3. Modeling A#

3.1. Characteristics of modeling#

(3.1)#\[ \ textrm {Modeling} \ mathrm {2D}\]
_images/100007CC000069BB000067DFBB97E607D5BD7D2E.svg

Boundary conditions:

\(\mathit{N1}\): \(\mathit{N2}\):

_images/Object_4.svg _images/Object_5.svg

Charging:

Traction on the \(\mathrm{[}34\mathrm{]}\) side (SEG2 mesh) + assignment of the same temperature on all knots

The total number of increments is 20 (10 increments between \(t\mathrm{=}\mathrm{0s}\) and \(\mathrm{1s}\), 10 increments between \(t\mathrm{=}\mathrm{1s}\) and \(\mathrm{2s}\))

Behavior:

For mechanical calculation, the keyword META_LEMA_ANI is used, with the following parameters (see [R4.04.05] and [R4.04.05]):

\(\mathit{YoungModulus}=80000\mathit{MPa}\)

\(\mathit{PoissonRatio}=0.35\)

\({\alpha }_{f}=0.\)

\({\alpha }_{c}=0.00004\)

\({a}_{3}=\mathrm{253,5497}\mathit{MPa}\)

\({m}_{3}=0.\)

\({n}_{3}=4.39\)

\({Q}_{3}=0.K\)

\({M}_{\mathit{rrrr}}^{3}=1.\)

\({M}_{\theta \theta \theta \theta }^{3}=1.\)

\({M}_{\mathit{zzzz}}^{3}=1.\)

\({M}_{r\theta r\theta }^{3}=0.75\)

\({M}_{\mathit{rzrz}}^{3}=0.75\)

\({M}_{\mathrm{\theta }z\mathrm{\theta }z}^{3}=0.75\)

\(\mathit{TDEQ}=809.\)

\(K=1.135E-2\)

\(\text{NEQ}=2.187\)

\(T1C=831.\)

\(T2C=0.0\)

\(\text{QSR\_K}=14614\)

\(\mathit{AC}=1.58E-4\)

\(M=\mathrm{4,7}\)

\(T1R=949.1\)

\(T2R=\mathrm{0,0}\)

\(\mathit{AR}=-5.725\)

\(\mathit{BR}=\mathrm{0,05}\)

The parameters corresponding to the cold phase and to the \(\alpha \beta\) mixture do not play a role and are taken to be arbitrary.

3.2. Characteristics of the mesh#

Number of knots: 4

Number of meshes: 2

1 QUAD4

1 SEG2

3.3. Tested sizes and results#

The stresses and deformations are compared with the B model.

Identification

Reference

Reference type

Tolerance

\(t=0.3\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\))

-91.7598

Other_Aster (B modeling)

1.00%

\(t=0.8\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\))

-92.5802

Other_Aster (B modeling)

1.00%

\(t=1.3\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\))

70.1846

Other_Aster (B modeling)

1.00%

\(t=2.0\) Constraints \(\mathit{SIGYY}\) (\(\mathit{N3}\))

84.4144

Other_Aster (B modeling)

1.00%

Identification

Reference

Reference type

Tolerance

\(t=1.3\) Total deformations \(\mathit{EPYY}\) (\(\mathit{N3}\))

0.006

Other_Aster (B modeling)

0.0001%

\(t=2.0\) Total deformations \(\mathit{EPYY}\) (\(\mathit{N3}\))

0.02

Other_Aster (B modeling)

0.0001%

Identification

Reference

Reference type

Tolerance

\(t=0.8\) Beta phase proportion (\(V6\))

1.0

Analytical

0.0001%

\(t=1.3\) Beta phase proportion (\(V6\))

1.0

Analytical

0.0001%

\(t=2.0\) Beta phase proportion (\(V6\))

1.0

Analytical

0.0001%

Identification

Reference

Reference type

Tolerance

\(t=0.8\) Thermal Deformations \(V7\) (\(\mathit{N3}\))

0.0096

Analytical

0.0001%

\(t=1.3\) Thermal Deformations \(V7\) (\(\mathit{N3}\))

0.0156

Analytics

0.0001%

\(t=2.0\) Thermal Deformations \(V7\) (\(\mathit{N3}\))

0.024

Analytical

0.0001%

Identification

Reference

Reference type

Tolerance

\(t=0.8\) Hill equivalent stress \(V8\) (\(\mathit{N3}\))

92.5802

Other_Aster (B modeling)

0.0001%

\(t=1.3\) Hill equivalent stress \(V8\) (\(\mathit{N3}\))

70.1846

Other_Aster (B modeling)

0.0001%

\(t=2.0\) Hill equivalent stress \(V8\) (\(\mathit{N3}\))

84.4144

Other_Aster (B modeling)

0.0001%

Identification

Reference

Reference type

Tolerance

\(t=0.8\) Beta phase viscous stress \(V11\) (\(\mathit{N3}\))

92.5802

Other_Aster (B modeling)

0.0001%

\(t=1.3\) Beta phase viscous stress \(V11\) (\(\mathit{N3}\))

70.1846

Other_Aster (B modeling)

0.0001%

\(t=2.0\) Beta phase viscous stress \(V11\) (\(\mathit{N3}\))

84.4144

Other_Aster (B modeling)

0.0001%

Identification

Reference

Reference type

Tolerance

\(t=0.8\) Phase Change Indicator \(V12\) (\(\mathit{N3}\))

0.0

Analytics

0.0001%

\(t=1.3\) Phase Change Indicator \(V12\) (\(\mathit{N3}\))

0.0

Analytics

0.0001%

\(t=2.0\) Phase Change Indicator \(V12\) (\(\mathit{N3}\))

0.0

Analytics

0.0001%

Identification

Reference

Reference type

Tolerance

\(t=1.3\) Mechanical deformations \(\mathit{EPSYY}\) (\(N3\))

-0.0096

Other_Aster (B modeling)

0.0001%

\(t=2.0\) Mechanical deformations \(\mathit{EPSYY}\) (\(N3\))

-0.004

Other_Aster (B modeling)

0.0001%

Identification

Reference

Reference type

Tolerance

\(t=1.3\) Anelastic deformations \(\mathit{EPSYY}\) (\(N3\))

-0.0105

Other_Aster (B modeling)

0.0001%

\(t=2.0\) Anelastic deformations \(\mathit{EPSYY}\) (\(N3\))

-0.0051

Other_Aster (B modeling)

0.0001%