1. Reference problem#

1.1. Geometry#

The following surfaces are defined:

Face \(\mathrm{YZ1}\): containing nodes \(\mathrm{P1},\mathrm{P3},\mathrm{P5}\) and \(\mathrm{P7}\).
Face \(\mathrm{YZ2}\): containing nodes \(\mathrm{P9},\mathrm{P10},\mathrm{P11}\) and \(\mathrm{P12}\).
Face \(\mathrm{XY1}\): containing nodes \(\mathrm{P1},\mathrm{P2},\mathrm{P9},\mathrm{P3},\mathrm{P4}\) and \(\mathrm{P10}\).
Face \(\mathrm{XY2}\): containing nodes \(\mathrm{P5},\mathrm{P6},\mathrm{P11},\mathrm{P7},\mathrm{P8}\) and \(\mathrm{P12}\).
Face \(\mathrm{XZ1}\): containing nodes \(\mathrm{P3},\mathrm{P4},\mathrm{P10},\mathrm{P7},\mathrm{P8}\) and \(\mathrm{P12}\).
Face \(\mathrm{XZ2}\): containing nodes \(\mathrm{P1},\mathrm{P2},\mathrm{P9},\mathrm{P5},\mathrm{P6}\) and \(\mathrm{P11}\).

and the following items:

Element \(\mathrm{M1}\): containing nodes \(\mathrm{P1},\mathrm{P2},\mathrm{P3},\mathrm{P4},\mathrm{P5},\mathrm{P6},\mathrm{P7}\) and \(\mathrm{P8}\).
Element \(\mathrm{M2}\): containing nodes \(\mathrm{P2},\mathrm{P9},\mathrm{P4},\mathrm{P10},\mathrm{P6},\mathrm{P11},\mathrm{P8}\) and \(\mathrm{P12}\).

Two materials are used:

Young’s module: \(\mathit{E1}\mathrm{=}200000\mathit{MPa}\)

Poisson’s ratio: \({\nu }_{1}\mathrm{=}0.3\)

Young’s module: \(\mathrm{E2}=100000\mathrm{MPa}\)

Poisson’s ratio: \({\nu }_{2}=0.3\)

First calculation:

It’s a simple traction calculation following direction \(X\):

A linear elastic deformation \({\varepsilon }_{\mathit{xx}}\mathrm{=}1\) is imposed on the surface \(\mathrm{YZ2}\).
Surface \(\mathrm{YZ1}\) does not move in the \(X\) direction.

Second calculation:

It’s a simple traction calculation following direction \(Y\):

A linear elastic deformation \({\varepsilon }_{\mathit{yy}}\mathrm{=}1\) is imposed on the surface \(\mathrm{XZ2}\).
Surface \(\mathrm{XZ1}\) does not move in the \(Y\) direction.