R. Simkovics

Identification of material tensors for piezoceramic materials

A new iterative scheme for the exact reconstruction of piezoelectric material parameters from electric impedance measurements is proposed. It is based on finite element simulations of the full piezoelectric equations, combined with a Newton-conjugate gradient inversion scheme. Experiments for a thickness resonator demonstrate that this method is able to avoid (undesirable) inaccuracies occurring in conventional simplified model parameter estimation techniques.

Nonlinear finite element analysis of piezoelectric transducers

In this paper a newly developed finite element method (FEM) is presented, which allows the numerical simulation of the nonlinear behavior of piezoelectric materials. Since both, material as well as geometric nonlinearities are taken into account, full large-signal analysis of the piezoelectric effect is provided. In the implemented constitutive model, the mechanical, piezoelectric, and dielectric tensor elements may depend in a multifunctional way on the current states of the mechanical stresses and the electric field. Therewith, measured material data can be directly used as input for the numerical simulations. In the case of geometric nonlinearities, both large displacements and strains can be modeled. As a practical application, the electric input impedance of an ultrasonic transducer being subjected to mechanical and electric prestressing is considered. Comparisons of simulated and measured resonance frequency shifts due to the nonlinear dependency of the material coefficients on the electric field as well as mechanical stress is presented.

Finite element analysis of ferroelectric hysteresis effects in piezoelectric transducers

The acoustic output power of piezoelectric actuators, such as high intensity focused ultrasound transducers used in medical therapy, is more and more increasing. Thus, the nonlinear material behavior of piezoelectric ceramics has to be considered during the design process and, therewith, the need for an appropriate modeling tool arises. In this paper an extension of a recently developed numerical calculation scheme, allowing the precise simulation of the nonlinear behavior of piezoceramic actuators, is presented. The inclusion of a macroscopic ferroelectric hysteresis model in the numerical calculation scheme offers the great advantage to consider changes in the state of electric polarization. Therewith, the nonlinear dependencies of the material parameter on the electric field strength and the mechanical stresses as well as the changes in polarization due to the loading history can be computed.

Identification of material nonlinearities in piezoelectric ceramics

Large signal excitation of piezoelectric ceramics, as occurring in many actuator applications, leads to a nonlinear dependence of the piezoelectric material parameters on the electric field and/or the mechanical strain. In order to precisely determine these nonlinear parameter curves, we propose a new inversion algorithm, that is based on numerical simulation of the nonlinear piezoelectric PDEs and that automatically fits the searched for parameters to voltage-current measurements. We will present the theory and numerical case studies of the inverse scheme as well as measurements for the electric field dependency of Pz27 material.

Determination of piezoelectric material parameters using a combined measurement and simulation technique

In this paper we describe the extension of our parameter identification algorithm for extracting the full parameter set of piezoelectric materials. The scheme is based on the FE solution of the according partial differential equations and on impedance measurements on appropriate test transducers. The results obtained by applying the scheme to a multilayer stack actuator as well as an ultrasound array antenna material will demonstrate the applicability of the developed parameter identification scheme.

Finite element analysis of hysteresis effects in piezoelectric transducers

The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.

Use of modern simulation for industrial applications of high power ultrasonics

The numerical simulation of high power ultrasonic devices is a highly challenging task, since a multi-field problem based on nonlinear partial differential equations has to be solved. We will concentrate on the numerical simulation of piezoelectric and electromagnetic pulsed acoustic power sources as well as on a piezoelectric driven cw-source. Our calculation scheme is based on the Finite Element Method. It is capable to handle both the transducer and acoustic nonlinearities. Practical applications will demonstrate the applicability of our simulation scheme.

Nonlinear finite element analysis of magnetostrictive transducers

We have developed a numerical simulation scheme for magnetostrictive transducers, which is based on the magnetic vector potential formulation. Therewith, magneto-dynamic problems including eddy currents can be treated and the restriction to magnetostatic problems is eliminated. Furthermore, the full coupling of magnetic and mechanical systems including magnetically induced mechanical strains and permeability changes due to mechanical stresses is taken into account. As an application, we will present numerical simulations for a magnetostrictive rod actuator and compare these results with measured data.

Nonlinear finite element analysis of piezoceramic multilayer actuators

Piezoelectric multilayer actuators combine the advantages of large deflections, fast response time and, accurate repeatability. By using cofired multilayer structures deflections up to several microns in the case of stacked actuators and several millimeters for transducers operating in bending mode can be achieved. The high driving levels, however, lead to nonlinearities mainly caused by the ferroelectric hysteresis of the piezoceramic material. For an improved design of these complex transducers finite element analysis of the complete system is utilized. We have established a calculation scheme, now allowing full 3D-modeling of a piezoceramic multilayer actuator taking the nonlinear material behavior into account. The hysteretic effects caused by ferroelectricity are modeled using a macroscopic Preisach model describing the actual state of polarization. Furthermore, dependencies of the material parameters on the electric field strength and the mechanical stresses are considered by the implemented constitutive relation. Therewith, the calculation scheme allows the precise numerical analysis of a complex multilayered stack actuator.

Numerical modeling of sensing and actuating electromechanical transducers

A numerical scheme for the modeling of coupled field problems arising in sensor and actuator technology is reported. This scheme has been implemented in software and allows the precise numerical computation of coupled field problems (linear and nonlinear) as typically arising in the design of electrostatic, magnetomechanical and piezoelectric transducers (sensors and/or actuators). This software is based on finite elements (FEM), boundary elements (BEM) and, FEM-BEM procedures. In addition, we implemented modules which allow the integrated simulation of (electronic) controllers within a FEM or BEM run or, by running the controller software on a separate processor, via process interconnection. Having the simulation of a controller within the loop is especially helpful for the modeling of the complete process loop, meaning that we can simultaneously analyze the sensor, the actuator and the controller behavior.