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


Geometry
---------


.. image:: images/Object_1.svg
    :width: 380
    :height: 198


.. _RefImage_Object_1.svg:


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

Isotropic elasticity :math:`E=145000\mathrm{MPa}` :math:`\nu =0.3`

Elasto-plasticity with memory effect (modeling A): model VISC_CIN2_MEMO


+-------------------------------------+----------------------+----+-----------------------+
|Isotropic work hardening                                         |                       |
+-------------------------------------+----------------------+----+-----------------------+
|R_0                                  |:math:`35\mathrm{MPa}`|B   |12                     |
+-------------------------------------+----------------------+----+-----------------------+
|Memory                                                           |                       |
+-------------------------------------+----------------------+----+-----------------------+
|MU                                   |19                    |Q_0 |:math:`\mathrm{140MPa}`|
+-------------------------------------+----------------------+----+-----------------------+
|ETA                                  |0.5                   |Q_M |:math:`\mathrm{460MPa}`|
+-------------------------------------+----------------------+----+-----------------------+
|Kinematic work hardening (modeling A)                                                    |
+-------------------------------------+----------------------+----+-----------------------+
|C1                                   |0                     |G1_0|0                      |
+-------------------------------------+----------------------+----+-----------------------+
|C2                                   |0                     |G2_0|0                      |
+-------------------------------------+----------------------+----+-----------------------+

Viscoplasticity with memory effect (B and C models): model VISC_CIN2_MEMO

Parameters the same as the previous values except:


+-------------------------------------+------------------------------------------------------------+----+----+
|LEMAITRE                                                                                               |    |
+-------------------------------------+------------------------------------------------------------+----+----+
|UN_SUR_K                             |:math:`1/70{(\mathrm{MPa}{S}^{1/N})}^{\text{-1}}` =0.0142857|N   |24  |
+-------------------------------------+------------------------------------------------------------+----+----+
|Kinematic work hardening (B modeling)                                                                       |
+-------------------------------------+------------------------------------------------------------+----+----+
|C1                                   |1950 MPa                                                    |G1_0|50  |
+-------------------------------------+------------------------------------------------------------+----+----+
|C2                                   |65000 MPa                                                   |G2_0|1300|
+-------------------------------------+------------------------------------------------------------+----+----+

Viscoplasticity model VISCOCHAB (B and C models)


.. csv-table::

    ":math:`k` "," :math:`35\mathit{MPa}` ", "B", "12"," 12", "ETA "," 0.5", "C2"," :math:`65000\mathit{MPa}`"
    "A_K", "0", "M_R", "1", "C1"," :math:`1950\mathit{MPa}` ", "M_2", "1"
    "A_R", "1", "G_R", "0", "0", "M_1", "1", "D2", "1"
    "K_0"," :math:`70\mathrm{MPa}{S}^{1/N}` ", "MU", "19", "19", "D1", "1", "G_X2", "0"
    "N", "24", "Q_M", "460", "460", "G_X1", "0", "G2_0"," :math:`1300\mathit{MPa}`"
    "ALP ", "0 MPa ", "Q_0", "Q_0", "40 MPa ", "40 ", "G1_0"," :math:`50\mathit{MPa}` ", "A_I", "1"
    "", "", "QR_0 ", "200 MPa ", "", "", "", "", ""



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


.. csv-table::

    ":math:`\mathit{N6}` "," :math:`\mathit{dy}\mathrm{=}\mathit{dz}\mathrm{=}0`"
    ":math:`\mathit{N2}` "," :math:`\mathit{dy}\mathrm{=}0`"
    ":math:`\mathit{FACE1YZ}` "," :math:`\mathit{dx}\mathrm{=}0`"




.. csv-table::

    "Traction (modeling A):", ":math:`\mathit{FACEYZ}` "," "," :math:`\mathit{Fx}\mathrm{=}\mathrm{-}0.25\mathrm{\times }\mathit{coef}` "," :math:`\mathit{Coef}\mathrm{=}120` for :math:`t\mathrm{=}\mathrm{8s}`."



.. csv-table::

    "Pre-work hardening (B modeling)", ":math:`\mathit{FACEYZ}` "," :math:`\mathit{Sxx}\mathrm{=}250\mathit{MPa}\mathrm{\times }\mathit{coef2}` "," :math:`\mathit{Sxx}\mathrm{=}250\mathit{Mpa}\mathrm{\times }\mathit{coef2}`"


     :math:`\mathit{coef}2\mathrm{=}1` for :math:`t\mathrm{=}\mathrm{10s}`, then unload (:math:`\mathit{coef2}\mathrm{=}0`) for :math:`t\mathrm{=}\mathrm{11s}`.

     From :math:`\mathrm{11s}`, 20 cycles in imposed deformation (+/- 0.5%)