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


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

The behavior tested is MOHR_COULOMB, in 3D.


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

The internal variables have the following meanings:


* :math:`V1`: plastic volume deformation :math:`{\mathrm{\epsilon }}_{v}^{p}=\frac{1}{3}\mathit{trace}\left({\mathrm{\epsilon }}^{p}\right)`


* :math: `V2`: plastic volume deformation:math: `| {\ mathrm {\ epsilon}} _ {d} ^ {p} |=\ sqrt {\ frac {2} {3} {3}\ left ({\ mathrm {\ epsilon}}\ left ({\ mathrm {\ epsilon}}\ left ({\ mathrm {\ epsilon}}} _ {v} {3}}\ left ({\ mathrm {\ epsilon}}\ left ({\ mathrm {\ epsilon}}} _ {v} {3}}\ left ({\ mathrm {\ epsilon}}\ left ({\ mathrm {\ epsilon}} I\ right)\ mathrm {:}\ left ({\ mathrm {\ epsilon}}} ^ {p} - {\ mathrm {\ epsilon}}} _ {v} ^ {p} I\ right)} `


* :math:`V3`: plasticity indicator

3D modeling:


.. csv-table::

    "Discrepancies (%)", ":math:`{T}_{\mathit{Pa}}` "," :math:`{T}_{\mathit{sym}}` "," "," :math:`{T}_{\mathit{rot}}` "," :math:`N1` "," :math:`N5` "," :math:`N25`"
    ":math:`V1` ", "0", "0", "0", "0", "0", "1.19", "0.4", "0"
    ":math:`V2` ", "0", "0", "0", "0", "0", "1.19", "0.4", "0"
    ":math:`V3` ", "0", "0", "0", "0", "0", "0", "0"
    ":math:`\mathit{VMIS}` ", "0", "0", "0", "0", "0", "5.88", "1.79", "0"
    ":math:`\mathit{TRACE}` ", "0", "0", "0", "0", "0", "1.82", "0.63", "0"


Tangent matrix:


.. csv-table::

    "Discrepancies", ":math:`N25`"
    ":math:`\mathit{Max}(\mathit{Ktgte}-\mathit{Kpert})` ", "0"