Modeling A
==============

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

The discrete element is stressed uniaxially. It is imposed on him:

• a constant temperature :math:`T=0°C`,

• a :math:`{F}_{P}={5.10}^{4}N` prestress force and

• a displacement of the :math:`(\mathrm{0x})` :math:`{U}_{\mathrm{tot}}={10}^{-3}\mathrm{mm}` axis.


Characteristics of the mesh
----------------------------

The mesh consists of two nodes connected by an element SEG2 with an axis :math:`\mathit{Ox}`.


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

We choose :math:`{U}_{1}={2.10}^{-4}\mathrm{mm}` and :math:`{U}_{2}={8.10}^{-4}\mathrm{mm}`.

After digital application, the reference solutions are:

:math:`{F}_{1}={4.10}^{4}N`

:math:`{F}_{2}=\mathrm{1,05}{.10}^{5}N`


.. csv-table::

    "**Nodes**", ":math:`U` ", "**Reference**"
    ":math:`\mathrm{N1}` "," :math:`{2.10}^{-4}\mathrm{mm}` "," :math:`-{4.10}^{4}N`"
    ":math:`\mathrm{N2}` "," :math:`{2.10}^{-4}\mathrm{mm}` "," :math:`{4.10}^{4}N`"
    "", "", ""
    ":math:`\mathrm{N1}` "," :math:`{8.10}^{-4}\mathrm{mm}` "," :math:`-\mathrm{1,05}{.10}^{5}N`"
    ":math:`\mathrm{N2}` "," :math:`{8.10}^{-4}\mathrm{mm}` "," :math:`\mathrm{1,05}{.10}^{5}N`"