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


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

The aim of the reference solution is to analytically calculate the threshold value at which creep occurs.

Some non-regression results on the movements at the last time step are added to verify the overall rigidity of the system.

For the analytical calculation of the threshold we have:

As long as the structure remains elastic and due to the boundary conditions, the stress tensor is written as:

For the first time step between :math:`0` and :math:`106s`


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, and in second and

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in :math:`\mathrm{MPa}`. The other components of the tensor are zero.

For the others no time,

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But we have:


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Let it be as in this case

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, we obtain immediately by solving :math:`D=1` the value of the time from which the creep occurs: :math:`{t}_{1}=4.08181818{10}^{6}s`

Thus for a time equal to :math:`{t}_{1}`, the viscous deformations are zero and :math:`D` is equal to 1.


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

Internal variable :math:`\mathrm{V1}` and :math:`\mathrm{V2}` at the point :math:`A`, :math:`B`, :math:`C` and :math:`E` as well as the movement from point :math:`B` to the last time step


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


1. P. DE BONNIERES: Integrating viscoelastic relationships in STAT_NON_LINE [:ref:`R5.03.08 <R5.03.08>`] February 2001