1. Reference problem

1.1. Geometry

The diagram is not to scale, the gap between the two cylinders has been amplified for better visibility.

\({R}_{1}\)	0.82
\({R}_{2}\)	0.92
\({R}_{3}\)
\({R}_{4}\)

1.2. Material properties

The pellet is composed of an elastic material, the sheath is made of a viscoelastic material.

The elastic data is consistent for both materials.

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 \(\frac{1}{K}\mathrm{=}1\), \(\frac{1}{m}\mathrm{=}0\), \(n\mathrm{=}1\)

1.3. Boundary conditions and loading

Boundary conditions:

The cylinder is locked at \(\mathit{DY}\) on the \(\mathrm{[}\mathit{AP},\mathit{BP}\mathrm{]}\), \(\mathrm{[}\mathit{AG},\mathit{BG}\mathrm{]}\) and \(\mathrm{[}\mathit{CP},\mathit{PD}\mathrm{]}\mathrm{[}\mathit{CG},\mathit{PG}\mathrm{]}\) sides.

Charging:

The cylinder is subjected to an internal pressure on \(\mathrm{[}\mathit{DP},\mathit{AP}\mathrm{]}\), this pressure is calculated so that at time \(t\mathrm{=}0\), the sheath behaves the same as the cylinder modelled in the ssna104a test.

with

,

,

with \({P}_{0}\mathrm{=}1.E\mathrm{-}3\mathit{MPa}\), ssna104a test pressure.

,

,

,

The contact between the two cylinders is treated.