "**Type**", "**Aster**"
    "Max of: :math:`{\sigma }_{\mathit{yy}}` on the element", "NON_REGRESSION ", "721.68884425907"
    "Min of: :math:`{\sigma }_{\mathit{yy}}` on the item", "NON_REGRESSION ", "721.68884425907"