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


Geometry
---------


.. image:: images/100002000000061500000800E410EB20C594714E.png
    :width: 2.4272in
    :height: 2.7626in


.. _RefImage_100002000000061500000800E410EB20C594714E.png:

We assign any value to the inclination, :math:`\beta \mathrm{=}37\mathit{degrés}`.

We choose :math:`a=1.E-3m`.


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

The material is isotropic linear elastic, with a Young's modulus :math:`E=2.E11\mathrm{Pa}` and a Poisson's ratio :math:`\nu =0.3`.

The traction curve is defined as:


* the slope is equal to 3.


* the elastic limit is equal to :math:`1.88\mathrm{GPa}`.

The hypothesis of plane constraints is applied.


Boundary conditions and loads
-------------------------------------


* Arbitrary mesh domain limits:

:math:`-{x}_{\mathrm{max}}\le x\le {x}_{\mathrm{max}}` with :math:`{x}_{\mathrm{max}}=\mathrm{10a}`

:math:`-{y}_{\mathrm{max}}\le y\le {y}_{\mathrm{max}}` with :math:`{y}_{\mathrm{max}}=\mathrm{20a}`


* Boundary conditions:

In order to exclusively block the 3 rigid plane modes.

:math:`\mathrm{UX}=\mathrm{UY}=0` at the bottom left corner of the full model.

:math:`\mathrm{UY}=0` at the bottom right corner of the full model.

On the bottom edge, we impose :math:`\mathrm{UY}=0`


* Charging: uniform tension :math:`{\sigma }_{\mathrm{yy}}={\sigma }_{0}` on the top edge:

The value of :math:`{\sigma }_{0}` is :math:`\mathrm{100MPa}`, in plane constraints.