Piezocomposite transducer

Prerequisites: complete the PMUT Unit cell - Ultrasound 001 tutorial first.

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 element combines a soft PZT with an epoxy filler with a 40% volume fraction. It 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

1-3 piezocomposite transducer element with its PZT pillar array

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`
minvel	Minimum acoustic wave velocity in the model (epoxy shear) [m/s]	`1110`
epw	Number of elements per wavelength	`4`
element_size	Mesh element max size [m]	`minvel/freq/epw`

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]
minvel,1110,Minimum acoustic wave velocity in the model (epoxy shear) [m/s]
epw,4,Number of elements per wavelength
element_size,minvel/freq/epw,Mesh element max size [m]

Step 2 - Build the geometry

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
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
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)
Confirm model changes.

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`

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

Finished geometry:

Finished piezocomposite geometry with 25 pillars in epoxy filler

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:

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

PZT region covering the 25 pillars, with the epoxy filler excluded

Material 2 - Epoxy

Create a new material for the epoxy filler:

Material Target

Epoxy Polymer filler volume
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 $\rm F/m$
Add the target as a region.

Material	Target
Epoxy	Polymer filler volume

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`	$\rm F/m$

Epoxy filler region and its material properties

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

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)

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

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

Step 5 - Generate a mesh

Go to the Simulations section to create a new mesh with basic settings.

In mesh settings, convert mesh element size to Absolute.
Set mesh element max size to element_size (defined as minvel/freq/epw in Step 1).
Run meshing.
Check the preview:

Basic mesh preview with mesh metrics

Using a single mesh element max size for the model is OK, but can be inefficient if you have a large area of ‘fast’ material which will be overmeshed. A Mesh refinement customization can be added for each material independently to maintain accuracy and efficiency.

Optional: Autotransfinite meshing

You can also create a mesh using an Autotransfinite mesh customization. Autotransfinite is designed for blocky geometries laid out in a XYZ-aligned grid, so it is a great option for the PZT pillars in this case.

Mesh with autotransfinite on PZT and refinement on epoxy — Example mesh using autotransfinite and mesh refinement customizations. Autotransfinite is targetting the PZT region, and refinement is targetting epoxy, with both sizes set as 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/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)

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

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: