3. Modeling A#

3.1. Characteristics of modeling#

3D (1 HEXA8, 2 PENTA6, 1 **, 1 **HEXA20, 2 PENTA15)

It is an 8-node cube and two 6-node prisms linked by linear relationships to a 20-node cube and two 15-node prisms. The assembly is subjected to uniaxial traction in direction \(x\). The following dimensions \(y\) and \(z\) are unitary. The dimensions in the \(x\) direction are chosen so that all the elements have the same characteristic length (this is equal to the cubic root of the volume for quadratic elements, and the cubic root of the volume multiplied by \(\sqrt{2}\) for the linear elements).

The stress and deformation fields are uniform.

In \(\mathrm{3D}\), we validate the coupling of laws BETON_DOUBLE_DP and VMIS_ISOT_LINE with law GRANGER_FP.

3.2. Characteristics of the mesh#

Number of knots: 46

Number of meshes and type: 1 HEXA8, 2 PENTA6, 1 HEXA20, 2 PENTA15

3.3. Tested sizes and results#

The components \(\mathrm{xx}\) of the stress field SIGM_ELNO, of the creep deformation field EPFP_ELNO, and of the plastic deformation field EPSP_ELNO are tested.

For coupling with law BETON_DOUBLE_DP, in the case where the drying is constant and the analytical solution is known, these values were tested at the point \(\mathrm{C1}\) located at the interface between the linear elements and the quadratic elements, and at the point \(\mathrm{F1}\) located at the end of the structure, where the imposed displacement is applied (in \({x}_{\mathrm{max}}\)).

When the drying varies, the analytical solution has not been calculated: the same components as before are therefore tested but only at point \(\mathrm{F1}\) located at the end of the structure. The solution obtained with BETON_DOUBLE_DPest tested as a non-regression, but the values obtained then serve as a reference for the VMIS_ISOT_LINE model.

The tests are carried out at instant 10, when the plasticity has not started, only creep is present, and at time 100, after the start of the plasticization of the concrete.

3.3.1. Calculation with law BETON_DOUBLE_DP in isotherm (Reference)#

Coupling GRANGER_FP/BETON_DOUBLE_DP

to the point \(\mathrm{C1}\)

Identification	Reference	Aster	% difference
\({\sigma }_{\mathit{xx}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}4}\)	3.07786	3.07786	3.07787	1.9.10-4
\({\varepsilon }_{\mathit{xx}}^{\mathit{fl}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}4}\)	7.14171 10-7	7.140035 10-7	-0.023
\({\sigma }_{\mathit{xx}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)	4.0	3.999999	-2.0.10-5
\({\varepsilon }_{\mathit{xx}}^{\mathit{fl}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)	1.73162 10-5	1.731596 10-5	-0.001
\({\varepsilon }_{\mathit{xx}}^{p}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)	8.53652 10-4	8.536546 10-4	3.1 10-4

to the point \(\mathrm{F1}\)

Identification	Reference	Aster	% difference
\({\sigma }_{\mathit{xx}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}4}\)	3.07786	3.07786	3.07787	1.9.10-4
\({\varepsilon }_{\mathit{xx}}^{\mathit{fl}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}4}\)	7.14171 10-7	7.140035 10-7	-0.023
\({\sigma }_{\mathit{xx}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)	4.0	3.999998	-6.0.10-5
\({\varepsilon }_{\mathit{xx}}^{\mathit{fl}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)	1.73162 10-5	1.731596 10-5	-0.001
\({\varepsilon }_{\mathit{xx}}^{p}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)	8.53652 10-4	8.536023 10-4	-0.006

3.3.2. Calculation with law BETON_DOUBLE_DP in non-isotherm (Non regression)#

These are non-regression tests, the values are not indicated.

to the point \(\mathrm{F1}\)

Variable tested

\({\sigma }_{\mathit{xx}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}4}\)

\({\varepsilon }_{\mathit{xx}}^{\mathit{fl}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}4}\)

\({\sigma }_{\mathit{xx}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)

\({\varepsilon }_{\mathit{xx}}^{\mathit{fl}}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)

\({\varepsilon }_{\mathit{xx}}^{p}\) for \({\varepsilon }_{\mathit{xx}}{10}^{\mathrm{-}3}\)

3.4. Calculation with law VMIS_ISOT_LINE in non-isothermal#