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

Calculation method
-----------------

The formulas used are from BPEL 83. They are also found in NFEN1992 -1-1 October 2005, AFCEN ETC -C2010, with a few small variations.

:math:`{\mathrm{\sigma }}_{p}\left(x\right)={\mathrm{\sigma }}_{\mathit{pi}}\left(x\right)\left(1.0\phantom{\rule{2em}{0ex}}-\phantom{\rule{2em}{0ex}}\mathrm{\Delta }{\mathrm{\sigma }}_{p}\left(\mathrm{\mu },t\right)\right)`

:math:`\mathrm{\Delta }{\mathrm{\sigma }}_{p}\left(\mathrm{\mu },t\right)={k}_{1}.{\mathrm{\rho }}_{1000}{\left(\frac{t}{1000}\right)}^{\frac{3}{4}\left(1-\mathrm{\mu }\right)}.{e}^{\frac{10\mathrm{\mu }-7.5}{{k}_{2}}}` with :math:`\mathrm{\mu }=\frac{{\mathrm{\sigma }}_{\mathit{pi}}\left(x\right)}{{f}_{\mathit{prg}}}`, :math:`t` is in hours.

To be able to apply these formulas, the deformation must remain **constant**. :math:`{\mathrm{\sigma }}_{\mathit{pi}}` is the initial stress that corresponds to the initial deformation.

Validation will therefore be done on the 'a' and 'b' models, with these formulas. The test case 'c' will be a non-regression test case because we simulate retension of the cable, so the deformation will vary over time.

Reference quantities and results
-----------------------------------

The quantity tested will be the stress in the cable, at various times.


Uncertainty about the solution
----------------------------

No uncertainty, the reference solution is analytical.


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

beep [:ref:`1 <1>`] BPEL.

NF-EN-1992 [:ref:`2 <2>`] NF EN 1992-1-1 October 2005.

afcen [3] AFCEN ETC -C 2010.