Modeling A
==============

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

We use the SIMU_POINT_MAT command with SUPPORT = POINT.

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

The mesh does not exist and the calculations are restricted to a Gauss point.

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

The solutions are calculated at the Gauss point and compared to references for an identical loading path without micro-discharges. 
They are given in terms of deformations :math:`\varepsilon_{xy}`, plastic volume deformation :math:`{\epsilon }_{v}^{p}`,
and cyclic deviatory work hardening coefficients :math:`{r}_{ela}^{d,c}+{r}_{dev}^{c}`:
 
.. list-table:: Réponse de :math:`\varepsilon_{xy}`.

 *-**Identification**
   - **Reference type**
   - **Reference value**
   - **Tolerance**
 * - SIXY - INST :math:`=10`
   - AUTRE_ASTER
   - :math:`-1.95\times10^{-4}`
   - :math:`1`%
 * - SIXY - INST :math:`=25`
   - AUTRE_ASTER
   - :math:`1.94\times10^{-4}`
   - :math:`1`%
 * - SIXY - INST :math:`=40`
   - AUTRE_ASTER
   - :math:`1.95\times10^{-4}`
   - :math:`1`%

.. list-table:: Réponse de :math:`\varepsilon_v^p`.

 *-**Identification**
   - **Reference type**
   - **Reference value**
   - **Tolerance**
 * - SIXY - INST :math:`=10`
   - AUTRE_ASTER
   - :math:`-1.35\times10^{-5}`
   - :math:`2`%
 * - SIXY - INST :math:`=25`
   - AUTRE_ASTER
   - :math:`-4.28\times10^{-5}`
   - :math:`1`%
 * - SIXY - INST :math:`=40`
   - AUTRE_ASTER
   - :math:`-7.21\times10^{-5}`
   - :math:`1`%

.. list-table:: Réponse de :math:`{r}_{ela}^{d,c}+{r}_{dev}^{c}`.

 *-**Identification**
   - **Reference type**
   - **Reference value**
   - **Tolerance**
 * - SIXY - INST :math:`=25`
   - AUTRE_ASTER
   - :math:`0.23`
   - :math:`1`%
 * - SIXY - INST :math:`=40`
   - AUTRE_ASTER
   - :math:`0.23`
   - :math:`1`%


The comparison between solutions with and without microdischarge is particularly good, with generally less than :math:`1` percent error.