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


Geometry
---------

This is a test on a cubic mesh with a side of :math:`1` mm.


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

The material obeys the law of visco-hyper-elastic behavior. The hyperelastic behavior is of the Neo-Hookean type. The visco-elastic behavior is given by a Prony series of order :math:`3`.
The parameters of the law are:

.. csv-table::

    ":math:`{\mathrm{\nu }}=0.495` ", "Poisson's ratio"
    ":math:`{\mathrm{C_{10}}}=0.30,{\mathrm{C_{01}}}=\mathrm{C_{02}}=\mathrm{C_{20}}=0` ", "Long-term Mooney-Rivlin material parameters, i.e. for infinite behavior (MPa)"
    ":math:`{\mathrm{G}}=[1.33, 0.66, 0.33]` ", "List of values of the long-term shear modulus of the Prony series of order 3 (MPa)"
    ":math:`{\mathrm{\tau}}=[100, 10000, 1000000]` ", "List of relaxation time values from the Prony series of order 3 (s)"


.. _V6.04.518-conditions-aux-limites-et-chargements:

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

Symmetry conditions are imposed on the :math:`3` faces orthogonal to the :math:`3` directions of the coordinate system.

A displacement of :math:`0.2` mm is imposed on the stressed surface in :math:`1` s in order to generate a nominal stress state of the order of :math:`1` MPa. The load is
held for :math:`10` million seconds.