Piezoelectric Unit Cube

Problem Definition

All the files in this tutorial can be downloaded here.

This example illustrates the linear piezoelectric material, by considering a simple unit cube made from piezoelectric material. The faces of the cube are called like the compass, N (north), E (east), S (south), W (west) for the +y, +x, -y, -x normal faces, and T (top) and B (bottom) for the +z and -z normal faces, respectively. The lines are named by the adjoining faces, e.g. L_NW for the line created by the intersection of north-surface S_N and S_W surface-west. The same is done for corner points, e.g. P_NEB.

We set statically determined displacement BCs on three nodes, and apply an electric field in negative z-direction.

Sketch of the domain

+------+.
|`.    | `.
|  `+--+---+
|   |  |   |
+---+--+   |
 `. |   `. |
   `+------+

Mesing and CFS computation can be done by running ./run.sh.

Meshing

1. Type 'cubit' on the terminal.
2. On the Cubit GUI open up the journal file UnitCube.jou and run it.
3. A geometry of an unit cube is created.
4. Export the geometry as an ANSYS-cdb mesh file UnitCube.cdb
5. You can also save the created geometry as UnitCube.cub5 to open it directly on Cubit (optional).

The file UnitCube.cdb was created this way.

Simulation with CFS

The input file piezo_static.xml is the simulation input. In the file piezo_mat.xml the material porperties are defined.

To start the computation run the following command in the terminal

cfs -p piezo_static.xml job

where job can be any name you choose for the simulation.

CFS will write some output on the terminal, and produce the two files * job.info.xml, which contains some details about the run, and * job.cfs in the results_hdf5 directory, which you can view with ParaView.

Postprocessing

Open ParaView and choose File -> Load State ... to load the provided visualization pipeline post.pvsm

Further Suggestions

Is the deformation expected? You could also compute the results analytically from the linearized piezoelectric material law.

Additionally, you can modify the example to answer the following questions:

• Switch to fully constraint BCs and compute the stress state. Is the result expected?
• What happens when you change the orientation of the polarization?