Modeling A ============== Characteristics of modeling ----------------------------------- .. math:: :label: eq-1 \ textrm {Modeling} \ mathrm {2D} .. image:: images/100007CC000069BB000067DFBB97E607D5BD7D2E.svg :width: 220 :height: 216 .. _RefImage_100007CC000069BB000067DFBB97E607D5BD7D2E.svg: **Boundary conditions:** +-----------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+ |:math:`\mathit{N1}`: :math:`\mathit{N2}`:| | + + .. image:: images/Object_4.svg + | | :width: 220 | + + :height: 216 + | | | + + + | | .. image:: images/Object_5.svg | + + :width: 220 + | | :height: 216 | + + + | | | +-----------------------------------------+-----------------------------------------------------------------------------------------------------------------------------------------------------------------------+ **Charging:** Traction on the :math:`\mathrm{[}34\mathrm{]}` side (SEG2 mesh) + assignment of the same temperature on all knots The total number of increments is 20 (10 increments between :math:`t\mathrm{=}\mathrm{0s}` and :math:`\mathrm{1s}`, 10 increments between :math:`t\mathrm{=}\mathrm{1s}` and :math:`\mathrm{2s}`) **Behavior:** For mechanical calculation, the keyword META_LEMA_ANI is used, with the following parameters (see [:ref:`R4.04.05 `] and [:ref:`R4.04.05 `]): :math:`\mathit{YoungModulus}=80000\mathit{MPa}` :math:`\mathit{PoissonRatio}=0.35` :math:`{\alpha }_{f}=0.` :math:`{\alpha }_{c}=0.00004` :math:`{a}_{3}=\mathrm{253,5497}\mathit{MPa}` :math:`{m}_{3}=0.` :math:`{n}_{3}=4.39` :math:`{Q}_{3}=0.K` :math:`{M}_{\mathit{rrrr}}^{3}=1.` :math:`{M}_{\theta \theta \theta \theta }^{3}=1.` :math:`{M}_{\mathit{zzzz}}^{3}=1.` :math:`{M}_{r\theta r\theta }^{3}=0.75` :math:`{M}_{\mathit{rzrz}}^{3}=0.75` :math:`{M}_{\mathrm{\theta }z\mathrm{\theta }z}^{3}=0.75` :math:`\mathit{TDEQ}=809.` :math:`K=1.135E-2` :math:`\text{NEQ}=2.187` :math:`T1C=831.` :math:`T2C=0.0` :math:`\text{QSR\_K}=14614` :math:`\mathit{AC}=1.58E-4` :math:`M=\mathrm{4,7}` :math:`T1R=949.1` :math:`T2R=\mathrm{0,0}` :math:`\mathit{AR}=-5.725` :math:`\mathit{BR}=\mathrm{0,05}` The parameters corresponding to the cold phase and to the :math:`\alpha \beta` mixture do not play a role and are taken to be arbitrary. Characteristics of the mesh ---------------------------- Number of knots: 4 Number of meshes: 2 1 QUAD4 1 SEG2 Tested sizes and results ------------------------------ The stresses and deformations are compared with the B model. .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=0.3` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "-91.7598", "Other_Aster (B modeling)", "1.00%" ":math:`t=0.8` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "-92.5802", "Other_Aster (B modeling)", "1.00%" ":math:`t=1.3` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "70.1846", "Other_Aster (B modeling)", "1.00%" ":math:`t=2.0` Constraints :math:`\mathit{SIGYY}` (:math:`\mathit{N3}`)", "84.4144", "Other_Aster (B modeling)", "1.00%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=1.3` Total deformations :math:`\mathit{EPYY}` (:math:`\mathit{N3}`)", "0.006", "Other_Aster (B modeling)", "0.0001%" ":math:`t=2.0` Total deformations :math:`\mathit{EPYY}` (:math:`\mathit{N3}`)", "0.02", "Other_Aster (B modeling)", "0.0001%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=0.8` Beta phase proportion (:math:`V6`)", "1.0", "Analytical", "0.0001%" ":math:`t=1.3` Beta phase proportion (:math:`V6`)", "1.0", "Analytical", "0.0001%" ":math:`t=2.0` Beta phase proportion (:math:`V6`)", "1.0", "Analytical", "0.0001%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=0.8` Thermal Deformations :math:`V7` (:math:`\mathit{N3}`)", "0.0096", "Analytical", "0.0001%" ":math:`t=1.3` Thermal Deformations :math:`V7` (:math:`\mathit{N3}`)", "0.0156", "Analytics", "0.0001%" ":math:`t=2.0` Thermal Deformations :math:`V7` (:math:`\mathit{N3}`)", "0.024", "Analytical", "0.0001%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=0.8` Hill equivalent stress :math:`V8` (:math:`\mathit{N3}`)", "92.5802", "Other_Aster (B modeling)", "0.0001%" ":math:`t=1.3` Hill equivalent stress :math:`V8` (:math:`\mathit{N3}`)", "70.1846", "Other_Aster (B modeling)", "0.0001%" ":math:`t=2.0` Hill equivalent stress :math:`V8` (:math:`\mathit{N3}`)", "84.4144", "Other_Aster (B modeling)", "0.0001%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=0.8` Beta phase viscous stress :math:`V11` (:math:`\mathit{N3}`)", "92.5802", "Other_Aster (B modeling)", "0.0001%" ":math:`t=1.3` Beta phase viscous stress :math:`V11` (:math:`\mathit{N3}`)", "70.1846", "Other_Aster (B modeling)", "0.0001%" ":math:`t=2.0` Beta phase viscous stress :math:`V11` (:math:`\mathit{N3}`)", "84.4144", "Other_Aster (B modeling)", "0.0001%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=0.8` Phase Change Indicator :math:`V12` (:math:`\mathit{N3}`)", "0.0", "Analytics", "0.0001%" ":math:`t=1.3` Phase Change Indicator :math:`V12` (:math:`\mathit{N3}`)", "0.0", "Analytics", "0.0001%" ":math:`t=2.0` Phase Change Indicator :math:`V12` (:math:`\mathit{N3}`)", "0.0", "Analytics", "0.0001%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=1.3` Mechanical deformations :math:`\mathit{EPSYY}` (:math:`N3`)", "-0.0096", "Other_Aster (B modeling)", "0.0001%" ":math:`t=2.0` Mechanical deformations :math:`\mathit{EPSYY}` (:math:`N3`)", "-0.004", "Other_Aster (B modeling)", "0.0001%" .. csv-table:: "**Identification**", "**Reference**", "**Reference type**", "**Tolerance**" ":math:`t=1.3` Anelastic deformations :math:`\mathit{EPSYY}` (:math:`N3`)", "-0.0105", "Other_Aster (B modeling)", "0.0001%" ":math:`t=2.0` Anelastic deformations :math:`\mathit{EPSYY}` (:math:`N3`)", "-0.0051", "Other_Aster (B modeling)", "0.0001%"