3D Triaxial load primary creep (NAFEMS Test 11)


The aim of this test case is to validate the following functionalities:

  • creep material behavior
  • standard and reduced integration elements
  • automatic time stepping

The simulation results of SimScale were compared to the analytical results in [NAFEMS_R27]. The tetrahedral meshes used were created with the parametrized-tetrahedralization-tool on the SimScale platform.

Import validation project into workspace



Geometry of the Cube

  • Cube edge length l = 0.100 m

Analysis type and Domain

Tool Type : Code_Aster

Analysis Type : Static - nonlinear

Mesh and Element types :

Case Mesh type Number of nodes Element type
(A) second order hexahedral 20 3D isoparametric
(B) second order hexahedral 20 3D reduced integration
(C) second order tetrahedral 21 3D isoparametric
(D) second order tetrahedral 21 3D reduced integration

Mesh used for the SimScale cases (C) and (D)

Simulation Setup


  • linear elastic, isotropic: E = 200 GPa, \(\nu\) = 0.3
  • creep formulation: Time Hardening, A = 2.6041667e-46, n = 5, m = -0.5


The material Data of the reference was given in MPa, mm and h units and were converted to SI units using the following relation:
\(A_{SI} = \frac{1}{3600} \cdot \frac{1}{3600^m} \cdot \frac{1}{10^{6n}} \cdot A_{MPa\;h}\)
for the parameters as given in followig Time Hardening formulation:
\(\dot{\epsilon} = A \cdot \sigma^n \cdot t^m\)


  • face ADEH: \(d_{x} = 0.0\) m
  • face ABFE: \(d_{y} = 0.0\) m
  • face ABCD: \(d_{z} = 0.0\) m


  • face BCGF: \(\sigma_{xx}\) = 300 MPa
  • face CDHG: \(\sigma_{yy}\) = 200 MPa
  • face EFGH: \(\sigma_{zz}\) = 100 MPa

Advanced Automatic Time Stepping:

  • Retiming Event: Field Change
  • Target Field component: internal variable V1 (accumulated unelastic strain)
  • Threshold value: 0.0001
  • Timestep Calculation Type: mixed
  • Field Change Target Value: 0.00008

Reference Solution

\[\begin{equation}\label{ref1} \epsilon_{xx}^c = - \epsilon_{zz}^c = \frac{0.004218}{60} \sqrt{t} \end{equation}\]\[\begin{equation}\label{ref2} \epsilon_{eff}^c = \frac{0.004871}{60} \sqrt{t} \end{equation}\]\[\begin{equation}\label{ref3} \epsilon_{yy}^c = 0.0 \end{equation}\]

The equations used to solve the problem are derived in [NAFEMS_R27]. As the SimScale solution is calculated using SI units, the reference solution was adopted to a time unit of seconds instead of hours.


Comparison of the average creep strain \(\epsilon_{xx}^c\) of the cube after a creep time of 3.6e6 s (1000 h) with the analytical solution presented in [NAFEMS_R27]:

Comparison of the creep strain \(\epsilon_{xx}^c\)
Case time [s] [NAFEMS_R27] SimScale Error (%)
(A) 3600000 0.13338 0.133107 0.205
(B) 3600000 0.13338 0.133107 0.205
(C) 3600000 0.13338 0.133107 0.205
(D) 3600000 0.13338 0.133107 0.205