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


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

Behavior :math:`\mathrm{C1}`: isotropic work hardening, in :math:`\mathrm{3D}`. It is modelled in two ways:


* or using behavior VMIS_ISOT_TRAC, with traction curves given every :math:`10°C`, and interpolated for each temperature, which may be inaccurate,


* or using behavior VMIS_CIN1_CHAB, by cancelling non-linear kinematic work hardening, and by keeping only isotropic work hardening, which is precisely expressed in the form:


.. image:: images/Object_20.svg
    :width: 241
    :height: 32


.. _RefImage_Object_20.svg:


.. csv-table::

    "Then just take:", ":math:`{R}_{0}=\mathrm{SIGY}=200.` -1.7.T"
    "", ":math:`{R}_{I}=\mathrm{SIGY}+Q(T)=200.-\mathrm{1.7.T}+100.+\mathrm{1.7.T}=300`"
    "", ":math:`{C}_{I}={G}_{0}=0`"


1 time step between :math:`t=\mathrm{0s}` and :math:`t=\mathrm{1s}` and 20 time steps between :math:`t=\mathrm{1s}` and :math:`t=\mathrm{2s}`.


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

The mesh includes a HEXA8 mesh.


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

Behavior VMIS_ISOT_TRAC:


.. csv-table::

    "**Instant (** :math:`s` **)**", "**Plastic deformation by** :math:`Y` ", "**Reference**", "**Aster**", ":math:`\text{\%}` **difference**", "**difference**"
    ":math:`t=1.` "," :math:`\mathrm{EPYY}` ", "2.1072 10—03", "2.1096 10—03", "0.1"
    ":math:`\mathrm{t1}=1.45` "," :math:`\mathrm{EPYY}` ", "4.8108 10—03", "4.8135E-03", "0.056"
    "2"," :math:`\mathrm{EPYY}` ", "4.8108 10—03", "4.8135E-03", "0.056"


Behavior VMIS_CIN1_CHAB:


+-----------------------------+------------------------------------+-------------+-------------+---+--------------------------------++
|**Instant (** :math:`s` **)**|**Plastic deformation by** :math:`Y`|**Reference**|**Aster**        |:math:`\text{\%}` **Difference** |
+-----------------------------+------------------------------------+-------------+-------------+---+--------------------------------++
|:math:`\mathrm{t1}=1.`       |:math:`\mathrm{EPYY}`               |2.1072 10—03 |2.1096 10—03 |0.1                                 ||
+-----------------------------+------------------------------------+-------------+-------------+---+--------------------------------++
|:math:`\mathrm{t1}=1.45`     |:math:`\mathrm{EPYY}`               |4.8108 10—03 |4.81079 10—03    |0.0001                           |
+-----------------------------+------------------------------------+-------------+-------------+---+--------------------------------++
|2                            |:math:`\mathrm{EPYY}`               |4.8108 10—03 |4.81079 10—03    |0.0001                           |
+-----------------------------+------------------------------------+-------------+-------------+---+--------------------------------++