F modeling
==============




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

The modeling characteristics are the same as for modeling :math:`E`.




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

We discretize the structure in :math:`2\times (1\times 1\times 5)` finite elements PENTA6. The interface is therefore present within the central elements through level sets.


.. image:: images/100000000000017E0000032144CF89C9D8A78391.png
    :width: 1.6429in
    :height: 3.0992in


.. _RefImage_100000000000017E0000032144CF89C9D8A78391.png:

**Figure** 8.2-a **: F modeling mesh**




Piloting
--------

A specific control :math:`X-\mathrm{FEM}` SAUT_IMPOà is used using the group of nodes located immediately above the crack.




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

*Fashion* :math:`I` *:*

The values of contact Lagrangians LAGS_C are tested at all the nodes of the mesh crossed by the interface after convergence of the iterations of each STAT_NON_LINE operator, these values being uniform on the interface. To test all the values at once, we test the minimum and the maximum number of contact Lagrangians.


.. csv-table::

    "**No**", "**Identification**", "**Reference**", "**Tolerance (%)**"
    "0.5", "H1Z for all nodes", "1.36362396705485E-07", "1.0E-5"
    "0.5"," LAGS_Cpour all nodes", "3.66296853301E+05", "1.0E-5"
    "0.75", "H1Z for all nodes", "6.818119835274E-08", "1.0E-5"
    "0.75"," LAGS_Cpour all nodes", "1.8314842665E+05", "1.0E-5"
    "2", "H1Z for all nodes", "4.0908719011645E-07", "1.0E-5"
    "2"," LAGS_Cpour all nodes", "1.098890559903E+06", "1.0E-5"
    "3.5", "H1Z for all nodes", "7.49999999999582E-04", "1.0E-5"
    "3,5"," LAGS_Cpour all nodes", "1.75867720687844E+05", "1.0E-5"
    "4.5", "H1Z for all nodes", "2.49999999999582E-04", "1.0E-5"
    "4.5"," LAGS_Cpour all nodes", "58622.573562549", "1.0E-5"
    "5.5", "H1Z for all nodes", "7.49999999999582E-04", "1.0E-5"
    "5,5"," LAGS_Cpour all nodes", "1.75867720687844E+05", "1.0E-5"
    "7", "H1Z for all nodes", "1.49999999999958E-03", "1.0E-5"
    "7"," LAGS_Cpour all nodes", "28117.686527187", "1.0E-5"
    "9.5", "H1Z for all nodes", "2.49999999999582E-04", "1.0E-5"
    "9.5"," LAGS_Cpour all nodes", "4686.28108785798", "1.0E-5"
    "12", "H1Z for all nodes", "1.49999999999958E-03", "1.0E-5"
    "12"," LAGS_Cpour all nodes", "28117.686527187", "1.0E-5"
    "15", "H1Z for all nodes", "2.99999999999958E-03", "1.0E-5"
    "15"," LAGS_Cpour all nodes", "718.731177854856", "1.0E-5"


*Fashion* :math:`\mathrm{II}` *:*

The values of the Lagrangian friction values LAGS_F1 are tested at all the nodes of the mesh crossed by the interface after convergence of the iterations of each STAT_NON_LINE operator, these values being uniform on the interface. To test all the values at once, we test the minimum and the maximum of the Lagrangian friction values.


.. csv-table::

    "**No**", "**Identification**", "**Reference**", "**Tolerance (%)**"
    "0.5", "H1X for all nodes", "1.36362396705485E-07", "1.0E-5"
    "0.5"," LAGS_F1pour all nodes", "3.66296853301E+05", "1.0E-5"
    "0.75", "H1X for all nodes", "6.818119835274E-08", "1.0E-5"
    "0.75"," LAGS_F1pour all nodes", "1.8314842665E+05", "1.0E-5"
    "2", "H1X for all nodes", "4.0908719011645E-07", "1.0E-5"
    "2"," LAGS_F1pour all nodes", "1.098890559903E+06", "1.0E-5"
    "3.5", "H1X for all nodes", "7.49999999999582E-04", "1.0E-5"
    "3,5"," LAGS_F1pour all nodes", "1.75867720687844E+05", "1.0E-5"
    "4.5", "H1X for all nodes", "2.49999999999582E-04", "1.0E-5"
    "4.5"," LAGS_F1pour all nodes", "58622.573562549", "1.0E-5"
    "5.5", "H1X for all nodes", "7.49999999999582E-04", "1.0E-5"
    "5,5"," LAGS_F1pour all nodes", "1.75867720687844E+05", "1.0E-5"
    "7", "H1X for all nodes", "1.49999999999958E-03", "1.0E-5"
    "7"," LAGS_F1pour all nodes", "28117.686527187", "1.0E-5"
    "9.5", "H1X for all nodes", "2.49999999999582E-04", "1.0E-5"
    "9.5"," LAGS_F1pour all nodes", "4686.28108785798", "1.0E-5"
    "12", "H1X for all nodes", "1.49999999999958E-03", "1.0E-5"
    "12"," LAGS_F1pour all nodes", "28117.686527187", "1.0E-5"
    "15", "H1X for all nodes", "2.99999999999958E-03", "1.0E-5"
    "15"," LAGS_F1pour all nodes", "718.731177854856", "1.0E-5"





Comments
------------

The contact and friction values of the Lagrangians are calculated explicitly as a function of the displacement jump that is controlled. It is therefore natural to have almost zero errors.