B modeling
==============


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

Modeling: C_ PLAN. It is used to validate the 'VERSION3' keyword used for ALGO_LAGR in DEFI_CONTACT. The structure is a healthy square, in which an arc-shaped interface is introduced.

Contact/friction is treated with elements X- FEMquadratiques :math:`\text{P2}` (displacement) and :math:`\text{P1}` (pressure), i.e. carrying the degrees of freedom of movement on all the nodes and the Lagranges of contact/friction on the vertex nodes.


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

Number of knots: 6561

Number of meshes and types: 3200 TRIA6 for the plate and 160 SEG3 for the edges.


.. image:: images/100000000000031C00000315549C5EFE4167F9B4.png
    :width: 4.2472in
    :height: 4.0799in


.. _RefImage_100000000000031C00000315549C5EFE4167F9B4.png:


.. _Ref15420311611:

Figure 4.2‑a: 2D triangle mesh


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

The values only appear at the interface nodes from the new mesh.


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Precision**"
    ":math:`\text{LAGS\_C}` at points :math:`A` and :math:`C` (MIN)", "'ANALYTIQUE'", "-0.1"," 0.1%"
    ":math:`\text{LAGS\_C}` at point :math:`B` (MAX)", "'ANALYTIQUE'", "-0.06110"," 0.1%"
    ":math:`\text{LAGS\_F1}` at point :math:`B` (MIN)", "'ANALYTIQUE'", "0"," 0.1%"
    ":math:`\text{LAGS\_F1}` at point :math:`A` (MAX)", "'ANALYTIQUE'", "0.39894", "0.5%"



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

This test validates:


* the calculation of the stiffness matrix (the right offset when filling the matrix because the nodes do not have the same number of degrees of freedom),


* the calculation of contact matrices (integration on a SE3 at Gauss points),


* subdivision (curved interface configurations and elements with straight edges),


* the X- FEM post-processing of the :math:`\text{P2P1}` elements,


* the refinement of the mesh, makes it possible to obtain more accurate results (compared to modeling :math:`\text{A}`),


* the version 3 algorithm of equality relationships on cut edges, for quadratic elements in small slips, in order to satisfy LBB.