1. Reference problem

1.1. Geometry

We consider a disk with radius \(1000\mathit{mm}\) in the \((\mathrm{0,}X,Y)\) plane.

The thickness of the membrane is entered in AFFE_CARA_ELEM via the keyword EPAIS and is equal to \(1\mathit{mm}\).

1.2. Material properties

The material is isotropic hyperelastic whose properties are:

• \(E=2\mathit{Mpa}\)

• \(\mathrm{\nu }=\mathrm{0,3}\)

We validate two laws of behavior, the law of Saint Venant Kirchhoff and the Neo-Hookian law.

1.3. Boundary conditions and loads

The outer edge of the membrane is embedded. Uniform pressure is applied to the entire disk.

For Saint Venant Kirchhoff’s law the pressure is \(25\mathit{kPa}\). It is applied in 2 increments.

For the Neo-Hookean law, the pressure is controlled via the displacement at point \(O\) according to \(Z\), noted \(W\), in order to continue the calculation beyond the limit load. The calculation is then continued after the maximum pressure has been reached. The control is carried out in 10 increments, up to \(W=2500\mathit{mm}\). The piloted reference pressure is \(1\mathit{Pa}\). The quantity ETA_PILO then corresponds to the pressure value in \(N/{m}^{2}\).

1.4. Initial conditions

An initial voltage of \(1\mathit{Pa}\) is entered in AFFE_CARA_ELEM using the N_ INIT keyword. This tension disappears after the first Newton increment.