C modeling
==============

Characteristics of modeling
-----------------------------------

Same as modeling A, with nevertheless on the *HAUT* mesh, :math:`-\sigma_{zz}` increases from 0 to 10 MPa at time :math:`t=1` before decreasing to 10 kPa at time :math:`t=2` in 100 steps of time (uniformly distributed).

Tested sizes and results
------------------------------

The solutions are calculated at point NO8 at time :math:`t=1`. They are given in terms of total deformation :math:`\epsilon_{zz}` and volume plastic deformation :math:`\epsilon_v^p`. They are compared to solutions resulting from an *mtest* calculation at the hardware point. These are summarised by the two tables below.

.. list-table::

 *-**Size**
   - **MTest**
   - **Aster code**
 * - :math:`\epsilon_{zz}`
   - :math:`-0.054672`
   - :math:`-0.0546715`
 * - :math:`\epsilon_v^p`
   - :math:`-0.030513`
   - :math:`-0.0305132`

The correspondence is satisfactory. The following figure shows the evolution of the total deformation :math:`\epsilon_{zz}` with the stress :math:`\sigma_{zz}` applied. Positive work hardening is observed, in case of plastic flow (when :math:`Ip=1`), as well as elastic nonlinearity (when :math:`Ip=0`).

.. figure:: images/figure_modelisation_C.svg
 :align: center
 :width: 960
 :height: 360

 Response of the total deformation :math:`\epsilon_{zz}` with the stress :math:`\sigma_{zz}` applied. The plastic indicator :math:`Ip` is equal to 1 in case of plastic loading, and is equal to 0 otherwise.