Randomised material parameter piezoelectric impedance dataset with structured electrodes (RaPIDstruc)

Description of the dataset

This dataset contains the results of 652517 finite-element simulations of the complex, frequency-dependent electrical impedance of a piezoelectric disc with structured electrodes and randomised material parameters. Each impedance consists of 1500 samples in the frequency domain up to 9.37 MHz. The electrode structure is the result of a topology optimisation process with the aim to enhance the sensitivity of the impedance with respect to all material parameters (DOI: 10.5194/jsss-12-163-2023). The piezoelectric disc has a radius of 5 mm and a thickness of 1 mm. The transverse isotropic material parameters are sampled from independent uniform distributions with ranges that are intended to represent the behaviour of hard as well as soft piezoceramic materials. The parameters of the Rayleigh damping model (alpha_M and alpha_K) are sampled from a logarithmic distribution to account for the larger parameter range.

Parameter
Min
Max
Unit
Description

c11
115
150
GPa
Elastic stiffness 

c12
70
110
GPa
Elastic stiffness 

c13
65
95
GPa
Elastic stiffness 

c33
95
125
GPa
Elastic stiffness 

c44
18
25
GPa
Elastic stiffness 

eps11
5
18
nF/m
Dielectric permittivity

eps33
6
12
nF/m
Dielectric permittivity

e15
7
19
C/m^2
Piezoelectric coupling

e31
1
7.5
C/m^2
Piezoelectric coupling

e33
13
23
C/m^2
Piezoelectric coupling

alpha_M
2
150
1/ms
Mass-proportional damping

alpha_K
0.1
0.65
ns
Stiffness-proportional damping

density
7600
7850
kg/m^3
Density

Files

The dataset contains the following files:

dataset.hdf5: The main dataset file in HDF5 format. Refer to the next section on how to load the dataset.

simulation.xml: The file describing the parameters of the finite element simulation. This file can be used with openCFS along with the mesh and material file to simulate the behaviour of the piezoelectric ceramic in the frequency domain. This simulation file was used with randomised material parameters to generate the dataset.

material.xml: The material file used for the simulation with exemplary material parameters values.

piezo.geo: The gmsh geometry file with the axisymmetric representation of the piezoelectric disc and the electrode structure.

piezo.msh: The mesh file generated with gmsh using the piezo.geo file.

Loading the dataset

The dataset is stored as a HDF5 file, which can be opened with all libraries that support that format, e.g. in Python using the h5py library:

import h5py

# Open the dataset in read mode.
file = h5py.File("dataset.hdf5", "r")

# Impedances as a 652517 x 1500 array of complex numbers.
impedances = file["impedances"]
# Material parameter values as a 652517 x 13 array of real numbers.
parameters = file["parameters"]
# Frequency vector of the impedance with length 1500.
frequencies = file["meta"]["frequencies"]
# 13 strings with the identifiers of the material parameters.
parameter_labels = file["meta"]["parameter_labels"]

Simulating impedances

To generate a result for the electrical impedance using the supplied simulation files, download and install openCFS and call the executable with the simulation.xml, but omit the file extension, e.g.:

cfsbin.exe simulation

The path to the executable of openCFS will depend on your operating system and installation. Running the simulation will result in the creation of several files and folders. Among those files will be the result for the electric charge on one of the electrodes of the sample, which will be placed in the 'history' subfolder. We can determine the current by taking the time derivative of the charge and already know the voltage because we excited the piezoceramic with an electric potential of 1 V in the simulation. Because the simulation is conducted in the frequency regime, all we have to do is to divide voltage by current to get the frequency dependent electrical impedance. The loading of the result and calculation of the impedance is implemented in the following Python script as an example:

import numpy as np

# Load result file for electric charge
result_path = 'history/simulation-elecCharge-surfRegion-ground.hist'
data = np.loadtxt(result_path)

frequency = data[:, 0]
# Convert polar representation from file to complex numbers.
charge = data[:, 1] * np.exp(1j * 2 * np. pi / 360 * data[:, 2])

# Excitation potential is 1 V in simulation.
potential = 1
# Determine impedance by applying Z = V / I = V / (j omega Q).
impedance = potential / (1j * 2 * np.pi * frequency * charge)