7. E modeling#

7.1. Characteristics of modeling#

We take advantage of the symmetries of the problem to model only one eighth of the sphere.

_images/100000000000024800000218C6373DF2928F2F56.png

Three models are tested: AXIS_INCO_UPG (SIMO_MIEHE and GDEF_LOG) and AXIS_INCO_UP

7.2. Characteristics of the mesh#

The 441 node mesh contains 200 TRIA6 elements.

7.3. Tested sizes and results#

The stress trace and the cumulative plastic deformation are tested for the most eccentric and the least eccentric Gauss points.

MODELISATION =” AXIS_INCO_UPG “and DEFORMATION =” SIMO_MIEHE”

Identification

Reference type

Reference value

Tolerance

Least offset Gauss point - \(\mathit{tr}\sigma\) - Pa

“ANALYTIQUE”

-1038055558,5

1.5%

Outermost Gauss point - \(\mathit{tr}\sigma\) - Pa

“ANALYTIQUE”

287474941.41

0.1%

Least offset Gauss point - \(p\)

“ANALYTIQUE”

0.095807224561

16%

Outermost Gauss point - \(p\)

“ANALYTIQUE”

4.5056636601e-5

10%

MODELISATION =” AXIS_INCO_UPG “and DEFORMATION =” GDEF_LOG”

Identification

Reference type

Reference value

Tolerance

Least offset Gauss point - \(\mathit{tr}\sigma\) - Pa

“ANALYTIQUE”

-1036113143.5

1.5%

Outermost Gauss point - \(\mathit{tr}\sigma\) - Pa

“ANALYTIQUE”

“”

287474939.50

0.1%

Least offset Gauss point - \(p\)

“ANALYTIQUE”

0.096499343842

16%

Outermost Gauss point - \(p\)

“ANALYTIQUE”

4.5056643994e-5

10%

MODELISATION =” AXIS_INCO_UP “and DEFORMATION =” GDEF_LOG”

Identification

Reference type

Reference value

Tolerance

Least offset Gauss point - \(\mathit{tr}\sigma\) - Pa

“ANALYTIQUE”

-1036113143.5

1.5%

Outermost Gauss point - \(\mathit{tr}\sigma\) - Pa

“ANALYTIQUE”

“”

287474939.50

0.1%

Least offset Gauss point - \(p\)

“ANALYTIQUE”

0.096499343739

16%

Outermost Gauss point - \(p\)

“ANALYTIQUE”

4.5056643999e-5

10%

7.4. notes#

All incompressible formulations give good results. We can see from the that we no longer have oscillations in the value of the stress trace with incompressible formulations unlike standard elements AXIS.

_images/10000000000001ED00000123E5FF7B8F529F1384.png

Figure 7.4-a : Trace the constraints in \(\mathit{Mpa}\) for the formulations AXIS , AXIS_INCO **** and the analytical solution**