G modeling
==============


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


* Tested behavior: DruckerPrager.mfront. Associated elasto-plastic law of Drucker-Prager [:ref:`cf. R7.01.16 <cf. R7.01.16>`], the criterion being defined by: :math:`F(\sigma )={\sigma }_{\mathit{eq}}+a\mathit{tr}(\sigma )/3–k\le 0`

The coefficients a and k are defined on the basis of the material properties in the following way:

:math:`a=-3\frac{\tau –1}{\tau +1}` and :math:`k=2\frac{{\sigma }_{c}\tau }{\tau +1}`


* The modeling is equivalent to that of an Mfront mtest file (hardware point):

a material point is subject to an imposed deformation :math:`{\epsilon }_{\mathit{xx}}=5{10}^{-3}t`


* the material properties are: :math:`E=200\mathit{GPa},\nu =\mathrm{0,3},\tau =0.6,{\sigma }_{c}=150\mathit{MPa}`,


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

The reference solution is that of the Mfront reference tests:


.. csv-table::

    "**Identification (t=1)**", "**Reference**", "**Tolerance**"
    ":math:`{\sigma }_{\mathit{xx}}(\mathit{MPa})` ", "90"," 0.1%"