MUTs 002 - Piezocomposite transducer

In this example case, 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

Step 2 - Build the geometry

Geometric entity tags

Geometric entities (volumes, surfaces, curves and points) are referenced using tags throughout this tutorial.

Carefully replicate the geometry construction steps below in order to have correct tags. Incorrect entity tags can lead to errors or unexpected behavior during simulations.

1. Go the Geometry section.

2. Start building the model geometry by adding Box elements:

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   pzt	Box	X: 0	X: width	X: 0
   		Y: 0	Y: width	Y: 0
   		Z: thick_comp/2	Z: thick_comp	Z: 0

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   cut x	Box	X: 0	X: width	X: 0
   		Y: -width/2 + kerf/2 + pillar	Y: kerf	Y: 0
   		Z: thick_comp/2	Z: thick_comp	Z: 0

   Name	Element type	Center point [m]	Size [m]	Rotation [deg]
   cut y	Box	X: -width/2 + kerf/2 + pillar	X: kerf	X: 0
   		Y: 0	Y: width	Y: 0
   		Z: thick_comp/2	Z: thick_comp	Z: 0

3. 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 volume (25)	X: pitch	Yes	npillars - 2
   			Y: 0
   			Z: 0

   Name	Element type	Target	Translation [m]	Copy	Repeat count
   copy y	Translation	cut x volume (13)	X: 0	Yes	npillars - 2
   			Y: pitch
   			Z: 0

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

   Name	Element type	Target
   combine polymer	Union	cut volumes (13, 25-31)

5. Confirm model changes.

Finished geometry:

Step 3 - Define the materials

Go to the Physics section to define model materials.

Material 1 - PZT

Assign PZT to the piezoelectric pillars.

There are 25 of them in total. To save some clicks:

1. Select all volumes
2. Remove the epoxy filler volume (2) from your selection.

Shared region

Add the PZT target as a shared region for later convenience.

Material 2 - Epoxy

Create a new material for the epoxy filler:

Material	Target
Epoxy	Polymer filler volume (2)

Define 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	$\rm F/m$

Step 4 - Define the physics

Go to the Physics section.

The Elastic waves and Electrostatics physics are required for this example. Add both of them before moving on to define interactions.

Physics 1 - Elastic waves

• Let elastic waves target default to the whole geometry.
• Add the Elastic waves - Electrostatics coupling Piezoelectricity.
  • Select the PZT target shared 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 element	0

  

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

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

  

Electrode plates & computed shared regions

Picking target surfaces for the electrical boundary conditions on models such as this involves a lot of clicking. Introducing electrode plates on the BC surfaces can make the setup simpler. The interface surface of the gold plate and piezocomposite element can then be used for defining BCs.

Example of electrode plates on another model.

Computed shared regions are another tool, which can be useful to save some clicks.

Step 5 - Generate the mesh

Go to the Simulations section and create a new mesh:

1. Set Mesh quality to Expert settings.
2. Set Used mesher to Basic.
3. Set Max size to kerf.
4. Apply settings and mesh.
5. Check the preview:

Structured mesh

For simplicity’s sake, a simple mesh with element max size is used here. While setting up a structured mesh is more labor intensive, it is computationally lighter and provides more accurate results with a similar element size.

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/frequency	1/frequency/20

• Select the 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)

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: