B modeling
==============


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


.. math::
 :label: eq-1

    \ textrm {Modeling}
    \ mathrm {2D}


.. image:: images/100007CC000069BB000067DFBB97E607D5BD7D2E.svg
    :width: 220
    :height: 216


.. _RefImage_100007CC000069BB000067DFBB97E607D5BD7D2E.svg:

**Boundary conditions:**


+-----------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
|:math:`\mathit{N1}`: :math:`\mathit{N2}`:|                                                                                                                                                                         |
+                                         + .. image:: images/Object_55.svg                                                                                                                                         +
|                                         |    :width: 220                                                                                                                                                          |
+                                         +    :height: 216                                                                                                                                                         +
|                                         |                                                                                                                                                                         |
+                                         +                                                                                                                                                                         +
|                                         | .. image:: images/Object_56.svg                                                                                                                                         |
+                                         +    :width: 220                                                                                                                                                          +
|                                         |    :height: 216                                                                                                                                                         |
+                                         +                                                                                                                                                                         +
|                                         |                                                                                                                                                                         |
+-----------------------------------------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------+


**Charging:**

Traction on the :math:`[34]` side (SEG2 mesh) + assignment of the same temperature on all knots

The total number of increments is 20 (10 increments between :math:`t=\mathrm{0s}` and :math:`\mathrm{1s}`, 10 increments between :math:`t=\mathrm{1s}` and :math:`\mathrm{2s}`)

**Behavior:**

The keywords ELAS and LEMAITRE are used, with the following parameters:

:math:`E=80000\mathrm{MPa}`

:math:`\nu =0.35`

:math:`\alpha =0.00004`

:math:`n=4.39`

:math:`\frac{1}{K}=0.003944`

:math:`\text{UN\_SUR\_M}=0.`


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

Number of knots: 4

Number of meshes: 2

1 QUAD4

1 SEG2


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

The calculated deformations serve as a reference for modeling A.


.. csv-table::

    "**Identification**", "**Reference**", "**Tolerance**"
    ":math:`t=0.3` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "-91.7598"," 1.00%"
    ":math:`t=0.8` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "-92.5802"," 1.00%"
    ":math:`t=1.3` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "70.1846"," 1.00%"
    ":math:`t=2.0` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "84.4120"," 1.00%"



.. csv-table::

    "**Identification**", "**Reference type**"
    ":math:`t=1.3` Total deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"
    ":math:`t=2.0` Total deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"



.. csv-table::

    "**Identification**", "**Reference type**"
    ":math:`t=1.3` Plastic deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"
    ":math:`t=2.0` Plastic deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"



.. csv-table::

    "**Identification**", "**Reference type**"
    ":math:`t=0.8` Thermal deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"
    ":math:`t=1.3` Thermal deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"
    ":math:`t=2.0` Thermal deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"



.. csv-table::

    "**Identification**", "**Reference type**"
    ":math:`t=1.3` Mechanical deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"
    ":math:`t=2.0` Mechanical deformations :math:`\mathit{EPSYY}` (:math:`\mathit{N3}`)", "Non-regression"