SHORT DESCRIPTION

Virtual prototyping tool for solving coupled mechanical-piezoelectric-acoustic problems. To learn more about PZFlex, visit www.pzflex.com.

OVERVIEW

PZFlex is the premier computer modeling package for the development and design of piezoelectric and ultrasonic devices, such as medical imaging transducers. Based on a time-domain finite-element program for solving coupled mechanical-piezoelectric-acoustic problems, it has proven to be a powerful tool for industry and academia.

PZFlex employs a mixed explicit-implicit time integration algorithm that results in decreased model size and large improvements in model computation speed for most problems. Although frequency domain results are often of interest and are still readily available via a discrete Fourier transform, the algorithm’s advantages become substantial in the mid- to high-frequency regime common to medical ultrasound and broadband applications in general.

Specialized for piezoelectric, ultrasonic, and bioengineering wave-propagation problems, PZFlex has been applied to:

• Piezoelectric transducer analysis: medical ultrasound, naval sonar and imaging systems, and wire bonding tools
• Piezo-composite transduction systems: 1-3 and 2-2 piezocomposites
• Diagnostic ultrasound: imaging and wave propagation in biological tissues and other media
• Therapeutic ultrasound: "B/A" nonlinear wave propagation in biological tissues
• Noise and vibration control: smart structures

Currently, PZFlex is used by major U.S. and Japanese medical transducer manufacturers, as well as by prominent academic and research institutions that conduct studies in diagnostic and therapeutic medical ultrasound or investigate novel transduction concepts and materials. Research sponsored by DARPA, ONR, NSF, and NIH has accelerated development of the software, which continues.

The accuracy of the program has been verified by analyzing standard benchmark problems for which analytic solutions are known. Code results have also been compared with those from other computer programs and with experimental data. The numerical errors resulting from spatial and temporal discretization have been quantified by solving the discrete equations analytically.

CAPABILITIES

PZFlex has a wide range of capabilities, including:

Transducer Modeling

2-D and 3-D electromechanical transducer models with electrical circuits attached to electrodes
Time-domain continuum and structural finite elements
Treatment of "infinite" media with efficient radiation (or absorbing) boundary conditions
Material absorption/damping/attenuation in solids and fluids

Vibration and Parameter Studies

Impedance or admittance plots by FFT post-processing of calculated transient response
Material parameter variation
Time-domain analysis of steady-state response and fields

Ultrasound Modeling

Ultrasound interaction with soft and hard tissue
Elastic and acoustic material absorption and attenuation
Nonlinear tissue model (B/A)

Wave Propagation Studies

Focused beams from baffled actuators or transducers
Integral equation-based wave field extrapolation for beam patterns, farfield waveforms, and plane wave pulse-echo
Transient or steady-state wave phenomena

Models can be 2-D plane-strain, 2-D axisymmetric (cylindrical symmetry), or 3-D. Materials can be isotropic elastic, anisotropic elastic, piezoelectric, or nonlinear. Viscoelastic, Rayleigh damping, and Newtonian viscosity models are also available. Volumetric (longitudinal) and deviatoric (shear) damping levels can be specified. PZFlex computational models typically range in size from 10,000-element 2-D models that require less than one minute run-time on a workstation to multimillion-element 3-D models that require several hours. Model size is limited only by the available computer memory.

Output includes time histories and/or snapshots of field variables such as voltage, charge, displacement, velocity, stress, pressure, strain, and electric fields. Steady-state quantities are available through post-processing. Data are saved during an analysis for later post-processing. The data structures of the various output files are kept simple so that data can be easily manipulated for use with the user’s on-site graphics capabilities.

ADDITIONAL INFORMATION

The PZFlex package includes REVIEW, a post-processor that can be used to compute impedance, analyze FFT signals, plot results, and display on-screen movies. Experimental results are readily imported for cross-plotting. Time-shifting, scaling, differentiation, integration, and so on are included to facilitate comparisons. The program also implements Kirchhoff extrapolation for continuing to the far field and other integral-based equations to obtain beam patterns.