Reference problem
=====================


Geometry
---------


.. image:: images/10000200000001E9000000FFB3DA534FC96FD2A1.png
    :width: 5.0972in
    :height: 2.6528in


.. _RefImage_10000200000001E9000000FFB3DA534FC96FD2A1.png:


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

Isotropic elasticity :math:`E\mathrm{=}145000\mathit{MPa}` :math:`\nu \mathrm{=}0.3`

Viscoplasticity model VISCOCHAB


.. csv-table::

    ":math:`k` "," :math:`35\mathit{MPa}` "," :math:`B` ", "" 12", ":math:`\mathit{ETA}` "," :math:`0.04`"
    ":math:`{A}_{K}` "," :math:`1.` "," :math:`{M}_{R}` ", "2"," :math:`\mathit{C1}` "," :math:`1950\mathit{MPa}`"
    ":math:`{A}_{R}` "," :math:`0.65` "," :math:`{G}_{R}` "," "," :math:`2{10}^{\mathrm{-}7}` "," :math:`{M}_{1}` "," :math:`4`"
    ":math:`{K}_{0}` "," :math:`70\mathit{MPa}{S}^{1\mathrm{/}N}` "," :math:`\mathit{MU}` ", "19"," :math:`\mathit{D1}` "," :math:`0.397{10}^{\mathrm{-}3}`"
    ":math:`N` ", "24"," :math:`{Q}_{M}` "," "," :math:`460` "," :math:`{G}_{\mathit{X1}}` "," :math:`2.{10}^{\mathrm{-}13}{\mathit{MPa}}^{\mathrm{-}\mathit{m1}}{S}^{\mathrm{-}1}`"
    ":math:`\mathit{ALP}` "," :math:`0\mathit{MPa}` "," :math:`{Q}_{0}` "," "," :math:`40\mathit{MPa}` "," :math:`{\mathit{G1}}_{0}` "," :math:`50\mathit{MPa}`"
    "", "", ":math:`{\mathit{QR}}_{0}` "," :math:`200\mathit{MPa}` ", "", ""



.. csv-table::

    ":math:`\mathit{C2}` "," :math:`65000\mathit{MPa}`"
    ":math:`{M}_{2}` "," :math:`4`"
    ":math:`\mathit{D2}` "," :math:`0.552{10}^{\mathrm{-}1}`"
    ":math:`{G}_{\mathit{X2}}` "," :math:`1.{10}^{\mathrm{-}12}{\mathit{MPa}}^{\mathrm{-}\mathit{m1}}{S}^{\mathrm{-}1}`"
    ":math:`{\mathit{G2}}_{0}` "," :math:`1300\mathit{MPa}`"
    ":math:`{A}_{I}` "," :math:`0.5`"
    "", ""



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


.. csv-table::

    ":math:`\mathit{N6}` "," :math:`\mathit{dx}\mathrm{=}\mathit{dy}\mathrm{=}\mathit{dz}\mathrm{=}0` ", "Face :math:`\mathit{XZ}`: :math:`\mathit{FX}\mathrm{=}–{\tau }_{d}\mathrm{/}4`"
    ":math:`\mathit{N7}` "," :math:`\mathit{dx}\mathrm{=}\mathit{dy}\mathrm{=}0` ", "Face :math:`\mathit{YZ}`: :math:`\mathit{FY}\mathrm{=}–{\tau }_{d}\mathrm{/}\mathrm{4,}\mathit{FX}\mathrm{=}–{\sigma }_{d}\mathrm{/}4`"
    ":math:`\mathit{N2}`, :math:`\mathit{N3}` "," :math:`\mathit{dy}\mathrm{=}0` ", "Face :math:`\mathrm{1XZ}`: :math:`\mathit{FX}\mathrm{=}{\tau }_{d}\mathrm{/}4`"
    ":math:`\mathit{N2}`, :math:`\mathit{N3}`, :math:`\mathit{N6}`, :math:`\mathit{N7}` "," :math:`\mathit{dx}\mathrm{=}0` ", "Face :math:`\mathrm{1YZ}`: :math:`\mathit{FY}\mathrm{=}{\tau }_{d}\mathrm{/}\mathrm{4,}\mathit{FZ}\mathrm{=}{\sigma }_{d}\mathrm{/}4`"



Initial conditions
--------------------

Zero stresses and deformations at :math:`t\mathrm{=}0`.


.. image:: images/100002000000009300000080436E48A4D243374A.png
    :width: 1.528in
    :height: 1.3335in


.. _RefImage_100002000000009300000080436E48A4D243374A.png:

:math:`{\sigma }_{d}(t)` and :math:`{\tau }_{d}(t)` linear, with the point :math:`P` being reached in :math:`10s` with :math:`{\sigma }_{d}(10)\mathrm{=}150\mathit{MPa}` and :math:`{\tau }_{d}(10)\mathrm{=}60\mathit{MPa}`.