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=80000\mathit{MPa}`


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


* :math:`n=4.39`


* :math:`K=253.5497\mathit{MPa}\mathrm{.}{s}^{-1}`


* :math:`\alpha =0.00004`


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

The bar, of initial length

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, stuck in the direction

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on the side [:ref:`1,2 <1,2>`] is subjected to a uniform temperature

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and to a mechanical tensile displacement u on face :math:`\mathrm{[}\mathrm{3,}4\mathrm{]}`. The loading sequences are as follows:


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The imposed temperature is linear in °C: :math:`T=1200+300t`

Reference temperature :math:`{T}_{\mathit{ref}}=1200°C`