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# 3D Triaxial Load Primary Creep (NAFEMS Test 11)

This triaxial load primary 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 of SimScale were compared to the analytical results derived from [NAFEMS_R27]$$^1$$.

## Geometry

The geometry consists of a cube with edge length $$l$$ = 0.1 $$m$$.

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

## Analysis Type and Mesh

Tool Type: Code Aster

Analysis Type: Nonlinear static

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.

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

## Simulation Setup

Material:

• Steel (linear elastic)
• $$E$$ = 200 $$GPa$$
• $$\nu$$ = 0.3
• $$\rho$$ = 7870 $$kg/m³$$
• Creep formulation: Time hardening
• A = 2.6041667e-46 $$1/s$$
• N = 5
• M = -0.5

Boundary Conditions:

• Constraints
• $$d_x$$ = 0 on face ADHE;
• $$d_y$$ = 0 on face ABFE;
• $$d_z$$ = 0 on face ABCD.
• $$t_x$$ = 300 $$MPa$$ on face BCGF;
• $$t_y$$ = 200 $$MPa$$ on face CDHG;
• $$t_z$$ = 100 $$MPa$$ on face EFGH.

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.

$$\epsilon_{xx}^c = – \epsilon_{zz}^c = \frac{0.004218}{60} \sqrt{t} \tag{1}$$

$$\epsilon_{eff}^c = \frac{0.004871}{60} \sqrt{t} \tag{2}$$

$$\epsilon_{yy}^c = 0.0 \tag{3}$$

## Result Comparison

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).

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.

Last updated: July 21st, 2020