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


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

Meshing with ``3D_ INCO_UPG "and" DEFORMATION =' SIMO_MIEHE '``elements
incompressible type TETRA10 only


.. image:: images/100147DE000069D5000048C34BB63DF767058DA9.svg
    :width: 366
    :height: 252


.. _RefImage_100147DE000069D5000048C34BB63DF767058DA9.svg:

:math:`\mathit{AB}` is on the :math:`\mathit{OX}` axis
(in contrast to modeling A).

The mesh was obtained with GMSH for a density of :math:`\mathrm{0,01}`.

The boundary conditions are:

* Zero vertical displacement on 'FACSUP' and 'FACINF' faces
  :math:`\mathit{AEFD}` (:math:`z=0` and :math:`z=0.01`): DZ = 0.
* Movement blocked in dy on the 'FACEAB' side (side :math:`\mathit{AB}`,
  DY = 0)
* Normal movement stuck on side 'FACEEF' (side :math:`\mathit{EF}`,
  DNOR = 0.)
* Radial displacement imposed on the inside face of the 'FACEAE' cylinder:
  face :math:`\mathit{AE}` DNOR = -6.10-5


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

Number of knots: 2064

Number of meshes: 1121 TETRA10


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

Displacements and constraints SIGM_NOEU are evaluated at points :math:`A`
and :math:`F`.
The components of field SIEQ_NOEU are tested at point :math:`A` only.


+------------------+----------------------------+------------------+-------------+-------------+
|**Identification**                             |**Reference type**|**Reference**|**Tolerance**|
+------------------+----------------------------+------------------+-------------+-------------+
|:math:`A`         |:math:`\mathit{u}` (X)      |ANALYTIQUE        | #. 10-5     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{v}` (DY)     |ANALYTIQUE        |             | #. 10-5     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xx}}`|ANALYTIQUE        |-59.9955     |0.025        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{yy}}`|ANALYTIQUE        |99.9566      |0.02         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{zz}}`|ANALYTIQUE        |19.9326      |0.03         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xy}}`|ANALYTIQUE        |             |0.03         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |VMIS                        |ANALYTIQUE        |138.5226     |0.01         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |TRESCA                      |ANALYTIQUE        |159.9521     |0.01         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_1                      |ANALYTIQUE        |-59.9955     |0.025        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_2                      |ANALYTIQUE        |19.9326      |0.03         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_3                      |ANALYTIQUE        |99.9566      |0.015        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |VMIS_SG                     |ANALYTIQUE        |138.5226     |0.01         |
+------------------+----------------------------+------------------+-------------+-------------+


+------------------+----------------------------+------------------+-------------+-------------+
|**Identification**                             |**Reference type**|**Reference**|**Tolerance**|
+------------------+----------------------------+------------------+-------------+-------------+
|:math:`F`         |:math:`\mathit{u}` (X)      |ANALYTIQUE        |2.1217 10-5  | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{v}` (DY)     |ANALYTIQUE        |2.1217 10-5  | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xx}}`|ANALYTIQUE        |20.003       |0.005        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{yy}}`|ANALYTIQUE        |20.003       |0.005        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{zz}}`|ANALYTIQUE        |20.003       |0.005        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xy}}`|ANALYTIQUE        |-20.003      |0.01         |
+------------------+----------------------------+------------------+-------------+-------------+


notes
---------

The results obtained are completely correct since the constraints
are obtained with a precision of less than :math:`\text{3%}`
See :math:`\text{1 %}` at point F. The gap is a bit bigger here.
only for HEXA20, but can be explained by the fact that loading
is imposed here in a slightly less precise manner since the displacement u
at point A, is only set to a precision of :math:`\text{0.158%}`
against :math:`\text{0.077%}` (evening the factor 2, which can be found on
constraints).