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3D Triaxial Displacement Secondary Creep (NAFEMS Test 6(b))

The secondary creep validation case belongs to solid mechanics. This test case aims to validate the following parameters:

  • Creep material behavior
  • Standard and reduced integration elements
  • Automatic time stepping

The simulation results were compared to the results presented in [NAFEMS]\(^1\).


The geometry consists of a cube with an edge length \(l\) = 0.1 \(m\).

geometry of the cube used in secondary creep validation case
Figure 1: Simple cube geometry used in this validation case

The coordinates for the points in the cube geometry are as tabulated below:

Table 1: Cube dimensions in meters

Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Nonlinear static

Mesh and Element Types: The mesh for cases A through D is a second-order tetrahedral mesh, generated in SimScale by the standard algorithm.

CaseMesh TypeNumber of NodesElement TypeCreep FormulationElement Technology
AStandard2352nd order tetrahedralNortonStandard
BStandard2352nd order tetrahedralNortonReduced integration
CStandard2352nd order tetrahedralTime HardeningStandard
DStandard2352nd order tetrahedralTime HardeningReduced integration
Table 2: Overview of the validation cases. The element technology integration and creep formulation change between the cases.

Find below the standard mesh used for cases A through D:

generated second order mesh in simscale which has 235 nodes for secondary creep validation
Figure 2: Generated second order mesh with SimScale for cases A through D

Simulation Setup


  • Steel (linear elastic)
    • Isotropic: \(E\) = 200 \(GPa\)
    • \(\nu\) = 0.3
    • \(\rho\) = 7870 \(kg/m³\)
    • Creep formulation:

Boundary Conditions:

  • Constraints:
    • Fixed value:
      • Face ADEH: \(d_x\) = 0 \(m\)
      • Face ABFE: \(d_y\) = 0 \(m\)
      • Face ABCD: \(d_z\) = 0 \(m\)
    • Displacement in x-direction
      • Face BCGF: \(d_x\) = 0.3 \(mm\)
    • Displacement in y-direction
      • Face CDHG: \(d_y\) = 0.2 \(mm\)
    • Displacement in z-direction
      • Face EFGH: \(d_z\) =0.1 \(mm\)

Advanced Automatic Time Stepping

For all cases, the following advanced automatic time stepping settings were defined under Simulation control:

  • Retiming event: Field change
  • Target field component: Internal variable V1 (accumulated unelastic strain)
  • Threshold value: 0.00005
  • Timestep calculation: Mixed
  • Field change target: 0.00004

Result Comparison

The secondary creep movement validation is done by comparing the stress (\(\sigma_{xx}\)) after a creep time of 1000 hours. Below you will find the SimScale and reference results from [NAFEMS]\(^1\):

CaseNAFEMS R27 \([MPa]\)SimScale \([MPa]\)Error [%]
Table 3: Stress comparison between the reference and the simulation results

In all configurations, the results obtained with SimScale show a good agreement with the reference values. The displacement of the geometry can be seen below:

visualization of displacement of a cube
Figure 3: Displacement observed in case A


If you still encounter problems validating your simulation, then please post the issue on our forum or contact us.

Last updated: July 21st, 2021