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

Geometry
---------


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

The material obeys Norton's law of viscoplastic behavior (particular case of Lemaître's law, where the parameter UN_SUR_M is zero, confer [:ref:`R5.03.08 <R5.03.08>`]), whose parameters are:

Young's module: :math:`E\mathrm{=}80000\mathit{MPa}`

Poisson's ratio: :math:`\nu \mathrm{=}0.35`

:math:`n\mathrm{=}4.39`

:math:`K\mathrm{=}\frac{1}{0.003944}{\mathit{MPa.s}}^{\text{-1}}`


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

The bar, of initial length :math:`{I}_{0}`, locked in the direction :math:`\mathrm{Ox}` on the face on the face :math:`[\mathrm{1,}2]`, is subjected to a uniform temperature :math:`T` and to a mechanical tensile movement :math:`{u}^{\mathit{meca}}` on the face :math:`[\mathrm{3,}4]`. The loading sequences are as follows:


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Reference temperature: :math:`{T}_{\mathrm{réf}}=700°C`.

**Note:**

*The uniform temperature imposed on the element, constant over time and equal to the reference temperature, is only used to operate the model* META_LEMA_ANI *. There is no thermal expansion.*