1. Reference problem#

1.1. Geometry and boundary conditions#

Figure 1.1-a : geometry of the studied structure

The structure studied is a hollow sphere under pressure \(p=\mathrm{1MPa}\). The symmetry properties of the problem will be used.

The inner radius is \({R}_{\text{int}}=100\mathrm{mm}\) and the outer radius is \({R}_{\text{ext}}=200\mathrm{mm}\)).

Law of behavior

Elastic behavior

Plastic behavior

Damaging behavior

Damaging behavior (weakened zone)

VMIS_ISOT_LINE

\(E\mathrm{=}200.000\mathit{MPa}\)

\(\nu \mathrm{=}\mathrm{0,3}\)

\({\sigma }_{y}\mathrm{=}300\mathit{MPa}\)

\({E}_{T}\mathrm{=}0\)

\({\sigma }_{y}\mathrm{=}5\mathit{MPa}\)

\({E}_{T}\mathrm{=}\mathrm{-}10000\mathit{MPa}\)