MUTs 002 - Piezocomposite transducer

What you’ll learn

• How to build a 1-3 piezocomposite geometry using translate (copy) and union operations, and define a custom epoxy filler material.
• How to couple Elastic waves and Electrostatics with piezoelectricity, drive the element with a wavelet voltage via Lump V/Q, and run a transient simulation with Generalized alpha timestepping.

Prerequisites: complete any one step-by-step tutorial first so you are comfortable with the Allsolve project layout (Geometry, Physics, Simulations, Results).

In this example, a piezocomposite ultrasound transducer is simulated. Their main application is in medicine, where they are used for ultrasound imaging and medical therapeutics. Other applications include sonar and non-destructive testing.

The model captures a single element of a 1-3 piezocomposite linear array. The piezocomposite combines a soft PZT with an epoxy filler with a 40% volume fraction. The piezocomposite sits on a backing layer, and utilizes a 1/4 wavelength matching layer for better coupling into the water load. The centre element of the array is driven with a short voltage pulse to allow the wideband behaviour, or impulse response, of the device to be captured. Key outputs are:

• Drive voltage and current
• Pressure in the load
• Electrical impedance

Demo project: Piezocomposite demo V1

Simulation setup guide

Here you’ll find a simplified, example case level guide for setting up a piezocomposite transducer simulation in Quanscient Allsolve.

Step 1 - Define variables

Start out in the Common sidebar by defining variables.

Name	Description	Expression
frequency	Frequency [Hz]	1.25e6
ncycles	Number of cycles	5
npillars	Number of pillars	5
thick_comp	Composite thickness [m]	1e-3
kerf	Cut width [m]	0.15e-3
pitch	Distance between cuts [m]	0.4e-3
pillar	Pillar width [m]	pitch-kerf
width	Element width [m]	npillars*pitch - kerf

You can import the variables as a CSV file:

Name,Expression,Description
freq,1.25e6,Frequency [Hz]
ncycles,5,Number of cycles
npillars,5,Number of pillars
thick_comp,1e-3,Composite thickness [m]
kerf,0.15e-3,cut width [m]
pitch,0.4e-3,Distance between cuts [m]
pillar,pitch-kerf,pillar width [m]
width,npillars*pitch-kerf,Element width [m]

Step 2 - Build the geometry

1. Start building the model geometry by adding Box elements with Alignment = Corner:

   Name	Element type	Corner point [m]	Size [m]	Rotation [deg]
   pzt	Box	X: 0	X: width	X: 0
   		Y: 0	Y: width	Y: 0
   		Z: 0	Z: thick_comp	Z: 0

   Name	Element type	Corner point [m]	Size [m]	Rotation [deg]
   cut x	Box	X: 0	X: width	X: 0
   		Y: pillar	Y: kerf	Y: 0
   		Z: 0	Z: thick_comp	Z: 0

   Name	Element type	Corner point [m]	Size [m]	Rotation [deg]
   cut y	Box	X: pillar	X: kerf	X: 0
   		Y: 0	Y: width	Y: 0
   		Z: 0	Z: thick_comp	Z: 0

2. Use the Translate operation to copy the cuts in X and Y directions:

   Name	Element type	Target	Translation [m]	Copy	Repeat count
   copy x	Translation	cut y	X: pitch	Yes	npillars - 2
   			Y: 0
   			Z: 0

   Name	Element type	Target	Translation [m]	Copy	Repeat count
   copy y	Translation	cut x	X: 0	Yes	npillars - 2
   			Y: pitch
   			Z: 0

3. Use the Union operation to merge all the multiplied cuts to a single volume:

   Name	Element type	Target
   combine polymer	Union	copy x and copy y assemblies (all cut volumes)

4. Confirm model changes.

Finished geometry:

Step 3 - Define the materials

Go to the Physics section to define model materials.

Material 1 - PZT

Add PZT from the library and assign it to the piezoelectric pillars:

1. Go to Target -> Pick with rule -> Select all volumes as target
2. Remove the epoxy filler volume from the selection by clicking on the model view.
3. Add the final target with 25 pillars as a region.

Material 2 - Epoxy

1. Create a new material for the epoxy filler:

   Material	Target
   Epoxy	Polymer filler volume

2. Define material properties for Epoxy:

   Property	Value	Units
   Density	1134	$\rm kg/m^3$
   Elasticity matrix	Poisson’s ratio: 0.37
   	Young’s modulus: 3.831e9	$\rm Pa$
   Electric permittivity	4*epsilon0	$\rm F/m$

3. Add the target as a region.

Step 4 - Define the physics

The Elastic waves and Electrostatics physics are required for this example. Add both of them to your physics set before defining interactions, in order to couple them together.

Physics 1 - Elastic waves

• Let elastic waves target default to the whole geometry.
• Add the Elastic waves - Electrostatics coupling Piezoelectricity.
  • Select the PZT region as target.

Physics 2 - Electrostatics

• Let Electrostatics target default to the whole geometry.

• Add a Constraint interaction which acts as a ground on the bottom surface:

  Interaction	Target	Constraint value
  Constraint	Bottom surface of the whole element	0

  

  Region rule selector

  To create a region easily for the bottom surface of the composite block, go to common sidebar -> create region -> rule selector -> bounding box -> pick similar. Click on the epoxy filler bottom surface. This creates a bounding box with all the pillar bottom surfaces included.

  

  The same procedure works for the top surface.

• Add a Lump V/Q interaction which drives a voltage on the top surface with wavelet:

  Interaction	Target	Voltage
  Lump V/Q	Top surface of the element	wavelet(frequency, 1.2)

  

Step 5 - Generate the mesh

Go to the Simulations section and create a new mesh:

1. Add an Autotransfinite mesh customization targetting the PZT region.
2. Set element max size to 0.1e-3 (100 um) for example.
3. Run meshing.
4. Check the preview:

Wavelength based meshing

Autotransfinite meshing is great for the PZT pillars in this example and similar blocky, grid-like geometries.

Experiment with element max size and parameterize it based on wavelength, for example.

Step 6 - Simulate

In the Simulations section, create a new simulation:

• Set Analysis type to Transient.

• Select timestepping options:

  Timestep algorithm	Start time [s]	End time [s]	Timestep size [s]
  Generalized alpha	0	ncycles/freq	1/freq/20

• Select a mesh.

• Add Outputs:

  Output type	Name	Output expression	Skin only
  Field	Displacement field u	u	Yes
  Custom value	Voltage	lump.V
  Custom value	Current	dt(lump.Q)

Skin only & Output every Nth step

To reduce data size, see field output parameters:

• Enable Skin only to store the field on outer surfaces only.
• Set Filter to Output every Nth step and Output interval to 5 (for example) so transient field results are written every fifth timestep instead of every step.

Your simulation is now ready to run.

Step 7 - Results

In the Simulations section, you can add plots to see value output results and visualizations to see field output results.

• Voltage:

  

• Current:

  

• Displacement field: