# 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

### 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).