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

The damage :math:`D(t)` is calculated from the data of the stress tensor :math:`\sigma (t)` and the cumulative plastic deformation :math:`p(t)` resulting from a thermomechanical calculation. The damage kinetics is given by:


.. csv-table::

    ":math:`\dot{D}=\frac{1}{{(1-D)}^{\mathrm{2s}}}{\left[\frac{1}{\mathrm{3ES}}(1+\nu ){\sigma }_{\mathrm{eq}}^{2}+\frac{3}{\mathrm{2ES}}(1-2\nu ){\sigma }_{H}^{2}\right]}^{s}\dot{p}` ", "if :math:`p>{p}_{d}`"
    ":math:`D=0` ", "otherwise"


:math:`{\sigma }_{\mathrm{eq}}` is the equivalent von Mises stress

:math:`{\sigma }_{H}` is the hydrostatic stress

:math:`{p}_{d}` represents the damage threshold

:math:`S` is a material characteristic (:math:`\mathrm{MPa}`)

:math:`s` is a material characteristic


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


+-------------------------+-----------------------+-----------+-----------------------+---------------+---------+------+
|:math:`\mathrm{Temp}(°C)`|:math:`E(\mathrm{MPa})`|:math:`\nu`|:math:`S(\mathrm{MPa})`|:math:`{P}_{d}`|:math:`s`       |
+                         +                       +           +                       +               +---------+------+
|                         |                       |           |                       |               |Case 1   |Case 2|
+-------------------------+-----------------------+-----------+-----------------------+---------------+---------+------+
|                         |143006.0E+6            |0.33       |7.0                    |1.005E-6       |0.8      |1.003 |
+-------------------------+-----------------------+-----------+-----------------------+---------------+---------+------+
|                         |143006.0E+6            |0.33       |7.0                    |1.005E-6       |0.8      |1.003 |
+-------------------------+-----------------------+-----------+-----------------------+---------------+---------+------+
|                         |143006.0E+6            |0.33       |7.0                    |1.005E-6       |0.8      |1.003 |
+-------------------------+-----------------------+-----------+-----------------------+---------------+---------+------+

Two exponent values

.. image:: images/Object_11.svg
    :width: 12
    :height: 14


.. _RefImage_Object_11.svg:

are successively used for the validation of developments in CALC_CHAMP.


Loading
----------

The loading corresponds to a tensile test at constant temperature and at a fixed deformation rate. It is defined in paragraph [:ref:`§2.2 <§2.2>`].