Mesh and Element Types: The meshes for cases A and B are second-order hexahedral one-element meshes. They were created locally and imported to SimScale. For cases C and D, the standard algorithm was used to generate a second-order tetrahedral mesh.

Case

Mesh Type

Number of Nodes

Element Type

(A)

2nd order hexahedral

20

Standard

(B)

2nd order hexahedral

20

Reduced integration

(C)

2nd order standard

235

Standard

(D)

2nd order standard

235

Reduced integration

Table 2: Mesh characteristics.

Find below the mesh used for cases C and D. It’s a standard mesh with second-order tetrahedral cells.

For cases A through D, the following advanced automatic time stepping settings were defined under simulation control:

Retime event: field change;

Target field component: internal variable V1 (accumulated unelastic strain);

Threshold value: 0.0001;

Time step calculation type: mixed;

Field change target value: 0.00008.

Reference Solution

The equations used to solve the problem are derived in [NAFEMS_R27]\(^1\). As SimScale uses SI units, the reference solution was adopted to a time unit of seconds instead of hours.

Find below a comparison between SimScale’s results and the analytical solution presented in [NAFEMS_R27]\(^1\) for the average creep strain \(\epsilon_{xx}^c\) of the cube. The creep time is 3.6e6 \(s\) (equivalent to 1000 hours).

Case

[NAFEMS_R27]

SimScale

Error (%)

(A)

0.133380

0.133123

-0.192

(B)

0.133380

0.133123

-0.192

(C)

0.133380

0.133107

-0.205

(D)

0.133380

0.133107

-0.205

Table 3: Comparison of SimScale’s results against an analytical solution.

In Figure 3, we can see how \(\epsilon_{xx}^c\), \(\epsilon_{yy}^c\), and \(\epsilon_{zz}^c\) are evolving for case D.

\(\epsilon_{yy}^c\) and \(\epsilon_{zz}^c\) also show very good agreement with the analytical solution, having an error of 0% and -0.205%, respectively.

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