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


Geometry
---------

Hardware point


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

Isotropic elasticity :math:`E\mathrm{=}184000\mathit{MPa}` :math:`\nu =0.3`


+-------------------------------------+-------------------------+----+----------------------------------+
|Isotropic work hardening                                            |                                  |
+-------------------------------------+-------------------------+----+----------------------------------+
|R_0                                  |:math:`97.83\mathit{MPa}`|B   |51.3                              |
+-------------------------------------+-------------------------+----+----------------------------------+
|Memory                                                              |                                  |
+-------------------------------------+-------------------------+----+----------------------------------+
|10                                   |                         |Q_0 |:math:`\mathrm{-}86.2\mathit{MPa}`|
+-------------------------------------+-------------------------+----+----------------------------------+
|ETA                                  |0.14                     |Q_M |:math:`270.5\mathit{MPa}`         |
+-------------------------------------+-------------------------+----+----------------------------------+
|Kinematic work hardening (modeling A)                                                                  |
+-------------------------------------+-------------------------+----+----------------------------------+
|C1                                   |182392 MPa               |G1_0|3079                              |
+-------------------------------------+-------------------------+----+----------------------------------+
|C2                                   |16678 MPa                |G2_0|178.7                             |
+-------------------------------------+-------------------------+----+----------------------------------+


+---------------------+----------------------------------------------------------------------+-+----+
|Viscosity of LEMAITRE                                                                         |    |
+---------------------+----------------------------------------------------------------------+-+----+
|UN_SUR_K             |:math:`1\mathrm{/}156.9{(\mathit{MPa}{S}^{1\mathrm{/}N})}^{\text{-1}}`|N|6.84|
+---------------------+----------------------------------------------------------------------+-+----+


+--------------------+---------+------+-------+
|Non-radiality effect                 |       |
+--------------------+---------+------+-------+
|DELTA1              |0.00306 2|DELTA2|0.01546|
+--------------------+---------+------+-------+


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

Non-proportional traction-torsional loading, with imposed deformation, with increments of 15 degrees, which amounts to a material point in imposing components :math:`{\varepsilon }_{\mathit{xx}}` and :math:`{\varepsilon }_{\mathit{xy}}`, with a phase difference between these two components. For each angle, the cycles are symmetric.


.. image:: images/10000000000003C6000001090FE60E93FABCE1B9.png
    :width: 6.1327in
    :height: 1.628in


.. _RefImage_10000000000003C6000001090FE60E93FABCE1B9.png:

The representation of the load in a :math:`\frac{2}{\sqrt{3}}{\varepsilon }_{\mathit{xy}}` - :math:`{\varepsilon }_{\mathit{xx}}` plane is as follows:


.. image:: images/10000000000003F900000412C8C117663ABEE64B.png
    :width: 2.3346in
    :height: 2.252in


.. _RefImage_10000000000003F900000412C8C117663ABEE64B.png:

To obtain an almost stabilized state, all of these cycles are applied 4 times.