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


Geometry
---------

The diagram is not to scale, the gap between the two cylinders has been amplified for better visibility.


.. image:: images/1000000000000214000001BA0E31AF0660E567AC.png
    :width: 3.828in
    :height: 3.0693in


.. _RefImage_1000000000000214000001BA0E31AF0660E567AC.png:


.. csv-table::

    ":math:`{R}_{1}` ", "0.82"
    ":math:`{R}_{2}` ", "0.92"
    ":math:`{R}_{3}` ", "1."
    ":math:`{R}_{4}` ", "2."



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

The pellet is composed of an elastic material, the sheath is made of a viscoelastic material.

The elastic data is consistent for both materials.

Young's module: :math:`E\mathrm{=}1\mathit{MPa}`

Poisson's ratio: :math:`\nu \mathrm{=}0.3`

Law of LEMAITRE:

:math:`g(\sigma ,\lambda ,T)\mathrm{=}{(\frac{1}{K}\frac{\sigma }{{\lambda }^{\frac{1}{m}}})}^{n}` with :math:`\frac{1}{K}\mathrm{=}1`, :math:`\frac{1}{m}\mathrm{=}0`, :math:`n\mathrm{=}1`


Boundary conditions and loading
------------------------------------

**Boundary conditions:**

The cylinder is locked at :math:`\mathit{DY}` on the :math:`\mathrm{[}\mathit{AP},\mathit{BP}\mathrm{]}`, :math:`\mathrm{[}\mathit{AG},\mathit{BG}\mathrm{]}` and :math:`\mathrm{[}\mathit{CP},\mathit{PD}\mathrm{]}\mathrm{[}\mathit{CG},\mathit{PG}\mathrm{]}` sides.

**Charging:**

The cylinder is subjected to an internal pressure on :math:`\mathrm{[}\mathit{DP},\mathit{AP}\mathrm{]}`, this pressure is calculated so that at time :math:`t\mathrm{=}0`, the sheath behaves the same as the cylinder modelled in the ssna104a test.


.. image:: images/Object_4.svg
    :width: 409
    :height: 80


.. _RefImage_Object_4.svg:

with


.. image:: images/Object_5.svg
    :width: 409
    :height: 80


.. _RefImage_Object_5.svg:

,

.. image:: images/Object_6.svg
    :width: 409
    :height: 80


.. _RefImage_Object_6.svg:

,

.. image:: images/Object_7.svg
    :width: 409
    :height: 80


.. _RefImage_Object_7.svg:

with :math:`{P}_{0}\mathrm{=}1.E\mathrm{-}3\mathit{MPa}`, ssna104a test pressure.


.. image:: images/Object_8.svg
    :width: 409
    :height: 80


.. _RefImage_Object_8.svg:

,

.. image:: images/Object_9.svg
    :width: 409
    :height: 80


.. _RefImage_Object_9.svg:

,

.. image:: images/Object_10.svg
    :width: 409
    :height: 80


.. _RefImage_Object_10.svg:

,

.. image:: images/Object_11.svg
    :width: 409
    :height: 80


.. _RefImage_Object_11.svg:

The contact between the two cylinders is treated.