F modeling
==============

Traction — compression pure elastoplastic behavior that is damaging (GLRC_DM + Von Mises).

In this test, we are interested in elastoplastic behavior. We can insert plastic behavior to the answer of model GLRC_DMvia, a "kit" that makes it possible to put model GLRC_DMavec into series, a classical Von Mises plastic model. This kit consists in imposing the same stress tensor on both models and in combining the two deformation tensors.




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


.. image:: images/100002000000016D000000DB15472CCCEBA66521.png
    :width: 3.6272in
    :height: 2.1193in


.. _RefImage_100002000000016D000000DB15472CCCEBA66521.png:

Figure 8.1-a: mesh and boundary conditions

Modeling: DKTG. :math:`L=1.0m`.

Boundary conditions:


* Embedding in :math:`{A}_{1}`;


* :math:`\mathrm{DX}=0.0` on the :math:`{A}_{1}-{A}_{3}` edge;


* :math:`\mathrm{DX}={U}_{0}\times f(t)` on the :math:`{A}_{2}-{A}_{4}` edge;

where :math:`{U}_{0}=3.0\times {10}^{-3}m` and :math:`f(t)` represent the magnitude of cyclic loading as a function of the (pseudo-time) parameter :math:`t` as follows:

Integration increment: :math:`\mathrm{8,50}\times {10}^{-3}s`.



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

Number of knots: 9

Number of stitches: 8 TRIA3; 8 SEG2.



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


.. csv-table::

    "**Identification**", "**Reference Type**", "Reference Value", "**Tolerance**"
    "At :math:`t=\mathrm{0,017}` traction - elastic phase", "", "", ""
    "*Movement* :math:`\mathrm{DY}` *en* :math:`\mathrm{A4}` "," NON_REGRESSION "," ", "1.44237 10-2", "1 10-4"
    "*Membrane effort* :math:`{N}_{\mathrm{xx}}` *en* :math:`\mathrm{A4}` "," AUTRE_ASTER ", "0", "5 10-3"
    "At :math:`t=\mathrm{0,085}` traction - damage phase", "", "", ""
    "*Move* :math:`\mathrm{DY}` *en* :math:`\mathrm{A4}` "," NON_REGRESSION "," ", "-4.84715 10-1", "1 10-4"
    "*Membrane effort* :math:`{N}_{\mathrm{xx}}` *en* :math:`\mathrm{A4}` "," NON_REGRESSION "," ", "-3.460140 10-3", "1 10-4"
    "At :math:`t=\mathrm{0,085}` traction - plasticity + damage phase", "", "", ""
    "*Membrane effort* :math:`{N}_{\mathrm{xx}}` *en* :math:`\mathrm{A4}` "," NON_REGRESSION ", "-0.069405040", "1 10-4"
    "At :math:`t=\mathrm{2,04}` traction - discharge phase", "", "", ""
    "*Membrane effort* :math:`{N}_{\mathrm{xx}}` *en* :math:`\mathrm{A4}` "," NON_REGRESSION "," ", "-1.11050 10+5", "1 10-4"
    "At :math:`t=\mathrm{0,017}` traction - elastic phase", "", "", ""
    "*Total deformation energy density in the slab in* :math:`\mathrm{A2}` "," NON_REGRESSION "," ", "4.642785", "1 10-5"
    "*Membrane deformation energy density in the slab in* :math:`\mathrm{A2}` "," NON_REGRESSION "," ", "4.642785", "1 10-5"
    "*Total deformation energy density in the mesh slab* :math:`\mathrm{M1}` "," NON_REGRESSION "," ", "4.642785", "1 10-5"
    "*Bending strain energy density in mesh slab* :math:`\mathrm{M1}` "," AUTRE_ASTER "," ", "0", "1 10-13"
    "At :math:`t=\mathrm{0,085}` traction - damage phase", "", "", ""
    "*Total deformation energy density in the slab in* :math:`\mathrm{A2}` "," NON_REGRESSION "," ", "48.15097", "1.5 10-1"
    "*Total deformation energy density in the mesh slab* :math:`\mathrm{M1}` "," NON_REGRESSION "," ", "48.15097", "1.5 10-1"
    "*Bending strain energy density in mesh slab* :math:`\mathrm{M1}` "," AUTRE_ASTER "," ", "0", "1 10-13"
    "At :math:`t=\mathrm{1,0}` end of charge", "", ""
    "*Bending strain energy density in mesh slab* :math:`\mathrm{M1}` "," AUTRE_ASTER "," ", "0", "1 10-13"
    "At :math:`t=\mathrm{0,017}` traction - elastic phase", "", "", ""
    "*Deformation energy in the slab", "NON_REGRESSION "," ", "4.642785", "1 10-5"
    "*External work*", "NON_REGRESSION ", "4.642785", "1 10-5"
    "At :math:`t=\mathrm{0,085}` traction - damage phase", "", "", ""
    "*Deformation energy in the slab", "NON_REGRESSION "," ", "54.78", "2 10-2"
    "*External work*", "NON_REGRESSION ", "54.78", "2 10-2"
    "At :math:`t=\mathrm{1,0}` end of charge", "", ""
    "*Deformation energy in the slab", "NON_REGRESSION "," ", "817.14", "2.5 10-3"