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


Geometry
---------

It is a material point, representative of a state of homogeneous stresses and deformations.


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


Isotropic elasticity coefficients
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Poisson's ratio: :math:`\nu =0.33`,

Young's module: :math:`E=184000.\mathrm{MPa}`


Flow law coefficients VISCOCHAB
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. code-block:: text

    VISCOCHAB =_F (Q_M=270.5400631,

    G_R=0.0,

    ETA =0.135

    C1=1.823924371 E5,

    G2_0=178.6588221,

    B=51.31782615,

    K_0=156.860705,

    K=97.82907013,

    N=6.835707681,

    C2=1.66796546 E4,

    A_I=0.5817571069,

    G1_0=3079.148555,

    MU=10.00231083,

    Q_0=-86.18795281,)


Hardening law coefficients VISC_CIN2_MEMO
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. code-block:: text

    MEMO_ECRO =_F (MU = 10.00231083,

    Q_M = 270.5400631,

    Q_0 = -86.18795281,

    ETA = 0.135),

    CIN2_CHAB =_F (B=51.31782615,

    C2_I=1.66796546 E4,

    C1_I=1.823924371 E5,

    G2_0=178.6588221,

    G1_0=3079.1485551,

    R_I=0.0,

    W=0.0,

    R_0=97.829070131,

    K=1.0,

    A_I=0.58175710691),

    LEMAITRE =_F (UN_SUR_K =6.37508292911937697 E-3, (=1./156.860705)

    UN_SUR_M =0.0,

    N=6.835707681),


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

The load is in imposed deformations: 13.5 amplitude cycles: :math:`{\varepsilon }_{\mathit{yy}}\mathrm{=}\mathrm{\pm }0.3\text{\%}`

Each cycle lasts :math:`\mathrm{3s}`, so the total charging time is :math:`40.5\text{s}`.

The time step for numerical resolution is for each of the 3 calculations in :math:`\mathrm{0.015s}`.


Initial conditions
--------------------

Zero stresses and deformations.