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


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

Meshing with ``3D_ INCO_UPG "and" DEFORMATION =' SIMO_MIEHE '``elements
incompressible type HEXA20 only

Face with imposed radial displacement

.. image:: images/10008724000069D500003780C1B929A3B101AFC0.svg
    :width: 540
    :height: 283


.. _RefImage_10008724000069D500003780C1B929A3B101AFC0.svg:

Following axis :math:`z`:


* total thickness :math:`e=0.01`


* 2 layers of elements

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.
* Normal movement stuck on the 'FACEAB' faces (side :math:`\mathit{AB}`,
  DX = 0) and 'FACEEF' (side :math:`\mathit{EF}`, DNOR = 0.)
* Imposed displacement on the inside of the cylinder 'FACEAE':
  face :math:`\mathit{AE}` DNOR = -6.10-5


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

Number of knots: 1501 knots

Number of meshes: 240 HEXA20


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     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{v}` (DY)     |ANALYTIQUE        | #. 10-5     | #. 10-3     |
+                  +                            +                  +             +             +
|                  |                            |                  |             |             |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xx}}`|ANALYTIQUE        |99.9566      |0.01         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{yy}}`|ANALYTIQUE        |-59.9955     |0.02         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{zz}}`|ANALYTIQUE        |19.9326      |0.035        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |:math:`\mathit{\sigma_{xy}}`|ANALYTIQUE        |             |0.012        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |VMIS                        |ANALYTIQUE        |138.5226     |0.02         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |TRESCA                      |ANALYTIQUE        |159.9521     |0.02         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_1                      |ANALYTIQUE        |-59.9955     |0.02         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_2                      |ANALYTIQUE        |19.9326      |0.035        |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |PRIN_3                      |ANALYTIQUE        |99.9566      |0.01         |
+------------------+----------------------------+------------------+-------------+-------------+
|                  |VMIS_SG                     |ANALYTIQUE        |138.5226     |0.02         |
+------------------+----------------------------+------------------+-------------+-------------+


+------------------+----------------------------+------------------+-------------+-------------+
|**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       |0.005        |
+------------------+----------------------------+------------------+-------------+-------------+

For Green-Lagrange deformations:


+------------------+-------------------------+------------------+-----------------+-------------+
|**Identification**                          |**Reference type**|**Reference**    |**Tolerance**|
+------------------+-------------------------+------------------+-----------------+-------------+
|:math:`A`         |:math:`{E}_{\mathit{xx}}`|ANALYTIQUE        |0.000599576100401|2.E-4        |
+------------------+-------------------------+------------------+-----------------+-------------+
|                  |:math:`{E}_{\mathit{yy}}`|ANALYTIQUE        |-0.00059885996551|2.2E-3       |
+------------------+-------------------------+------------------+-----------------+-------------+


notes
---------

Very good results are obtained since for all the quantities examined,
the difference between the solution obtained with the code and the analytical solution
is less than :math:`\text{0.1%}` for trips, less
to :math:`\text{3.5 %}` for constraints and below
to :math:`\text{0.03%}` for deformations.