Reference problem
=====================


Geometry
---------

Square plate


.. image:: images/10000A8C00000F3100000B443323552FBA79A62D.svg
    :width: 146
    :height: 108


.. _RefImage_10000A8C00000F3100000B443323552FBA79A62D.svg:


Material properties
-----------------------

These properties vary according to the time interval under consideration:


1. for :math:`0\le t\le 30s` and :math:`3630\le t\le 3660s`

:math:`E=178600\mathrm{MPa}`

:math:`\nu =0.3`

Plasticity with linear isotropic work hardening:


.. math::
: label: EQ-None

    {\ sigma} _ {y} =120\ mathrm {MPa}


1. for :math:`30\le t\le 3630s` and :math:`3660\le t\le 7260s`

:math:`E=178600\mathrm{MPa}`

:math:`\nu =0.3`

Lemaître viscoelastic behavior relationship:


.. image:: images/Object_1.svg
    :width: 146
    :height: 108


.. _RefImage_Object_1.svg:


Boundary conditions and loads
-------------------------------------

On :math:`A`: :math:`{u}_{x}={u}_{y}=0`

On the :math:`\mathrm{AB}` side: :math:`{u}_{x}=0`

Loading below (:math:`t=0` in :math:`0`)

Routes :math:`\mathrm{OA}` and :math:`\mathrm{AB}`, lasting 30 seconds.

Hold time in :math:`A` and :math:`B` of 3600 seconds.


.. image:: images/10000750000012B500000E29586FD877659B793B.svg
    :width: 146
    :height: 108


.. _refImage_10000750000012b500000e29586 FD877659B793B .svg: