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


Geometry
---------


.. image:: images/100000000000024C000000E8B7ED4ADDDD3227C2.jpg
    :width: 6.1898in
    :height: 2.4425in


.. _RefImage_100000000000024C000000E8B7ED4ADDDD3227C2.jpg:


Material properties
----------------------

Material with elasto-plastic behavior with linear work hardening:

Elasticity:


* :math:`E=2.1x{10}^{5}\mathrm{Pa}` Young's module


* :math:`\nu =0.3` Poisson's ratio

Plasticity:


* Slope of the traction curve in the plastic field :math:`\frac{\partial \sigma }{\partial \varepsilon }=2.\times {10}^{\mathrm{3 }}\mathrm{Pa}`


* Elastic limit :math:`{\sigma }_{e}=235.\mathrm{Pa}`


Boundary conditions and loads
-------------------------------------

The calculation is in nonlinear mechanics. The piece is embedded on its left side. Pressure is exerted on the lower horizontal part of the second hole (zone :math:`\mathrm{PRES1}` on the sketch). This pressure varies over time. We will look at the evolution of the displacement on a node of the base.

Edge *ENCASTR*: blocking movements by blocking degrees of freedom: DX = DY = 0.

Edge *PRES1* loading


* pressure imposed as a function of the moments:


.. csv-table::

    "Instant (*s*)", "Pressure (*Pa*)"
    "0. ", "0."
    "60. ", "15."
    "120. ", "20."
    "180. ", "20."
    "240. ", "30."
    "300. ", "30."
    "360. ", "20."
    "420. ", "15."
    "480. ", "10."


The other edges have zero stress.


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

The initial mesh before refinement.

Knots: 158

SEG3: 45

TRIA6: 57


.. image:: images/10000000000003D10000015378DB53C1C8B09DB2.jpg
    :width: 6.889in
    :height: 2.3902in


.. _RefImage_10000000000003D10000015378DB53C1C8B09DB2.jpg:

The discrete border is made up of 4643 knots and as many segments.


.. image:: images/10000000000003CE0000014B127DE5975A72F52A.png
    :width: 6.889in
    :height: 2.3409in


.. _RefImage_10000000000003CE0000014B127DE5975A72F52A.png:


Benchmark results
----------------------

DX and DY movements for the node group A1, consisting of a single node, after the 3rd adaptation:

DX = -3.897029x10-5

DY = -1.395493x10-4


Adapted meshes
-----------------

The Python mesh refinement loop has 3 iterations starting from the error indicator (ERME_ELEM). For each iteration, the characteristics of each mesh produced by the macro-command MACR_ADAP_MAIL are described.


Refined mesh: iteration 1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. image:: images/10000000000003CD000001519E5AC728F81BCBB2.jpg
    :width: 6.889in
    :height: 2.3854in


.. _RefImage_10000000000003CD000001519E5AC728F81BCBB2.jpg:

Knots: 179

SEG3: 48

TRIA6: 66


Refined mesh: iteration 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. image:: images/10000000000003CB0000014DBC6833FBBB8B113C.jpg
    :width: 6.889in
    :height: 2.3626in


.. _RefImage_10000000000003CB0000014DBC6833FBBB8B113C.jpg:

Knots: 200

SEG3: 51

TRIA6: 75


Refined mesh: iteration 3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


.. image:: images/10000000000003D200000150E65EC302E2EC493B.jpg
    :width: 6.889in
    :height: 2.3665in


.. _RefImage_10000000000003D200000150E65EC302E2EC493B.jpg:

Knots: 219

SEG3: 52

TRIA6: 84


notes
---------

We can see that the nodes resulting from the division of segments on the border will be placed on the fine description of the border.