Benchmark solution
=====================


Calculation method used for the reference solution
--------------------------------------------------------

In this case, the KICHENIN_NLet VMIS_CINE_LINE behavioral relationships lead to identical results. We recall the relationship between tangent stiffness :math:`{E}^{T}` (required by law VMIS_CINE_LINE) and the Prager constant:

:math:`\frac{1}{{E}^{T}}=\frac{1}{{E}^{p}}+\frac{2}{3C}`

Since the integration scheme is the same (implicit Euler of order 1), the difference between the results should not even depend on the discretization of the loading chronology.


Benchmark results
----------------------

We thus compare the results in terms of deformations, plastic deformations and cumulative plastic deformations obtained by the two models at the end of loading (:math:`\overline{t}=1`).


Uncertainties about the solution
----------------------------

Nil.


Bibliographical references
---------------------------

[:ref:`1 <1>`] E. Lorentz (2022) TUYAUTERIE 3- Robust behavioral relationship dedicated to polyethylene structure calculations. Internal note EDF 6125-1723-22-00150.