Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

Given the nature of the requests, the solution (constraints)

.. image:: images/Object_1.svg
    :width: 14
    :height: 12


.. _RefImage_Object_1.svg:

, deformations

.. image:: images/Object_2.svg
    :width: 14
    :height: 12


.. _RefImage_Object_2.svg:

and cumulative plastic deformation

.. image:: images/Object_3.svg
    :width: 14
    :height: 12


.. _RefImage_Object_3.svg:

) is homogeneous. At one point on the loading path :math:`\mathit{OA}`, we get:


.. image:: images/Object_4.svg
    :width: 14
    :height: 12


.. _RefImage_Object_4.svg:

The elastic deformation is equal to:


.. image:: images/Object_5.svg
    :width: 14
    :height: 12


.. _RefImage_Object_5.svg:

The viscoplastic deformation is equal to:


.. image:: images/Object_6.svg
    :width: 14
    :height: 12


.. _RefImage_Object_6.svg:

Finally, the total deformation is:


.. image:: images/Object_7.svg
    :width: 14
    :height: 12


.. _RefImage_Object_7.svg:

The reference solution is obtained by using a program written in Fortran that performs a step-by-step resolution of the problem with an implicit discretization scheme.


Benchmark results
----------------------

We will be interested in the values of the stresses and deformations at point :math:`A` of the loading path at the times :math:`t\mathrm{=}10s` and :math:`t\mathrm{=}60s`