2. Benchmark solution#

2.1. Calculation method#

The reference solution is analytical: the test is elementary, the cube is homogeneous deformation according to \(z\) (zero Poisson’s ratio). The force is therefore distributed according to the values of the shape functions on the nodes of the interface.

2.2. Reference quantities and results#

To move \(0.2\mathit{mm}\) down the \(A\) cube, we need to find (for QUAD4):

Cube

Point

DEPL \(\mathit{DZ}\)

REAC_NODA

\(\mathit{DZ}\)

\(A\)

\(\mathit{NH1}\)

-0,1

10000

\(A\)

\(\mathit{NH2}\)

-0,1

10000

\(A\)

\(\mathit{NH3}\)

-0,1

10000

\(A\)

\(\mathit{NH4}\)

-0,1

10000

\(A\)

\(\mathit{NH9}\)

-0,1

10000

\(A\)

\(\mathit{NH10}\)

-0,1

10000

\(A\)

\(\mathit{NH11}\)

-0,1

10000

\(A\)

\(\mathit{NH12}\)

-0,1

10000

\(A\)

\(\mathit{NH21}\)

-0,1

10000

\(B\)

\(\mathit{NB5}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB6}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB7}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB8}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB17}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB18}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB19}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB20}\)

-0,1

  • 10000

\(B\)

\(\mathit{NB26}\)

-0,1

  • 10000

To move \(0.2\mathit{mm}\) down cube A, we need to find (for QUAD8):

To move \(0.2\mathit{mm}\) down the \(A\) cube, we need to find (for QUAD9):

For the continuous formulation, contact pressures LAGS_C are tested in addition to the REAC_NODA nodal reactions. These are the true pressure values. So we have to find a pressure of \(p\mathrm{=}\mathit{E.}(0.1\mathrm{/}2)\mathrm{=}10000\) on the nodes \(\mathit{NH1}\), \(\mathit{NH2}\), \(\mathit{NH3}\),, \(\mathit{NH4}\), \(\mathit{NH9}\), \(\mathit{NH10}\), \(\mathit{NH11}\), \(\mathit{NH12}\) and \(\mathit{NH21}\).

2.3. Uncertainties about the solution#

None (analytical solution).