Piezoceramic Block Simulation

In this tutorial, you'll learn how to set up a simple 2D transducer model with a backing and matching layer and how to extract outputs such as impedance, directivity plots and transmit sensitivities.

We'll cover:

  • The basic simulation workflow in OnScale Designer
  • How to set up a 3D model
  • How to create a simple geometry
  • How to simulate piezoelectric materials
  • How to calculate impedance
  • How to plot a mode shape

Note: PZT, or lead zirconate titanate, is an inorganic compound with the chemical formula Pb[ZrxTi1-x]O3 (0≤x≤1). It's a ceramic perovskite material that shows a marked piezoelectric effect, meaning that the compound changes shape when an electric field is applied. It's used in a number of practical applications such as ultrasonic transducers and piezoelectric resonators. It's a white to off-white solid.

Model Definition

Characteristics of the Model

Model PZT block dimensions: 20 mm x 14 mm x 2 mm
Mesh Size 0.1 mm
Output Results
  • Impedance
  • Harmonic mode shape

Material Data

Name CTS 3203HD
Code Name pmt3
Density 7820 kg.m-3
Bulk Velocity 4708.36 ms-1
Shear Velocity 1687.891 ms-1

Note: Material data in OnScale is generally defined using the bulk velocity and the shear velocity parameters, instead of the more traditional Elastic Modulus and Poisson's Ratio. If you want to understand the relation between these parameters, check out Relationship between Ultrasonic Velocity and Elastic Moduli (external link).

Why This Simulation?

Piezoceramics are the core material in many transducers and resonator, and the accurate simulation of their behavior is a fundamental requirement.

To check how the simulation compares with experimental results, the resonances from the impedance response are commonly used.

The Simulation Process

Let's go through the simulation process step by step and see how to simulate this in OnScale!

Step 1: Create a New Project

  1. In the Home tab of the ribbon, click New Project. The New Project window shows.
  2. Type a name for the project.
  3. If desired, change the save location and/or project file name by clicking  beside Project File.
  4. For Analysis, select Mechanical Dynamic.
  5. Select the Advanced checkbox.
  6. For Distance, select mm.
  7. Click OK.

Step 2: Add the Materials

First we'll add the materials that we need from the Materials Database. We'll use pmt3 and water.

  1. In the Home tab of the ribbon, click Project Materials.
  2. Expand Piezoelectric and double-click pmt3.
  3. Click Done.

Step 3: Create Basic Geometry Shapes

Note: After making changes to X and Y, right-click the workspace and select Reset View.

  1. In the Home tab of the ribbon, click Cuboid.
  2. In the Properties window, for Material select pmt3.
  3. Set End (mm) as follows:
    1. X (mm) = 10
    2. Y (mm) = 7
    3. Z (mm) = 2

Step 4: Define a Time Function

We'll now add a Ricker Wavelet drive function for later use as our loads require a time function to be set.

  1. In the Model Tree, expand Forcing Functions and, beside Time, click .
  2. In the dropdown, select Ricker Wavelet.
  3. Click Insert.

Step 5: Choose the Right Mesh Size

Next we'll change the mesh settings to use 15 elements per wavelength.

  1. In the Model Tree, expand Mesh and then click Configuration to select it.
  2. In the Properties window, for Definitions select Wavelength Based.
  3. Set Elements Per Wavelength to 15.
  4. Change Mesh Velocity to Defined and change Value to 1500

Step 6: Create the Two Electrodes

Let's create the two electrodes. We'll drive the top electrode (load_1) and ground the bottom electrode (load_2).

Create the Top Electrode

  1. In the Model Tree, expand Boundary Conditions and then, beside Loads, click .
  2. For Creation Mode, select Geometry Interface.
  3. For Geometry, select primitive_1 (pmt3) (or click this in the model).
  4. For Interfacing Item, select side 6 (zmax).
  5. For Load Type, select Voltage.
  6. For Area Scaling, type 4.
  7. For Termination, select timefunc_1.
  8. Click Create Load.

Create the Bottom Electrode

The Load Definition window should still be open.

  1. For Geometry, select primitive_1 (pmt3) (or click this in the model).
  2. For Interfacing Item, select side 5 (zmin).
  3. For Termination, select Ground.
  4. Click Create Load.

Step 7: Define the Boundary Conditions

We need to change the X minimum boundary condition to symmetry, as this model is symmetrical along that axis.

  1. In the Model Tree, click Domain Boundaries to select it.
  2. In the Properties window, expand X Minimum and, for Boundary Type, select Symmetry.
  3. Expand Y Minimum and, for Boundary Type, select Symmetry.

Step 8: Define the Analysis Simulation Time

Next we'll set the model simulation time to be 5e-5 seconds.

  1. In the Model Tree, click Analysis to select it.
  2. In the Properties window, for Simulation Run Time (s) type 100e-06.

Step 9: Define the Output Results

Now we'll define one output.

Output Result: Shape Data

  1. In the Model Tree, beside Outputs, click .
  2. In the Properties window, for Output Type select Shape Data.
  3. For Frequency (Hz), type 70e3.

Step 10: Run on the Cloud

The model is now ready to be run on the cloud.

  1. In the Home tab of the ribbon, click Run on Cloud.
  2. If you wish, rename the job.
  3. Click Estimate.
  4. Click Run.

Download the Simulation Results

You'll need to download the simulation results from the cloud in order to analyze them in Post Processor. More experienced users may also wish to process time histories in Review.

  1. In the Home tab of the ribbon, click Storage.
  2. In the Job dropdown, select the job.
  3. Click Download and then select Download All.
  4. Select a folder to save the results to, and then click Select Folder.

Step 11: Check the Simulation Results

Switch to Post Processor

In the top-right of Designer, click Switch to Post Processor.


Calculate and Plot Impedance

  1. In File Explorer, double-click the Flex History File (.flxhst) to open it in Results Manager.
  2. In Results Manager, click pize load1:Charge to select it.
  3. In the Home tab of the ribbon, click Impedance. In Results Manager, two new records appear under Frequency History. 
  4. Double-click Impd:load1.amp to plot it.

Note: To zoom in on the plot, click and drag a box around the area you want to zoom in on. To zoom out again, right-click the plot.

Plot Shape Movie

  1. In File Explorer, double-click the Shape Output File (.flxdato) to open it in Results Manager.
  2. Expand Mode Shapes and double-click yvel. You'll be asked if you want to overwrite the view. Click Continue.
  3. In the Model Graphics tab of the ribbon, click Symmetry > About X and SymmetryAbout Y.
  4. In the Model Tree, right-click yvel and select Plot Shape Movie.
  5. In Plot Controls, click the Play button to animate the mode shape.

Try For Yourself

Now that you've worked through the tutorial, have a play around with some of the settings, add some other outputs or use this model as a starting point for your own.