J modeling
==============


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

We use 3D modeling in non-linear mechanics with hyper-reduction of the model. This
modeling tests the accuracy of the empirical modes obtained in modeling E on the
reduced domain created in the F modeling.

We therefore use the bases produced in modeling D and the reduced domain created in
modeling F. This modeling tests how to reconstruct fields on the domain
wholemeal


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

The mesh contains 27 elements of type HEXA8.


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

Values in the RID
~~~~~~~~~~~~~~~~~~~~~

We test the value of the displacements obtained with a hyper-reduced model compared to those
obtained in the complete model:


.. csv-table::

    "**Location**", "**Moment**", "**Component**", "**Movement (** DEPL **)**", "**Instant**", "**Precision**"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` ", "DX", ":math:`{0,0696319525128}\,{mm}` ", "0.0015"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` ", "DY", ":math:`{0,199062276741}\,{mm}` ", "0.0035"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` ", "DZ", ":math:`{0,529606351907}\,{mm}` 0.0015", "0.0025"


And the constraints:

.. csv-table::

    "**Location**", "**Instant**", "**Component**", "**Component**", "**Constraint (** SIEF_NOEU **)**", "**Precision**"
    "D knot in :math:`({3,1,0})` "," :math:`t=10s` "," "," SIXX "," "," :math:`{13300,4780377}\,{MPa}` ", "0, 20%"
    "D knot in :math:`({3,1,0})` "," :math:`t=10s` "," "," SIYY "," "," :math:`{13300,3220671}\,{MPa}` ", "0, 20%"
    "D knot in :math:`({3,1,0})` "," :math:`t=10s` "," "," SIZZ "," "," :math:`{13368,1442621}\,{MPa}` ", "0, 20%"



Values outside of RID
~~~~~~~~~~~~~~~~~~~~~

Values outside of RID cannot be obtained directly from the hyper-reduced calculation with
STAT_NON_LINE. It is necessary to rebuild the fields. We are testing the reconstruction of
fields "by hand" by retrieving the reduced coordinates and applying the formula with CREA_CHAMP:


.. csv-table::

    "**Location**", "**Moment**", "**Component**", "**Movement (** DEPL **)**", "**Instant**", "**Precision**"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` ", "DX", ":math:`-{0,208992921588}\,{mm}` ", "0.0015"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` ", "DY", ":math:`-{0,208992921588}\,{mm}` ", "0.003"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` ", "DZ", ":math:`{0,547254495773}\,{mm}` ", "0.0025"



.. csv-table::

    "**Location**", "**Instant**", "**Component**", "**Component**", "**Constraint (** SIEF_NOEU **)**", "**Precision**"
    "Node C in :math:`({0,0,0})` "," :math:`t=10s` "," "," SIXX "," :math:`{13300,4780377}\,{MPa}` "," 0.7%"
    "Node C in :math:`({0,0,0})` "," :math:`t=10s` "," "," SIYY "," :math:`{13300,3220671}\,{MPa}` "," 0.7%"
    "Node C in :math:`({0,0,0})` "," :math:`t=10s` "," "," SIZZ "," :math:`{13368,1442621}\,{MPa}` "," 9.7%"


We test the reconstruction of the fields by gappy- POD using the REST_REDUIT_COMPLET operator:


.. csv-table::

    "**Location**", "**Moment**", "**Component**", "**Move (** DEPL **)**", "-"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` ", "DX", ":math:`-{0,208992921588}\,{mm}` ", "0.0015"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` ", "DY", ":math:`-{0,208992921588}\,{mm}` ", "0.003"
    "Node B in :math:`({3,3,3})` "," :math:`t=10s` ", "DZ", ":math:`{0,547254495773}\,{mm}` ", "0.002"



.. csv-table::

    "**Location**", "**Instant**", "**Component**", "**Component**", "**Constraint (** SIEF_NOEU **)**", "**Precision**"
    "Node C in :math:`({0,0,0})` "," :math:`t=10s` "," "," SIXX "," :math:`{13300,4780377}\,{MPa}` ", "0.002"
    "Node C in :math:`({0,0,0})` "," :math:`t=10s` "," "," SIYY "," :math:`{13300,3220671}\,{MPa}` ", "0.002"
    "Node C in :math:`({0,0,0})` "," :math:`t=10s` "," "," SIZZ "," :math:`{13368,1442621}\,{MPa}` ", "0.002"


We are also testing PREDICTION =' EXTRAPOLE ':


.. csv-table::

    "**Location**", "**Moment**", "**Component**", "**Movement (** DEPL **)**", "**Instant**", "**Precision**"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` ", "DX", ":math:`{0,0696319525128}\,{mm}` ", "0.0015"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` ", "DY", ":math:`{0,199062276741}\,{mm}` ", "0.0015"
    "Node A in :math:`({1,0,3})` "," :math:`t=10s` ", "DZ", ":math:`{0,529606351907}\,{mm}` ", "0.033"



notes
---------

The reconstruction of fields, especially outside of RID, is giving excellent results in
terms of precision.