Torsion Bar Benchmarks

CSM toolbox documentation is available here.

1. Introduction

We simulate the torsion of a beam generated by a circular motion at one extremities and fixed to the other side. The material is considered NeoHookean compressible.

2. Inputs

We consider an hyper-elastic material

    "Models":
    {
        "equations":"Hyper-Elasticity"
    },

2.1. Parameters

    "Parameters":
    {
        "rotation":
        {
            //"value":"8"
            "value":"3"
        }
    },

2.2. Materials

    "Materials":
    {
        "OmegaSolid":{
            //"E":"1.4e6",
            "E":"124e6",
            "nu":"0.33",
            "rho":"8920"
        }
    },

2.3. Boundary Conditions

    "BoundaryConditions":
    {
        "displacement_y":
        {
            "Dirichlet":
            {
                "Torsion":
                {
                    "expr":"0.5 + (y - 0.5)*cos(rotation) - (z-0.5)*sin(rotation) - y :y:z:rotation"
                }
            }
        },
        "displacement_z":
        {
            "Dirichlet":
            {
                "Torsion":
                {
                    "expr":"0.5 + (y - 0.5)*sin(rotation) + (z-0.5)*cos(rotation) - z :y:z:rotation"
                }
            }
        },
        "displacement" :
        {
            "Dirichlet":
            {
                "Fixed":
                {
                    "expr":"{0,0,0}"
                }
            },
            "Neumann_scalar" :
            {
                "BoundaryForce":
                {
                    "expr":"0"
                }
            }
        }
    },

3. Outputs

We compute the followig fields:

  • the process id (domain partitioning)

  • the displacement of the beam,

  • the Von-Mises criterium

We monitor also the output VolumeVariation.

    "PostProcess":
    {
        "Exports":
        {
            "fields":["displacement","pressure","pid","Von-Mises"]
        },
        "Measures":
        {
            "VolumeVariation":""
        }
    }

4. Running the model

The configuration file is in /usr/local/share/feelpp/testcases/CSM/torsionbar/torsionbar.cfg. The command line in feelpp-toolboxes docker or singularity reads

Command line to execute the torsionbar testcase
$ mpirun -np 4 /usr/local/bin/feelpp_toolbox_solid_3d --config-file torsionbar.cfg

5. Results

5.1. 3D model

In the window below, you can manipulate the 3D model at the final time step.

Click top left button on opengl window to change basic visualisation features

5.2. Video

The video below shows the torsion of the beam at different steps.

Torsion of a NeoHookean beam

5.3. Volume variation

angle volume_variation

2.000000000e+01

-7.1205327110135420e-07

4.000000000e+01

-2.6027517259663583e-06

6.000000000e+01

-5.7130950210648768e-06

8.000000000e+01

-1.0111760640008077e-05

1.000000000e+02

-1.5894732445964629e-05

1.200000000e+02

-2.3184761044170456e-05

1.400000000e+02

-3.2130698649801578e-05

1.600000000e+02

-4.2906700095102244e-05

1.800000000e+02

-5.5711308518979796e-05

2.000000000e+02

-7.0766434915015033e-05

2.200000000e+02

-8.8316245737729603e-05

2.400000000e+02

-1.0862597054686069e-04

2.600000000e+02

-1.3198064153030495e-04

2.800000000e+02

-1.5868377398575725e-04

3.000000000e+02

-1.8905600553154056e-04

TorsionBarPlot

5.4. Expected performance

The results have been obtained in 868 second by using 24 cores on one node of the Atlas cluster (Intel Xeon E5-2680 v3 2.50GHz).