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


Geometry
---------


.. image:: images/100000000000039C000003586B407D8329B35E0C.png
    :width: 4.8126in
    :height: 4.4583in


.. _RefImage_100000000000039C000003586B407D8329B35E0C.png:

The aggregate is represented by a regulated hexahedral mesh occupying a volume with side 1.

It comprises 300 grains, defined by the belonging of each of the cells to a particular group of elements centered around a germ positioned randomly in the cube.


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


+----------------------+-----------------------------------------------------------------------------------------------------------------------+
|Elastic behavior with:|Young's module:                                                                                                        |
+                      +                                                                                                                       +
|                      |                                                                                                                       |
+                      + .. image:: images/Object_1.svg                                                                                        +
|                      |    :width: 111                                                                                                        |
+                      +    :height: 18                                                                                                        +
|                      |                                                                                                                       |
+                      +                                                                                                                       +
|                      |                                                                                                                       |
+                      +                                                                                                                       +
|                      |                                                                                                                       |
+----------------------+-----------------------------------------------------------------------------------------------------------------------+
|                      |Poisson's ratio:                                                                                                       |
+                      +                                                                                                                       +
|                      |                                                                                                                       |
+                      + .. image:: images/Object_2.svg                                                                                        +
|                      |    :width: 111                                                                                                        |
+                      +    :height: 18                                                                                                        +
|                      |                                                                                                                       |
+                      +                                                                                                                       +
|                      |                                                                                                                       |
+                      +                                                                                                                       +
|                      |                                                                                                                       |
+----------------------+-----------------------------------------------------------------------------------------------------------------------+


**Behavior** **mono-crystalline, with BCC24 sliding system.**

The behavior of the single crystal is defined by:

Type of flow: **MONO_VISC1** whose parameters are:


.. image:: images/Object_3.svg
    :width: 111
    :height: 18


.. _RefImage_Object_3.svg:

Isotropic work hardening type: **MONO_ISOT1** ** whose parameters are:


.. image:: images/Object_4.svg
    :width: 111
    :height: 18


.. _RefImage_Object_4.svg:


.. image:: images/Object_5.svg
    :width: 111
    :height: 18


.. _RefImage_Object_5.svg:


.. image:: images/Object_6.svg
    :width: 111
    :height: 18


.. _RefImage_Object_6.svg:


.. image:: images/Object_7.svg
    :width: 111
    :height: 18


.. _RefImage_Object_7.svg:

(interaction between sliding systems)

No kinematic work hardening: **MONO_CINE1**

.. image:: images/Object_8.svg
    :width: 111
    :height: 18


.. _RefImage_Object_8.svg:


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


+-------------------------+---------------------------------------------------------------------------------------------------------+
|Face :math:`z\mathrm{=}0`|:                                                                                                        |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         + .. image:: images/Object_9.svg                                                                          +
|                         |    :width: 111                                                                                          |
+                         +    :height: 18                                                                                          +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+-------------------------+---------------------------------------------------------------------------------------------------------+
|Face :math:`y\mathrm{=}0`|:                                                                                                        |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         + .. image:: images/Object_10.svg                                                                         +
|                         |    :width: 111                                                                                          |
+                         +    :height: 18                                                                                          +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+-------------------------+---------------------------------------------------------------------------------------------------------+
|Face :math:`x\mathrm{=}0`|:                                                                                                        |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         + .. image:: images/Object_11.svg                                                                         +
|                         |    :width: 111                                                                                          |
+                         +    :height: 18                                                                                          +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+-------------------------+---------------------------------------------------------------------------------------------------------+
|Face :math:`z\mathrm{=}1`|:                                                                                                        |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         + .. image:: images/Object_12.svg                                                                         +
|                         |    :width: 111                                                                                          |
+                         +    :height: 18                                                                                          +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+                         +                                                                                                         +
|                         |                                                                                                         |
+-------------------------+---------------------------------------------------------------------------------------------------------+


The load

.. image:: images/Object_13.svg
    :width: 111
    :height: 18


.. _RefImage_Object_13.svg:

is increasing linearly from 0 for :math:`t\mathrm{=}0` to :math:`0.1` for :math:`t\mathrm{=}\mathrm{100s}`.

To reduce the calculation time, this one is carried up to :math:`t\mathrm{=}\mathrm{1.8s}`, i.e. an imposed deformation of :math:`\text{0.18\%}`, in 3 increments.