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


Description
-----------

This test case comes from sheet 26795 reporting a sudden stop in Hujeux's law due to a segmentation error in a study of the construction by layers of an embankment dam.

It reproduces on a material point the loading path that caused the crash. This loading path leads to the failure of local Newton iterations and activates a heuristic mechanism for restarting the resolution.


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


Elastic properties of the material
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The material is of the type of dense sand. The elastic properties are:


* Young's modulus: :math:`E=2029431300.40069\mathit{Pa}`


* Poisson's ratio: :math:`\mathrm{\nu }=0.45`

The anelastic properties (Humjeux) are:


* power of the nonlinear elastic law: :math:`{n}_{e}=0`


* :math:`\mathrm{\beta }=200`


* :math:`d=3.5`


* :math:`b=0.6`


* friction angle: :math:`\mathrm{\phi }=40°`


* angle of expansion: :math:`\mathrm{\psi }=30°`


* critical pressure: :math:`{P}_{c0}=-\mathrm{2,24}\mathit{MPa}`


* reference pressure: :math:`{P}_{\mathit{ref}}=-1\mathit{MPa}`


* elastic radius of the isotropic mechanism: :math:`{r}_{\mathit{éla}}^{s}=0.01`


* elastic radius of the deviatory mechanism: :math:`{r}_{\mathit{éla}}^{d}=0.01`


* :math:`{a}_{\mathit{mon}}=0.03`


* :math:`{a}_{\mathit{cyc}}=0.00001`


* :math:`{c}_{\mathit{mon}}=0.0003`


* :math:`{c}_{\mathit{cyc}}=0.0003`


* :math:`{r}_{\mathit{hys}}=0.1`


* :math:`{r}_{\mathit{mob}}=0.9`


* :math:`{x}_{m}=2`


* :math:`\text{dila}=1`


Initial conditions and mechanical loading
--------------------------------------------


Initial conditions
~~~~~~~~~~~~~~~~~~~~~

The initial deformation conditions are as follows:


* :math:`\mathit{EPXX}0=-1.350354802792579E-021`


* :math:`\mathit{EPYY}0=-3.980032078861482E-007`


* :math:`\mathit{EPZZ}0=0`


* :math:`\mathit{EPXY}0=\frac{8.492341581286122E-008}{\sqrt{2}}`


* :math:`\mathit{EPXZ}0=0`


* :math:`\mathit{EPYZ}0=0`

The initial stress conditions are as follows:


* :math:`\mathit{SIXX}0=-125\mathit{kPa}`


* :math:`\mathit{SIYY}0=-125\mathit{kPa}`


* :math:`\mathit{SIZZ}0=-125\mathit{kPa}`


* :math:`\mathit{SIXY}0=0`


* :math:`\mathit{SIXZ}0=0`


* :math:`\mathit{SIYZ}0=0`

The initial internal variables are zero.


Loading
~~~~~~~~~~

The deformation increment applied is as follows:


* :math:`\mathrm{\Delta }\mathit{EPXX}=7.372770706199615E-006`


* :math:`\mathrm{\Delta }\mathit{EPYY}=4.632919275111915E-005`


* :math:`\mathrm{\Delta }\mathit{EPZZ}=0`


* :math:`\mathrm{\Delta }\mathit{EPXY}=\frac{1.733367998412452E-006}{\sqrt{2}}`


* :math:`\mathrm{\Delta }\mathit{EPXZ}=0`


* :math:`\mathrm{\Delta }\mathit{EPYZ}=0`