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


Geometry
---------

The stresses and deformations are homogeneous in the volume element. This can be represented by a plane or a solid element, for example:


.. image:: images/1000000000000109000000BAD6A0788DBB6F42AA.png
    :width: 2.5374in
    :height: 1.7972in


.. _RefImage_1000000000000109000000BAD6A0788DBB6F42AA.png:


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

Law of elastoplastic behavior with linear kinematic work hardening.


.. image:: images/10000000000000DF00000097125EB0AC85421A99.png
    :width: 1.9264in
    :height: 1.2626in


.. _RefImage_10000000000000DF00000097125EB0AC85421A99.png:

:math:`\begin{array}{}E=195000\mathrm{MPa}\\ \nu =0.3\\ {\sigma }_{\gamma }=181\mathrm{MPa}\\ {E}_{T}=1930\mathrm{MPa}\end{array}`


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

The volume element is locked along :math:`\mathrm{Ox}` along the :math:`[\mathrm{2,4}]` side while being subjected to a pull :math:`{\sigma }^{D}` and a shear force :math:`{\tau }^{D}`.


.. image:: images/100000000000010C000000A8A3A7163329D4436A.png
    :width: 2.4374in
    :height: 1.4543in


.. _RefImage_100000000000010C000000A8A3A7163329D4436A.png:


.. image:: images/10000000000000E50000009112D432FB70ABC472.png
    :width: 2.2902in
    :height: 1.45in


.. _RefImage_10000000000000E50000009112D432FB70ABC472.png:

The loading path is as follows:


.. csv-table::

    "", ":math:`{\sigma }^{D}\text{[MPa]}` "," :math:`{\tau }^{D}\text{[MPa]}`"
    ":math:`A` ", "151.2", "93.1"
    ":math:`B` ", "257.2", "33.1"