1. Reference problem

1.1. Geometry

We consider a hollow sphere with external radius \(30\mathit{mm}\) and internal radius \(20\mathit{mm}\), included in a hollow sphere with external radius \(40\mathit{mm}\) and internal radius equal to the external radius of the included sphere.

1.2. Material properties

The material is isotropic elastic whose properties are:

• \(E=2000\mathit{MPa}\)

• \(\nu =0.3\)

1.3. Boundary conditions and loads

Symmetry conditions \(\mathit{DX}=0\) on the surface \(\mathit{AD}\) and \(\mathit{DY}=0\) on the surface \(\mathit{BC}\) are imposed in order to model only a quarter of the model.

Pressure \(P=25\mathit{MPa}\) is imposed on the surface \(\mathit{AB}\), inside the first sphere. The two spheres are kept in contact at the interface.