Benchmark solution
=====================

Calculation method used for the reference solution
--------------------------------------------------------

Analytical solution for plastic deformation, identical to test HSNV124B.

For the displacements (structural elements): Comparison with the displacements obtained with *Code_Aster* for modeling A.


Benchmark results
----------------------

Evolution of the plastic deformation following :math:`y` and of the displacement following :math:`y` (the plastic deformation not being accessible for the structural elements).

Plastic deformation:

:math:`t=\mathrm{1s}` **(** :math:`T=0°C` **)**: :math:`{\varepsilon }^{p}=1\text{\%}`

**Heating:** Constant plastic deformation up to :math:`t=356/316=\mathrm{1.12658s}` :math:`T=12.658°C`

Then the plastic deformation decreases to reach :math:`t=\mathrm{2s}` :math:`{\varepsilon }^{p}=0.08\text{\%}`

We also test the components SIYY (constant) and SIZZ (zero, if the calculation is well performed under plane constraints).

.. csv-table::

    ":math:`T(s)` ", "Plastic deformation EPYY ", "DY (:math:`\mathrm{mm}`)", "SIYY (:math:`\mathrm{Mpa}`)", "SIZZ (:math:`\mathrm{Mpa}`)"
    "1", "0.01"," :math:`1.105{10}^{-2}` ", "210", "0"
    "1.1", "0.01"," :math:`1.115{10}^{-2}` ", "210", "0"
    "2"," :math:`{8.10}^{-4}` "," :math:`2.85{10}^{-3}` ", "210", "0"



Precision on the reference results
----------------------------------------

Analytics


Bibliographical references
--------------------------


1. IPSI: Phi2as study day on the nonlinear behaviors of materials on 30 March 2000