1. Reference problem#

1.1. Geometry#

_images/100000000000012D0000019FF96BCAF98D7BE59F.png

Cylinder dimensions:

\({R}_{0}\)

\(1m\)

\({R}_{1}\)

\(2m\)

Figure 1.1-a: Hollow cylinder cutting and loading

1.2. Material properties#

Young’s module: \(E\mathrm{=}1\mathit{MPa}\)

Poisson’s ratio: \(\nu \mathrm{=}0.3\)

Law of LEMAITRE:

\(g(\sigma ,\lambda ,T)\mathrm{=}{(\frac{1}{K}\frac{\sigma }{{\lambda }^{\frac{1}{m}}})}^{n}\) with \(\frac{1}{K}\mathrm{=}1\), \(\frac{1}{m}\mathrm{=}0\), \(n\mathrm{=}1\)

Law LEMA_SEUIL:

\(g(\sigma ,\lambda ,T)\mathrm{=}A(\frac{2}{\sqrt{3}}\sigma )\Phi\) with \(A\mathrm{=}\frac{\sqrt{3}}{2}\), \(\Phi \mathrm{=}1\) all over the mesh

\(S\mathrm{=}{10}^{\mathrm{-}10}\)

given the value of the various material parameters, the two laws are absolutely identical and can therefore be compared to the same analytical solution.

1.3. Boundary conditions and loading#

Boundary conditions:

The cylinder is locked at \(\mathit{DY}\) on the \([\mathrm{AB}]\) and \([\mathrm{CD}]\) sides.

Charging:

The cylinder is subjected to internal pressure on \(\mathrm{[}\mathit{DA}\mathrm{]}\mathit{P0}\mathrm{=}1.E\mathrm{-}3\mathit{MPa}\)