1. Reference problem#

1.1. Geometry#

Cylindrical test tube.

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1.2. Material properties#

For models \(A\) and \(B\), the material is assumed to be elastic and the material characteristics are constant to be able to validate the calculation with MECA_STATIQUE,

For modeling \(C\), we use the law of MAZARS and some parameters depend on hydration and drying.

Modeling \(E\) makes it possible to test the law ENDO_ISOT_BETON, with the method of NEWTON and IMPLEX, and the modeling \(F\) the coupling ENDO_ISOT_BETON/BETON_UMLV_FP, knowing that the material parameters of the law BETON_UMLV_FP are chosen so that there is no creep and therefore that we find the behavior of the law ENDO_ISOT_BETON. In both cases, the material characteristics are constant.

Note that given the loading (expansion, hydration and free drying), no damage develops: we therefore find the elastic solution in all cases.

Modeling

\(A\)

and

\(B\)

: Isotropic elasticity BELARY**

\(E=30000\mathrm{MPa}\) \(\nu =0.2\) \(\kappa =1.66{10}^{-5}{(l/{m}^{3})}^{-1}\) \({\beta }_{\mathrm{endo}}=1.5{10}^{-5}\) \(\alpha =1.0{10}^{-5}°{C}^{-1}\)

Modeling

\(C\)

**: **:

MAZARS

\(E=10000\mathrm{MPa}\) \(C=\mathrm{100l}/{m}^{3}\) \(30000\mathrm{MPa}\) \(C=\mathrm{80l}/{m}^{3}\) \(\nu =0.25\) for \(h=0\) 0.15 for \(h=1\) \(\kappa =1.66{10}^{-5}{(l/{m}^{3})}^{-1}\) \({\beta }_{\mathrm{endo}}=1.5{10}^{-5}\) \(\alpha =1.0{10}^{-5}°{C}^{-1}\) \({A}_{c}=1.4\) \({A}_{t}\mathrm{=}1.0\) for \(C=\mathrm{100l}/{m}^{3}\) \(0.8\) \(C=\mathrm{80l}/{m}^{3}\) \({B}_{c}=2000\) \(\mathrm{Bt}=10000\) for \(h=0\) \(11000\) for \(h=1\) \({\varepsilon }_{\mathrm{d0}}={10}^{-4}\) \(k\mathrm{=}0.7\)

Modeling

\(E\)

ENDO_ISOT_BETON

Modeling

\(F\)

**: **:

ENDO_ISOT_BETON/BETON_UMLV_FP See modeling \(E+\)

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MPa

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MPa

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MPa

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MPa .j

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MPa .j

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MPa .j.

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MPa .j

1.3. Boundary conditions and loads#

On the \(\mathrm{AB}\) side: \({u}_{z}=0\)

The following are varied uniformly over the structure:

  1. the temperature from \(T=20°C\) at the initial time to \(T=120°C\) at the final time

  2. the water content from \(100l/{m}^{3}\) at the initial time to \(80l/{m}^{3}\) at the final time

  3. hydration varies from 0. at the initial time to 1. at the final time.