# Piezoelectric Unit Cube

## Problem Definition

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 'trelis' on the terminal.
2. On the Trelis 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.trelis to open it directly on Trelis (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.