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    Validation Case: 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.

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

    cube geometry triaxial load primary creep validation
    Figure 1: Cube geometry for the present validation project

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

    ABCDEFGH
    x00.10.1000.10.10
    y000.10.1000.10.1
    z00000.10.10.10.1
    Table 1: Cube dimensions in meters

    Tool Type: Code Aster

    Analysis Type: Nonlinear static

    Mesh and Element Types: The mesh used in cases A and B was created using the standard algorithm within SimScale. The same mesh is used in both cases – the only difference between the runs is the element technology integration. Table 2 shows more details about the cases.

    CaseMesh TypeNumber of NodesElement TypeElement Technology
    (A)Standard2352nd order tetrahedralStandard
    (B)Standard2352nd order tetrahedralReduced integration
    Table 2: Mesh characteristics

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

    cube second order standard mesh
    Figure 2: Second-order standard mesh used for cases A and B.

    Material:

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

    Boundary Conditions:

    • Constraints
      • dx = 0 on face ADHE;
      • dy = 0 on face ABFE;
      • dz = 0 on face ABCD.
    • Surface loads
      • tx = 300 MPa on face BCGF;
      • ty = 200 MPa on face CDHG;
      • tz = 100 MPa on face EFGH.

    Advanced Automatic Time Stepping:

    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.

    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.

    (1)ϵxxc=ϵzzc=0.00421860t

    (2)ϵeffc=0.00487160t

    (3)ϵyyc=0.0

    Find below a comparison between SimScale’s results and the analytical solution presented in [NAFEMS_R27]1 for the average creep strain ϵxxc of the cube. The creep time is 3.6e6 s (equivalent to 1000 hours).

    Case[NAFEMS_R27]SimScaleError (%)
    (A)0.1333800.133107-0.205
    (B)0.1333800.133107-0.205
    Table 3: Comparison of SimScale’s results against an analytical solution for this primary creep validation case

    In Figure 3, we can see how ϵxxc, ϵyyc, and ϵzzc are evolving for case B.

    average creep strain plot
    Figure 3: Average creep strain plot for case B

    ϵyyc and ϵzzc also show very good agreement with the analytical solution, having an error of 0% and -0.205%, respectively.

    Last updated: November 29th, 2023