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


Geometry, boundary conditions and loads
------------------------------------------------

**Template** :math:`\mathrm{3D}`

Consider a tab with dimensions :math:`50\mathrm{\times }20\mathrm{\times }3.5\mathit{mm}`. It is embedded on the left surface :math:`(\mathrm{S4})` and a movement of :math:`49.4142\mathrm{mm}` following :math:`x` is imposed on the right face :math:`(\mathrm{S6})`.

Y

Next pull :math:`x`:

:math:`u=49.4142\mathrm{mm}`

:math:`v=w=0`

Face S6

Face S4

Embedding:

:math:`u=v=w=0`

X

Length: :math:`\mathrm{50mm}`

Height: :math:`\mathrm{20mm}`

Thickness: :math:`3.5\mathrm{mm}`

**Flat model** (plane deformations)

Consider a tab with dimensions :math:`100\times 25\mathrm{mm}`. It is embedded on the left surface :math:`(\mathrm{L4})` and a movement of :math:`50\mathrm{mm}` following :math:`x` is imposed on the right face :math:`(\mathrm{L2})`.

Y

Next pull :math:`x`:

:math:`u=50\mathrm{mm}`

:math:`v=0`

Embedding:

:math:`u=v=0`

L2 side

L4 side

X

Length: :math:`\mathrm{100mm}`

Height: :math:`\mathrm{25mm}`

The load is increasing, in 20 increments.


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

We test in Signorini-type hyperelasticity.


.. csv-table::

    "Behavior ELAS_HYPER ", "Signorin"
    ":math:`\mathit{C10}` "," :math:`2.668\mathrm{MPa}`"
    ":math:`\mathit{C01}` "," :math:`0.271\mathrm{MPa}`"
    ":math:`\mathrm{C20}` "," :math:`0.446\mathrm{MPa}`"
    ":math:`K` "," :math:`2939`"