8. F modeling#

8.1. Behavioral law and material parameters#

The law of behavior tested is” BETON_BURGER “, it is documented in doc [R7.01.35]. This law, implemented under Mfront, is used to model the natural creep of concrete, taking into account the distinction between volume creep and deviatoric creep in order to account for phenomena in cases of multi-axial creep. The test is carried out using D_ PLAN modeling (mesh QUAD4) with the command STAT_NON_LINE. The elastic parameters are as follows:

\(E(T)\), \(\mathrm{\nu }(T)\), and \(\mathrm{\alpha }(T)\)

The parameters of the visco-plastic law are as follows:

\({K}_{R}^{S}\), \({K}_{R}^{D}\), \({\eta }_{R}^{S}\), \({\eta }_{I}^{S}\), \({\eta }_{R}^{D}\),, \({\eta }_{I}^{D}\), and \(\kappa\).

Values of the parameters used:

Settings

\(T\mathrm{=}0°C\)

\(T=500°C\)

\(E(T)\)

\(11000\mathit{MPa}\)

\(31000\mathit{MPa}\)

\(\nu (T)\)

\(0.\)

\(0.\)

\(\alpha (T)\)

\(\mathrm{1,0}\times {10}^{-4}{K}^{-1}\)

\(\mathrm{2,0}\times {10}^{-4}{K}^{-1}\)

\({K}_{R}^{S}\)

\(4360\mathit{MPa}\)

\(4360\mathit{MPa}\)

\(\kappa\)

\(\mathrm{3,3}\times {10}^{-3}\)

\(\mathrm{3,3}\times {10}^{-3}\)

\({K}_{R}^{D}\)

\(3270\mathit{MPa}\)

\(3270\mathit{MPa}\)

\({\eta }_{R}^{S}\)

\(\mathrm{3,41}\times {10}^{9}\mathit{MPa}\mathrm{.}s\)

\(\mathrm{3,41}\times {10}^{9}\mathit{MPa}\mathrm{.}s\)

\({\eta }_{I}^{S}\)

\(\mathrm{5,76}\times {10}^{12}\mathit{MPa}\mathrm{.}s\)

\(\mathrm{5,76}\times {10}^{12}\mathit{MPa}\mathrm{.}s\)

\({\eta }_{R}^{D}\)

\(\mathrm{2,55}\times {10}^{9}\mathit{MPa}\mathrm{.}s\)

\(\mathrm{2,55}\times {10}^{9}\mathit{MPa}\mathrm{.}s\)

\({\eta }_{I}^{D}\)

\(\mathrm{4,32}\times {10}^{12}\mathit{MPa}\mathrm{.}s\)

\(\mathrm{4,32}\times {10}^{12}\mathit{MPa}\mathrm{.}s\)

8.2. Results#

Result at order number \(i\)

Name of the tested parameter

Name of the tested parameter

Reference type

Tolerance

RESU_0

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-31.50

0.10%

RESU_1

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-71.50

0.10%

RESU_2

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-120.75

0.10%

RESU_3

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-180.00

0.10%

RESU_4

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-250.00

0.10%

RESU_5

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-331.50

0.10%

RESU_6

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-425.25

0.10%

RESU_7

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-532.00

0.10%

RESU_8

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-652.50

0.10%

RESU_9

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-787.50

0.10%

RESU_10

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-937.75

0.10%

RESU_11

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-1104.00

0.10%

RESU_12

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-1287.00

0.10%

RESU_13

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-1487.50

0.10%

RESU_14

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-1706.25

0.10%

RESU_15

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-1944.00

0.10%

RESU_16

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-2201.50

0.10%

RESU_17

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-2479.50

0.10%

RESU_18

PRIN_1 (\(\mathrm{Pa}\))

AUTRE_ASTER

-2778.75

0.10%

RESU_19

PRIN_1 (\(\mathit{Pa}\))

AUTRE_ASTER

-3100.00

0.10%