3D Triaxial load primary creep (NAFEMS Test 11)

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.

Import validation project into workspace

Geometry

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

Material:

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

Important Information

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

$$A_{SI} = \frac{1}{3600} \cdot \frac{1}{3600^m} \cdot \frac{1}{10^{6n}} \cdot A_{MPa\;h}$$
$$\dot{\epsilon} = A \cdot \sigma^n \cdot t^m$$
Constraints:

face ADEH: $$d_x = 0.0m$$
face ABFE: $$d_y= 0.0m$$
face ABCD: $$d_z=0.0m$$

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: 0.0001
Timestep Calculation Type: mixed
Field Change Target Value: 0.00008

Reference Solution

$$\epsilon_{xx}^c = – \epsilon_{zz}^c = \frac{0.004218}{60} \sqrt{t}$$
$$\epsilon_{eff}^c = \frac{0.004871}{60} \sqrt{t}$$
$$\epsilon_{yy}^c = 0.0$$

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]: