Benchmark results
======================

The reference results are obtained by carrying out the same calculation with the Simo-Miehe large deformation model (DEFORMATION = 'SIMO - MIEHE'), validated elsewhere.

Behavior VMIS_ISOT_LINE with SIMO_MIEHE, in plane deformation:


.. csv-table::

    "Imposed displacement", "Size tested", "Reference :math:`(\mathrm{MPa})`"
    ":math:`500\mathrm{mm}` "," SIEQ_ELGA ", "1125"
    ":math:`700\mathrm{mm}` "," SIEQ_ELGA ", "1411"
    ":math:`900\mathrm{mm}` "," SIEQ_ELGA ", "1664"
    ":math:`1100\mathrm{mm}` "," SIEQ_ELGA ", "1891.7"


The values of the equivalent von Mises stresses are compared at the end of the traction phases and their invariance during the rotation phases is checked.

Behavior VMIS_ISOT_LINE with SIMO_MIEHE in plane stress


.. csv-table::

    "Imposed displacement", "Size tested", "Reference :math:`(\mathit{MPa})`"
    ":math:`500\mathit{mm}` "," SIEQ_ELGA ", "1019.57"
    ":math:`500\mathit{mm}` after rotation", "SIEQ_ELGA ", "1019.57"
    ":math:`700\mathit{mm}` "," SIEQ_ELGA ", "1271"


Finally, the quality of the tangent matrix is checked by comparison with a tangent matrix obtained by disturbance. With SIMO_MIEHE, we obtain an almost zero difference (norm of the difference: of the order of :math:`1.E-20`). We will therefore check the difference obtained on the tangent matrix for the large deformation formalisms tested here.