# 3D triaxial load secondary creep (NAFEMS Test 6(a))¶

## Overview¶

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.

## Analysis type and Domain¶

**Tool Type** : Code_Aster

**Analysis Type** : Static - nonlinear

**Mesh and Element types** :

Case | Mesh type | Number of nodes | Creep formulation | Element type |
---|---|---|---|---|

(A) | 2nd order hex | 20 | Norton | 3D standard |

(B) | 2nd order hex | 20 | Norton | 3D reduced |

(C) | 2nd order hex | 20 | Time Hardening | 3D standard |

(D) | 2nd order hex | 20 | Time Hardening | 3D reduced |

(E) | 2nd order hex | 20 | Strain Hardening | 3D standard |

(F) | 2nd order hex | 20 | Strain Hardening | 3D reduced |

(G) | 2nd order tet | 21 | Norton | 3D standard |

(H) | 2nd order tet | 21 | Norton | 3D reduced |

(I) | 2nd order tet | 21 | Time Hardening | 3D standard |

(J) | 2nd order tet | 21 | Time Hardening | 3D reduced |

## Simulation Setup¶

Material:

linear elastic, isotropic: E = 200 GPa, \(\nu\) = 0.3

- creep formulation:
– Norton, A = 8.6805556e-48, n = 5

– Time Hardening, A = 8.6805556e-48, n = 5, m = 0

– Strain Hardening, A = 8.6805556e-48, n = 5, m = 0

Important

- The material Data of the reference was given in
*MPa*,*mm*and*h*units and were converted to SI units using the following relation: - \(A_{SI} = \frac{1}{3600} \cdot \frac{1}{10^{6n}} \cdot A_{MPa\;h}\)

Constraints:

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

Loads:

- 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: 0.001
- Timestep Calculation Type: mixed
- Field Change Target Value: 0.0008

## Reference Solution¶

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*.

## Results¶

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]:

Case | time [s] | [NAFEMS_R27] | SimScale | Error (%) |
---|---|---|---|---|

(A) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(B) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(C) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(D) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(E) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(F) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(G) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(H) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(I) | 3600000 | 4.218 | 4.21875 | -0.0178 |

(J) | 3600000 | 4.218 | 4.21875 | -0.0178 |