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


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

Modeling AXIS.


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

The mesh consists of 1803 knots and 1852 meshes including a TRIA3 mesh for the rigid punch, and 1715 QUAD4 links for the solid (the rest of the meshes being SEG2 meshes for the contact surface).


Characteristics of behavior
--------------------------------

Incremental elastic behavior for the punch (COMPORTEMENT/ELAS).

Elasto-plastic behavior in large deformations with linear isotropic work hardening for the solid (COMPORTEMENT/VMIS_ISOT_LINE/SIMO_MIEHE).


Contact characteristics
---------------------------

Continuous contact method, pairing MAIT_ESCL, normal MAIT_ESCL and pairing is fixed, from normal :math:`(\mathrm{0,}-\mathrm{1,0})`. Integration at the nodes and increased Lagrangian regularization coefficient equal to 1000.


Tested quantities and results
------------------------------


.. csv-table::

    "**Tested value**", "**Instant**", "**Reference**", "**Type**", "**Tolerance**"
    "Displacement :math:`\mathrm{DY}` in :math:`A` ", "0.5", "-0.25", "" -0.25", "Analytical", "-0.80%"
    "", "0.5", "-0.24798", "Non-regression", ""
    "Reaction force :math:`\mathrm{DX}` in :math:`A` ", "0.5", "3.2482", "Non-regression", ""
    "Reaction force :math:`\mathrm{DY}` in :math:`A` ", "0.5", "-8,7703", "Non-regression", ""
    "Displacement :math:`\mathrm{DY}` in :math:`A`", "1.0", "-0.392", "Analytics", "-0.60%"
    "", "1.0", "-0.38944", "Non-regression", ""
    "Reaction force :math:`\mathrm{DX}` in :math:`A` ", "1.0", "1.81343", "Non-regression", ""
    "Reaction force :math:`\mathrm{DY}` in :math:`A` ", "1.0", "-4.8962", "Non-regression", ""



notes
---------

The nodal reaction force is in :math:`N/\mathrm{rad}` since the problem is axisymmetric. The difference in the analytical values of the displacement comes from the fact that the rigid punch is modeled by a material with a Young's modulus of finite stiffness.