2. Benchmark solution

2.1. Calculation method used for the reference solution

The aim of the reference solution is to analytically calculate the threshold value at which creep occurs.

Some non-regression results on the movements at the last time step are added to verify the overall rigidity of the system.

For the analytical calculation of the threshold we have:

As long as the structure remains elastic and due to the boundary conditions, the stress tensor is written as:

For the first time step between \(0\) and \(106s\)

, and in second and

in \(\mathrm{MPa}\). The other components of the tensor are zero.

For the others no time,

But we have:

Let it be as in this case

, we obtain immediately by solving \(D=1\) the value of the time from which the creep occurs: \({t}_{1}=4.08181818{10}^{6}s\)

Thus for a time equal to \({t}_{1}\), the viscous deformations are zero and \(D\) is equal to 1.

2.2. Benchmark results

Internal variable \(\mathrm{V1}\) and \(\mathrm{V2}\) at the point \(A\), \(B\), \(C\) and \(E\) as well as the movement from point \(B\) to the last time step

2.3. Bibliographical references

1. 16. DE BONNIERES: Integrating viscoelastic relationships in STAT_NON_LINE [R5.03.08] February 2001