Summary of results
======================

In this paragraph, we focus on the results of modeling A. 
For information purposes, the following curves represent the various comparisons between Code_Aster for the two types of loading mentioned. 
in the document (:math:`\mathrm{AD}`: With discharge; :math:`\mathrm{SD}`: Without discharge) and GEFDYN,
the finite element software developed at laboratory MSSMat at Ecole Centrale Paris. 
The curves repeat the quantities tested previously in the previous section, namely :math:`{\varepsilon }_{\mathrm{xy}}` (:numref:`v6.04.207-synthese_1`), 
:math:`{\epsilon }_{v}^{p}` (:numref:`v6.04.207-synthese_2`) and :math:`({r}_{\text{ela}}^{d,c}+{r}_{\text{dev}}^{c})` (:numref:`v6.04.207-synthese_3`).

.. _v6.04.207-synthese_1:

.. figure:: images/10000000000002D8000001E4F000CFBE5545596E.png
 :align: center
 :width: 400

 Deviatory stress as a function of distortion: comparison of Code_Aster and GEFDYN solutions.

.. _v6.04.207-synthese_2:

.. figure:: images/100000000000025200000203A542172EB8591862.png
 :align: center
 :width: 400

 Plastic volume deformation as a function of shear stress: comparison between Code_Aster and GEFDYN solutions.

.. _v6.04.207-synthese_3:

.. figure:: images/1000000000000293000002237857FCAD3A907DE4.png
 :align: center
 :width: 400

 Cyclic deviation radius as a function of loading times: comparison between Code_Aster and GEFDYN solutions.

The differences observed between GEFDYN and Code_Aster highlight a suspicious management by GEFDYN of the work hardening of cyclical deviatory circles 
in the imposed shear plane. While the model predicts elastic micro-discharge, GEFDYN proposes a complete work-hardening of the cyclic deviation circle 
until perfect plasticity, before defining a cyclic deviatory circle with elastic radius. The behavior of the Code_Aster respects the elastic character 
of this discharge and, at the outlet of this micro-discharge, resumes a work-hardening slope identical to that obtained previously.

The GEFDYN development team is aware of the discrepancies observed between the two calculation codes.