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


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

Type of modeling used: element MECA_HEXA8 (hexahedra with 8 nodes)

Boundary conditions:


.. csv-table::

    "DDL_IMPO =", "(GROUP_NO = 'TOUT', DZ = 0.)"
    "FACE_IMPO =", "(GROUP_MA = 'X0', DX = 0., DY = 0.)"


Shear on face :math:`\mathrm{XL}`: FORCE_FACE = (GROUP_MA = 'XL', FY = :math:`{h}_{y}`)


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

Number of knots: 250

Number of meshes and types: 96 HEXA8, 200 QUAD4


.. image:: images/10000000000002580000019E0EC3B5CA4643D2AE.png
    :width: 6.7484in
    :height: 4.6575in


.. _RefImage_10000000000002580000019E0EC3B5CA4643D2AE.png:


Tested values
---------------


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "Arrow in elasticity", "", ""
    "Node: :math:`P`, component: :math:`\mathrm{DY}` ", "3.72", "3.5934", "-3.4"
    "Node: :math:`P`, component: :math:`\mathrm{DX}` ", "—0.439", "—0.4243", "-3.35"
    "Arrow in plasticity", "", ""
    "Node: :math:`P`, component: :math:`\mathrm{DY}` ", "4.547", "4.0203", "-11.58"
    "Node: :math:`P`, component: :math:`\mathrm{DX}` ", "—0.5127", "—0.4621", "9.875"



Note We note that with the same number of meshes (and therefore knots), the results of standard HEXA8 are much worse, in terms of elasticity as well as in plasticity. Moreover, if the number of elements is increased, the reference arrow is never reached, which is the case with the stabilized element. On a mesh with fairly few nodes (250), the stabilized element is more efficient in terms of calculation time (-10%).
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