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Sensors and Actuators A 186 (2012) 223– 229

Contents lists available at SciVerse ScienceDirect

Sensors and Actuators A: Physical

jo u rn al hom epage: www.elsev ier .com/ locate /sna

generalized Preisach approach for piezoceramic materials incorporatingniaxial compressive stress

elix Wolf ∗, Alexander Sutor, Stefan J. Rupitsch, Reinhard Lerchhair of Sensor Technology, University of Erlangen-Nuremberg, Paul-Gordan-Str. 3/5, 91052 Erlangen, Germany

r t i c l e i n f o

rticle history:vailable online 23 December 2011

eywords:eneralized Preisach modelnalytic weight function

a b s t r a c t

For various piezoceramic actuator applications, the active materials are exposed to mechanical biasstresses. Such mechanical loading strongly modifies the hysteretic transfer characteristic of the actu-ators. An appropriate approach to model the hysteretic characteristic is based on the Preisach operator.However, the classical Preisach model is incapable of reflecting the influence of mechanical loading. Thescope of the present study is, thus, the development of a generalized Preisach model incorporating theimpact of compressive stress. To accomplish this goal, the effects of stress and mechanical creep on the

tress-dependent distribution functionniaxial prestressompressive stressZTiezoceramicserroelectric hysteresis

polarization hysteresis are characterized by means of measurements. For our model, we take advantageof an analytic Preisach distribution function, introduced in our recent work. This function is extendedto a formulation incorporating uniaxial compressive bias stress. As the results clearly demonstrate, theutilized distribution function is very promising to be further extended with respect to mechanical creepbehavior.

echanical creep

. Introduction

In recent years, a growing demand for piezoceramic materialsas been observed in industry. The growth is originated in theirnique properties, such as fast response times, large operatingorces and strokes. Among these materials, lead zirconate titanatePZT) is one of the most representative commercial piezoceram-cs. Typical applications are ultrasound transducers [1], micro- andanopositioning [2,3], energy harvesting [4,5] as well as smart com-osite structures [6–8] employed for a variety of tasks such asibration suppression [9] and health monitoring. The nonlinear,ysteretic transfer characteristic of the piezoceramic components

s a major limitation of such applications. For small-signal relatedssues, such as sensor devices and some actuator tasks, it is oftenufficient to describe this material behavior by linear constitu-ive equations, using a set of ten independent material parameters10]. The majority of modern actuator tasks is, however, operatedt higher excitation amplitudes. A consideration of the hystereticffects is thus indispensable. As a result of electro-mechanicaloupling, the ferroelectric (polarization) and ferroelastic (strain)ysteresis of piezoceramic materials is in addition strongly

nfluenced by mechanical stress applied to the materials. Suchtresses are observed for instance due to unavoidable shrinking inol–gel fabrication processes [11] or as result of electrical poling

∗ Corresponding author.E-mail address: felix.wolf@lse.eei.uni-erlangen.de (F. Wolf).

924-4247/$ – see front matter © 2011 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2011.12.031

© 2011 Elsevier B.V. All rights reserved.

procedures in the margin regions of stack actuators [12]. Apartfrom these undesired side-effects caused by fabrication processes,stress may also be applied on purpose: For instance to prevent stackactuators from tensile forces [12–14], or even to improve the trans-ducer properties. For stack actuators, an enhancement of energydensity and strain outputs up to 60% was observed by applyingmechanical stress [14]. In modern automation tasks, such actuatorsas described above are often employed in open- and closed-loopcontrols. It is therefore of utmost importance, to be able to pre-dict the actuator output for a given input signal. Consequently,there is a need for efficient hysteresis models, describing thetransfer characteristic of piezoceramic actuators under combinedelectro-mechanical loading conditions. A well-known and widelyused class of phenomenological approaches are the Preisach-typehysteresis models. The classical Preisach model [15] is howeverrestricted to solely one input and one output. Generalized Preisachmodels for ferroelectric materials, incorporating the influences ofmechanical stress are very limited [16]. Furthermore, experimen-tal studies on piezoceramic materials considering both, combinedelectro-mechanical loading and creep behavior are still quite rare.

Two issues are therefore discussed in the present study: First,the characterization of the material response of a soft piezo-ceramics under combined electro-mechanical loading, includingmechanical creep effects. Second, the development of a general-

ized Preisach hysteresis model, incorporating uniaxial compressivebias stress. In addition the influences of mechanical creep arehighlighted and a first approach toward modeling these effects ispresented.

2 Actuators A 186 (2012) 223– 229

iamcppc

2

rsbeotsbWvsmrosessttDcbda

2

apvTtFpdppcimpoeetwsthic

Coercive field strength Ec (Fig. 3(a)) and remanent polarizationPrem (Fig. 3(b)) represent the values for positive zero polarizationand positive zero field, respectively. The energy required for a full

24 F. Wolf et al. / Sensors and

The paper is organized as follows: After a short review on exper-mental studies, Section 2 explains our experimental proceduresnd discusses results. Section 3 introduces the utilized hysteresisodel and gives a short overview on generalizations of the classi-

al Preisach model considering mechanical stress. Afterwards, weresent our progress toward a generalized Preisach model incor-orating compressive bias stress and creep behavior. Section 4oncludes the paper.

. Experimental

The influence of mechanical stress on the piezoceramic mate-ial behavior has been of interest for numerous experimentaltudies. Especially its impact on the small-signal parameters haseen intensively studied for a variety of materials [17–22]. Sev-ral publications can also be found, dealing with the influencef compressive stress on ferroelectric hysteresis, i.e. for excita-ion with large electrical field strengths in addition to the appliedtress [23–28]. For both cases, strong deviations can be observedetween increasing and decreasing mechanical stress amplitudes.hereas these hysteretic effects are frequently described for the

ariation of small-signal material parameters [19–21], it is rathereldom reported for the large-signal behavior [27]. Piezoceramicaterials additionally show a significant time-dependence in their

esponse to compressive stress. In literature, this is often neglectedr simplified by waiting a certain amount of time after changing thetress amplitude [17,19,26]. However, there are also some studies,xplicitly investigating these creep effects, induced by compres-ive mechanical depolarization [29–33]. It is observed, that certainmall signal properties [30,31] as well as strain and the depolariza-ion charge [32,33] show a logarithmic dependence of time. Thisype of creep behavior is referred to as primary or transient creep.ue to the large time constants, it is important to understand andonsider these effects for applications with dynamic mechanicalehavior. Thus, further measurements are indispensable for theevelopment of a generalized, stress-dependent Preisach modelnd its parameter identification.

.1. Experimental setup and procedures

For the measurement of the electrical polarization, we use modified Sawyer–Tower circuit [34], already described in ourrevious publications [35,36]. Simply speaking, it is a capacitiveoltage divider between the sample and a measuring capacitance.o guarantee a defined initial loading condition, this capacitance isemporarily short-circuited before each polarization measurement.or the present study, we investigate Pz27, a soft (donor-doped)iezoceramics, manufactured by Ferroperm Piezoceramics A/S. Theiscoidal transducers (diameter: 25 mm, thickness: 2 mm) havelane-parallel front-faces covered by silver electrodes. Every sam-le is poled to full remanence by the manufacturer. In our setup, theompressive mechanical stress T3 is induced by applying a mechan-cal force F3 to the samples, using a Zwick/Roell material testing

achine. To prevent from dielectric breakdown, the setup com-rises a polycarbonate oil reservoir (Fig. 1) filled with transformeril (Shell Diala D). The samples are carefully placed between thelectrodes, which also serve as clamping jaws. A ball joint providesxact uniaxial mechanical loading in parallel to the applied elec-rical excitation field E3. The whole setup is computer-controlledith digital signal generation and recording of the relevant mea-

uring data. All measurements have been performed at room

emperature. Note that for all figures displaying time-dependentysteresis properties, these quantities are assigned to the point

n time when the respective cycle of the electrical excitation isompleted.

Fig. 1. Schematic view of the high-voltage, compressive load test fixture.

2.2. Measurements: results and discussion

In order to illustrate the influence of compressive mechani-cal stress on the polarization hysteresis, the mechanical load wasincreased from T3 = 0 in steps of 5 MPa. For each stress level,the stress was held constant by means of closed-loop control. Asinusoidal electrical excitation signal of 2 kV/mm amplitude at afrequency of 0.1 Hz was then applied for 5 min (30 cycles) to thespecimen. After reaching the maximum stress amplitude of 80 MPa,the bias stress was equally decreased to T3 = 0 with measurementsat each step. Fig. 2 depicts hysteresis loops (30th cycle, after 5 min)at equal stress levels for both, increasing (T+

3 ) and decreasing (T−3 )

stress. A hysteretic behavior can be observed between polarizationand stress amplitude. This becomes more obvious, when lookingat characteristic hysteresis properties over stress as displayed inFig. 3(a)–(d) for T+

3 and T−3 . All of these properties have been deter-

mined for the second cycle (20 s) and for the last cycle after 5 min.

Fig. 2. Influence of uniaxial compressive stress on polarization hysteresis curve forincreasing (T+

3 , —) and decreasing (T−3 , - - -) bias stress levels (30th cycle).

F. Wolf et al. / Sensors and Actuators A 186 (2012) 223– 229 225

Fig. 3. Change of hysteresis properties with increasing and decreasing compressive bias stress levels T±3 after 20 and 300 s (2nd and 30th cycle). Coercive field strength Ec

( differential permittivity εTr,d

(d).

pTdppttr

spsfcP

isPcert

a), remanent polarization Prem (b), polarization energy density wpol (c) and relative

olarization reversal is equal to the area inside the hysteresis loop.his stress-dependent parameter is termed as polarization energyensity wpol (Fig. 3(c)). Fig. 3(d) displays the relative differentialermittivity εT

r,d. This value represents the large-signal dielectricroperties at constant stress and is equal to the slope of the hys-eresis loop at remanent polarization. Fig. 3(a)–(d) also illustratehe large influence of the point in time when the hysteresis loop isecorded.

In order to demonstrate this time-dependent behavior, Fig. 4hows the polarization energy density wpol(t) for different com-ressive bias stress levels. As expected, the hysteresis propertiesuch as wpol(t) show the same transient creep behavior, as reportedor other quantities in literature [29–33]. Note that this type ofreep is equally observed for further hysteresis properties such asrem and Ec.

To understand these stress-dependent variations of the polar-zation hysteresis, a consideration of the material on its microscopiccale is essential. Below Curie temperature, the crystal unit cells ofZT are of tetragonal or rhombohedral shape and exhibit electri-

al dipoles orientated along the longest crystal axes. Regions withqual dipole orientation are referred to as domains. They can beeorientated by applying external loads. For pure electrical excita-ion, the domains switch in such a way, that the dipoles and thus the

Fig. 4. Time dependence of polarization energy density wpol for decreasing stresslevels T−

3 = 75 MPa . . . 40 MPa in steps of 5 MPa. Measurement and fit according toEq. (5) (see Section 3.2).

2 Actuat

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cldofscdnmpdw

3

am

f

Tnsp

�

Fciaslia

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TttMlm

cBpmt[

26 F. Wolf et al. / Sensors and

ongest crystal axes are orientated in parallel to the electrical field.n contrast, pure compressive mechanical loading provokes domainwitching yielding dipole orientations perpendicular to the appliedtress. Thus, the mechanical bias stress T3 applied to the specimenefore electrical excitation E3 leads from a macroscopic point ofiew to a partial depolarization of the material. This is accompaniedy a nonlinear decrease of the characteristic properties Ec, Prem andpol. Contrary to that, an increase of εT

r,d can be observed up to aritical prestress level of about 30 MPa. This enhancement of thearge-signal dielectric properties can be directly explained by theomains, switched perpendicular to the electrical field by reasonf the applied stress. On account of this fact, the energy requiredor a polarization reversal induced by E3 is minimized. If the biastress T3 is further increased above the critical level, the electri-al loading applied to the specimen is too low to reorientate theseepolarized domains. A more detailed description of these phe-omena can be found in literature [25,26]. An explanation for theechanical creep behavior is given in [33], attributing the observed

henomena to ion diffusion and domain pinning effects within theoped piezoceramic materials. Other authors directly relate creepith the time-dependence of the domain wall movements [30].

. Modeling

The classical Preisach hysteresis model [15] is a well-knownnd widely used hysteresis model in the field of ferroelectric andagnetic materials

(t) = H[u](t) =∫ ∫

˛≥ˇ

�(˛, ˇ)�˛ˇ[u](t)d ̨ dˇ.

he Preisach operator H, applied to any time-dependent input sig-al u(t) yields the output f(t) by superimposing a set of fundamentalwitching operators, defined by the thresholds ̨ and ̌ (t− is thereceding point in time)

˛ˇ[u](t) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

+1 : u(t) ≥ ˛

�˛ˇ[u](t−) : ̌ < u(t) < ˛

−1 : u(t) ≤ ˇ. (1)

or the simulation of ferroelectric hysteresis, we use the electri-al field strength E3,n(k) and the electrical polarization P3,n(k) asnput and output for the model. Both quantities are normalizednd discretized with respect to time. The weighting �(˛, ˇ) of thewitching operators primarily defines the shape of the hysteresisoops and is therefore crucial to precise and well-defined model-ng. As previously published [35–38], we take advantage of a newnalytic weight function (also referred to as distribution function)

DAT (˛, ˇ) = B

1 + {[( ̨ + ˇ)�1]2 + [( ̨ − ̌ − h)�2]2}�. (2)

he analytical formulation offers more flexibility for the identifica-ion procedure [35] as well as benefits with respect to computationime. The model parameters are determined by means of an Inverse

ethod [10,39]. We use a standard Newton algorithm with aeast-squares objective function minimizing the error between

easurements and simulations.The classical Preisach model does not establish any physi-

al relationship between model parameters and model output.ecause of this high level of abstraction, it is classified as

henomenological hysteresis model. In contrast to that, micro-echanic and thermodynamic motivated models usually describe

he observed phenomena on the level of ferroelectric domains40,41]. This physics-based description is useful for a deeper

ors A 186 (2012) 223– 229

material understanding but inherently involved with a higher com-putational effort. The Preisach models are instead faster, but include– speaking for the classical Preisach approach – the major limitationof solely one input and one output. It is evident that dependen-cies of the hysteresis on quantities like temperature or mechanicalstress cannot be described with such kind of model. To overcomethis shortage, a lot of research has been carried out toward general-ized Preisach models with more than one input. The enhancementof our model with regard to creep and the impact of the electricalexcitation frequency has already been published elsewhere [35,38].

3.1. Generalized Preisach models incorporating mechanical stress

The majority of publications dealing with generalized Preisachhysteresis models for ferroelectric materials focus on influences ofcreep and rate dependence. Here, we address instead the challengeof incorporating the effects of uniaxial compressive mechanicalstress into the classical Preisach model. This issue is restricted,to the best of the authors knowledge, to very few publications.Hughes and Wen [42] pointed out the need for a two-input modelbut did not further consider this matter. Freeman and Joshi [16]proposed instead a new hysteron for the simulation of the effectsof mechanical prestress. However, the model has not been verifiedby measurements and the influence of creep on the model out-put (Section 2) is not considered within the formulation. Far morestress-dependent Preisach hysteresis models have been developedfor magnetostrictive materials. Since they may be suitable for ferro-electric materials to some extent, a short overview is given withinthe next paragraph.

Adly et al. [43] proposed a two input model

f2(t) = H[u, v](t) =∫ ∫

˛≥ˇ

�(˛, ˇ, v(t))�˛ˇ[u](t)d ̨ dˇ

+∫ ∫

˛≥ˇ

�(˛, ˇ, u(t))�˛ˇ[v](t)d ̨ d ̌ (3)

with two weight functions �(˛, ˇ, v(t)) and �(˛, ˇ, u(t)) dependingon the other input, respectively. In doing so, cross-coupling canbe modeled. For this theoretical approach, no further informationis provided on the identification process of the weight functions.Bergqvist and Engdahl suggested an additional approach [44] byintroducing an effective field ueff(u(t), v(t), ˛, ˇ) as input for theclassical Preisach operator

f3(t) = H[u](t) =∫ ∫

˛≥ˇ

�(˛, ˇ)�˛ˇ[ueff](t)d ̨ dˇ.

However, each switching operator is allowed to have its owneffective-field function. Consequently, simplicity of the model getslost. Both approaches, a stress-dependent weight function [45–47]as well as an effective input function for the classical Preisach model[48] have been utilized since then in modified versions for magne-tostrictive materials. Further approaches are the introduction of ahysteron with pseudostates [49] as well as the stress-dependentparameterization of the Everett function [50]. Sipeky and Ivanyi[45] are the sole authors mentioned above to utilize analyticweight functions within the generalized model. However, for bothapproaches – a Gaussian and a Gaussian–Lorentzian weight func-tion – a comparatively large set of parameters is required for themodel extension. Thus, the simplicity of the model and possiblyalso the uniqueness of the model parameters inherently gets lost.

Note that all of the generalized Preisach models describedabove do not feature an additional input for time. For this reasonand due to further differences between magnetic and ferroelec-tric hysteresis, the models are not directly transferable to describe

F. Wolf et al. / Sensors and Actuators A 186 (2012) 223– 229 227

B h η

Fs

te

3

ppweo�

(

Tbtt�stwtacaottw

ig. 5. Variation of model parameters B, h and � by ±20%. For every graph, the sametart values are utilized and only one parameter was altered.

he dynamic behavior of piezoceramic materials under combinedlectro-mechanical loading.

.2. Generalized model: results and discussion

To our opinion, the approach of Adly et al. [43] is the mostromising of the introduced generalized models with respect toiezoceramic materials. We intent to implement a modified versionith a single, stress-dependent weight function which is, however,

xtended by an additional input for time. The following propertiesf such an analytic stress- and time-dependent weight functionTDAT (˛, ˇ, T3, t) are of utmost importance:

(i) Each of the model parameters describing the polarization hys-teresis for a single stress level (i.e., the parameters of thestress-independent weight function �DAT) has a distinct influ-ence on the shape of the hysteresis and shows robust behaviorat parameter identification.

(ii) A preferably small set of these parameters is sufficient to reflectthe influences of the additional input T3.

iii) These parameters follow a distinct and smooth characteristicwith a variation of the additional input.

he robustness of the utilized weight function �DAT has alreadyeen successfully demonstrated for least-squares parameter iden-ification [37]. In our recent work [36] we illustrated, that onlyhree parameters, namely B, h and � of the analytic weight function

DAT are relevant to describing the influence of uniaxial compres-ive bias stress. As Fig. 5 reveals, each of these parameters modifieshe shape of the hysteresis loop in a different way. Simulationsith ±20% of the respective parameter starting from the same ini-

ial values are performed for these graphs. Whereas B exclusivelyffects the maximum polarization Pmax, h mainly alters the coer-ive field strength Ec. The parameter � changes the slope and themplitude and is, thus, the only parameter influencing εT

r,d. As result

f these considerations, the parameters are excellently applicableo describe the influences of compressive bias stress on the hys-eresis as observed in Fig. 2. In addition, condition (ii) is satisfiedith only three parameters required. To find a stress-dependent

a b

Fig. 7. Parameter evolution with compressive bias stress T±3 . The esti

Fig. 6. Comparison of measurements and simulations for decreasing mechanicalstress levels T−

3 (30th cycle).

formulation, a parameter study was performed using the measure-ments described in Section 2.2. For each single bias stress T±

3 andeach cycle, the parameters B, h and � were identified separately,keeping the other parameters fixed. Fig. 6 shows a comparison ofmeasurements and simulations at decreasing stress levels T−

3 forthe 30th cycle. Similar results are obtained for increasing stresslevels (see also [36]). The parameter variation of B, h and � for dif-ferent mechanical stress levels T±

3 is displayed in Fig. 7 for the 2ndand the 30th cycle. As can be seen, condition (iii) is satisfied as well.The smooth characteristics allow for an analytic description of theparameter variations with stress. However, by reason of the time-dependence of the mechanical response, also the stress-parametercurves B(T3), h(T3) and �(T3) show to be time-dependent (Fig. 7). It isfound, that B(T3), h(T3) and �(T3) follow the same transient creep asobserved for the hysteresis properties, described in Section 2. Thisbehavior reflects the outstanding uniqueness and robustness of theparameters B, h and �. A characteristic attribute of such transientcreep is that the creep-influenced quantity reaches a final valuefor infinite time (t→ ∞). Hence, after a sufficient amount of time,the mechanical hysteresis as observed in Fig. 3(a)–(d) yields a singlenonlinear, non-hysteretic curve for both, increasing and decreasingstress levels T±

3 . This can also be explained on a microscopic levelwith diffusion processes and stress-induced switching being com-

pleted for infinite time. Consequently, also the parameters N ∈ {B,h, �} can be described by such non-hysteretic characteristics. Theexpected final values of B(T3), h(T3) and �(T3) are displayed in Fig. 7

c

mated value for infinite time (t→ ∞) is displayed additionally.

228 F. Wolf et al. / Sensors and Actuat

Table 1Parameters for stress-dependent formulation of B(T3), h(T3) and �(T3) for t→ ∞ asdetermined with Eq. (4).

p1 p2 p3

B 53.4509 218.3137 −0.0499

ae

N

TT�scwsioino

N

TcNomdataoaa

Fs4

h 0.4060 0.1992 −0.0197� 0.6933 0.5297 −0.0397

s dashed lines. These curves can be described very well by anxponential function

(T3, t → ∞) = p1 + p2 · e(p3 · (T3/1 MPa)), with N ∈ {B, h, �} (4)

he values for each of the parameters are displayed inable 1. Hence, an analytic formulation of a weight functionTDAT (˛, ˇ, T3, t → ∞) incorporating the effects of mechanical

tress is involved with only six additional parameters. Mechanicalreep is yet not considered within this formulation. For applicationsith quasi-static mechanical bias stress, this description is already

ufficient, when looking at the rather small deviations betweenncreasing and decreasing stress levels after 5 min and 30 cyclesf electrical excitation (Fig. 2). If the dynamic mechanical behav-or has to be considered in addition, mechanical creep cannot beeglected. In such cases, it can be simulated for instance by meansf a set of appropriate functions

(T3, t) = N(T3, t1) + m ·(

t

1 s

)n

with N ∈ {B, h, �}. (5)

his formulation is similarly described in literature for transientreep of other quantities [32,33]. However, for every parameter

∈ {B, h, �} at every mechanical stress level T±3 , a different set

f parameters m, n is required. This is involved with an enor-ous increase of complexity, asking for analytic expressions to

escribe the dependency of m and n on the mechanical stressmplitude. Fig. 8 displays representatively the evolution of theime-dependent parameter B(t) with increasing stress levels T+

3nd the fitting results according to Eq. (5). The systematic change

f the parameter creep, also observed for h and � with increasingnd decreasing bias stress levels is very promising toward a futurenalytic formulation of this phenomenon.

ig. 8. Comparison of model parameters B, determined by identification andimulations according to Eq. (5) for increasing mechanical stress levels T+

3 =0 MPa . . . 80 MPa in steps of 5 MPa.

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ors A 186 (2012) 223– 229

4. Conclusion

In this contribution, we concentrated on two main aspects: First,we demonstrated the impact of uniaxial compressive bias stressand mechanical creep on the polarization hysteresis by measure-ments. It is shown that for dynamic applications, the influenceof mechanical creep cannot be neglected due to the large time-constants. Second, a generalized Preisach model was presented,incorporating the effects of quasi-static compressive bias stress.The model takes advantage of a stress-dependent analytic dis-tribution function with only six additional parameters. As thecomparison of measurements and simulations reveals, a reliabledescription of the material behavior with varying bias stresses isprovided with the model. This is especially of interest for open-as well as closed-loop control applications. A first approach toalso modeling mechanical creep behavior is presented in addition.Future research will be focused on further investigating the influ-ence of mechanical creep and on incorporating these effects intoour model.

Acknowledgment

The underlying research is gratefully supported by the GermanResearch Foundation (DFG) as part of SFB/TR39.

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Biographies

Felix Wolf was born in Geislingen an der Steige, Germany, in 1981. He receivedhis M.S. (Dipl.-Ing.) degree in Electrical Engineering from the Friedrich-Alexander-University of Erlangen-Nuremberg, Germany in 2007. Currently, he is a PhD Studentand assistant lecturer at the Chair of Sensor Technology of the University of Erlangen-Nuremberg. His research is focused on the characterization of ferroelectric materialsby means of simulation and measurements.

Alexander Sutor was born in 1970 in Aschaffenburg, Germany. He received his M.S.degree (Dipl.-Ing.) in Electrical Engineering in 1997 and his Ph.D. degree (Dr.-Ing.)in 2004 from the Friedrich-Alexander-University of Erlangen-Nuremberg. He hasbeen working as assistant lecturer at the Institute of Technical Electronics until 1999and now as a researcher and lecturer at the Chair of Sensor Technology, Universityof Erlangen-Nuremberg. His major research interests are in the fields of materialproperty determination of magnetic, magnetostrictive and piezoelectric materialsfor sensor and actuator applications. He deals with measurement setups for bulk andthin film materials, as well as model and simulation based measurement methods.

Stefan J. Rupitsch was born in Kitzbuehel, Austria, in 1978. He received hisDiploma and Ph.D. degrees in Mechatronics from the Johannes Kepler University,Linz, Austria, in 2004 and 2008, respectively. In 2004, Dr. Rupitsch was a JuniorResearcher at the Linz Center of Mechatronics. From 2005 to 2008, he was with theInstitute for Measurement Technology, Johannes Kepler University, Linz. In 2009,he received the Award of the Austrian Society of Measurement and AutomationTechnology for his Ph.D. thesis. Currently, he is a Postdoctoral Researcher at theFriedrich-Alexander-University Erlangen-Nuremberg (Chair of Sensor Technology),Germany. His research interests include electromechanical transducers, simulation-based material characterization, digital signal and image processing as well asnoncontacting measurements.

Reinhard Lerch was born in Lauterbach, Germany in 1953. He received the Mas-ter’s degree in 1977 and the Ph.D. degree in 1980 in Electrical Engineering from theTechnical University of Darmstadt, Germany. From 1977 to 1981, he was engagedin the development of a new type of audio transducer based on piezoelectric poly-mer foils at the Institute of Electroacoustics at the University of Darmstadt. From1981 to 1991, he was employed at the Research Center of Siemens AG in Erlangen,Germany, where he was responsible for the implementation of new computer toolssupporting the design and development of piezoelectric transducers. Dr. Lerch isauthor of more than 100 papers in the field of electromechanical sensors and actu-ators, transducers, acoustics, and signal processing. In 1982, he received the Awardof the German Nachrichtentechnische Gesellschaft for his work on piezopolymermicrophones. In 1990, he was honored with the Outstanding Paper Award of theIEEE-UFFC Society and in 1991, he was the recipient of the German Philipp-Reis-Award. From 1991 to 1999, he had a full professorship for Mechatronics at theUniversity of Linz, Austria. Since 1999 he is head of the Chair of Sensor Technology atthe Friedrich-Alexander-University of Erlangen-Nuremberg, Germany. His current

research is directed toward establishing a computer-aided design environment forelectromechanical sensors and actuators, especially piezoelectric ultrasound trans-ducers and microacoustic components. Further areas of research are piezoelectricand magnetic sensors in thin film technology. In 2009, he was honored with theDistinguished Service Award of the IEEE-UFFC Society.