7. F modeling#
7.1. Characteristics of modeling#
7.1.1. Simulation 1#
This is a thermomechanical test with zero imposed deformation along axis \(x\). The test is performed on an element of BARRE with the STAT_NON_LINE command. The temperature varies from \({T}_{0}=20°C\) to \({T}_{\mathrm{max}}=100°C\). The material is able to be plasticized. The transition consists of NCAL steps. The reference temperature is \({T}_{\mathrm{ref}}=20°C\).
7.1.2. Simulation 2#
It’s about looping over NCAL mechanical calculations. For each calculation \(i\), the imposed load consists of the thermal deformation \({\varepsilon }_{\mathrm{xx}}=-{\varepsilon }_{\mathrm{th}}=-\alpha (T)({T}_{i}-{T}_{\mathrm{Ref}})\). The initial load consists of the deformations, stresses and internal variables from the previous mechanical calculation.
7.2. Material properties#
The law of behavior tested is” PINTO_MENEGOTTO “documented in doc [R5.03.09]. This law is an elasto-plastic uniaxial isothermal law modeling the response of steel reinforcements in reinforced concrete under cyclic loading.
The elastic parameters are as follows:
\(E(T)\), \(\nu (T)\), and \(\alpha (T)\)
The elastoplastic parameters are as follows:
\({\sigma }_{y}^{0}\), \({\varepsilon }_{u}\), \({\sigma }_{u}\), \({\varepsilon }_{h}\), \(b\),, \(\mathrm{R0}\), \(\mathrm{a1}\), \(\mathrm{a2}\),, \(L/D\), \(\mathrm{a6}\),,,,,,,,,,,, \(c\) \(a\)
Values of the parameters used:
Settings |
\(T=20°C\) |
|
\(E(T)\) |
|
\(1.E11\) Pa |
\(\nu (T)\) |
|
|
\(\alpha (T)\) |
|
|
Parameters |
Parameters |
|||
\({\sigma }_{y}^{0}\) |
\(2.E8\) Pa |
\(\mathrm{a1}\) |
\(18.5\) |
|
\({\varepsilon }_{u}\) |
\(3.E-2\) |
\(\mathrm{a2}\) |
\(0.15\) |
|
\({\sigma }_{u}\) |
\(2.58E8\) Pa |
\(L/D\) |
\(4.9\) |
|
\({\varepsilon }_{h}\) |
\(0.0023\) |
\(\mathrm{a6}\) |
\(620.\) |
|
\(b\) |
\(0.01\) |
\(c\) |
\(0.5\) |
|
\(\mathrm{R0}\) |
\(20.\) |
\(a\) |
\(0.008\) |
|
7.3. Tested sizes and results#
Validation is carried out by comparing the fields calculated at each step of the transient on the one hand and the result of a mechanical calculation on the other hand.
The command used is TEST_TABLE which tests the reference value against the calculated value.
The reference value being the field component extracted at a given time \(i\) from the first thermo-mechanical simulation performed over NCAL times. The calculated value is the one obtained at the end of the mechanical calculation \(i+1\) of the loop on the NCAL.
Result at order number \(i\) |
Name of the tested parameter |
Name of the tested parameter |
Reference type |
Tolerance |
RESU_i |
|
VALE_REF |
|
|
RESU_19 |
N |
NON_REGRESSION |
-2.58E8 |
|
RESU_19 |
V4 |
|
-9.6E-2 |
|
RESU_19 |
V5 |
|
-7.08E-3 |