Download - Vienna University of ecThnology...David Schrade 1, R. Mu ller 1, and D. Gross 2 1 Institute of Applied Mechanics, Department of Mechanical and Pro cess Engineering, TU Kaiserslautern,

Vienna University of Technology

Organizers: Univ.Prof. Dipl.-Ing. Dr.techn. Manfred Kaltenbacher,Dipl.-Ing.(FH) Dipl.-Ing. Dr.techn. David Tumpold,Ruth Katharina Polterauer,Institute of Mechanics and Mechatronics / E325-A4Vienna University of TechnologyGetreidemarkt 9 (BA)A-1060 Vienna

10th International Workshop Direct and Inverse Problems on Piezoelectricity 1

Timetable

19:00 – 21:00ARRIVAL,COMEYTOGETHER

19:00 – 21:00BANQUET

08:45 – 09:00OPENINGYSESSION09:00 – 10:30SESSIONY1



10:30 – 11:00COFFEEYBREAK



11:00 – 12:30SESSIONY2

12:30 – 13:30LUNCH

11:00 – 12:30SESSIONY6

11:00 – 12:30SESSIONY8

13:30 – 15:00SESSIONY3


12:30 – 13:30LUNCH

12:45 – 13:30LUNCH

12:30 – 12:45CLOSINGYSESSION

15:30 – 18:15SESSIONY4

14:30 – 16:30GUIDEDYCITYYTOUR

Su 21.09.2014 Mo 22.09.2014 Tu 23.09.2014 We 24.09.2014

Sunday, 21.09.2014

afternoon Arrival

19:00-21:00 Come together

19:00-21:00 Continuing with the successful series of the recent workshops in piezoelec-tricity, we want to invite you to the Café Restaurant Resselpark for a cometogether and meet and greet. Traditional Vienna dumplings will be served ina lax and friendly atmosphere. Di�erent experts of various �elds of researchas well as from the industrial sector will be participating the workshop.

You will �nd us at: Wiedner Hauptstraÿe 1, 1040 Wien - next to the University,where the workshop will take place.


Monday, 22.09.2014

08:45-09:00 Opening

09:00-10:30 Session 1

09:00-09:45 F. Endres: Molecular static simulations of domain wall behaviour of ferroelec-tric barium titanate in the rhombohedral phase

09:45-10:30 D. Schrade: Phase �eld simulations of domain evolution in ferroelectric singleand polycrystals

10:30-11:00 Co�ee break

11:00-12:30 Session 2

11:00-11:45 M. Labusch: Product properties of magneto-electric composites in considera-tion of ferroelectric switching

11:45-12:30 B. Kaltenbacher: Modelling Ferroelectric and Ferroelastic Hysteresis: Ther-modynamical Consistency by Hysteresis Potentials

12:30-13:30 Lunch

13:30-15:00 Session 3

13:30-14:15 J. Rautenberger: A new measurement setup for an increased sensitivity of elec-trical impedance to all piezoelectic material parameters with one piezoelectric

disk

14:15-15:00 M. Schneider: Characterization of the Mechanical and Piezoelectrical Proper-ties of Aluminium Nitride Thin Films at Varying Film Thickness

15:00-15:30 Co�ee break

15:30-17:00 Session 4

15:30-16:15 P. Nicolay: Sti�ness constants determination (and optimisation) up to 800◦C,using simultaneous BAW and SAW measurements.

16:15-17:00 M. Weiss: Inverse Method for characterizing material parameters of active andpassive components

17:00-17:45 F. Bause: Modeling and inverse identi�cation of a high bandwidth ultrasonicmeasurement setup based on piezoelectric 1-3 composites

17:45-18:15 B. Ayech: Piezoelectric d15 shear sensing mechanism experimental evaluationsunder parallel and series connections


Tuesday, 23.09.2014

8:45-09:00 Opening

09:00-10:30 Session 5

09:00-09:45 N. Kraynyukova: On the modeling of nonlinear electro-mechanical response inferroelectrics

09:45-10:30 D. Natroshvili: Regularity properties of solutions to mixed interface crack prob-lems of thermo-electro-magneto-elasticity

10:30-11:00 Co�ee Break

11:00-12:30 Session 6

11:00-11:45 G. Chkadua: Mixed type Interaction Problem of Acoustic Waves and Piezo-electric Structures

11:45-12:30 M. Krommer: Nonlinear modeling of thin piezoelectric shells using an extendedmultiplicative decomposition of the deformation gradient

12:30-13:30 Lunch

14:00-16:00 Guided city tour

14:00-16:00 The most beautiful spots of the old parts of the city. Stories and legends whichenable an amusing insight.Vienna at its best: the multicultural tradition of the city. In a humorousway you will be informed about the roots and the mentality of the Viennese.Old Vienna is revived - a city populated by musicians, students, Jewsand monks, victorious against the sieges of the Turks and surviving themenaces of the plague. Although you might think to have covered quitea distance on your walk you will �nd yourself almost at the same spotwhere you started - the paths are tortuous. Just like on a string of pearlsyou will discover the most attractive picture postcard sights along yourway. Hear about the manifold denominations in our city which live andpractice peacefully in close vicinity to each other. The tour will makeyou acquainted not only with the historical development of one of themost glorious cities of the past, but also with the charm of this mixtureof a population which has preserved its "Gemütlichkeit" up to the present day.

This tour is available in English or German Language. Ms. Polterauer willcollect 14e in advance for all city tour participants. Please register as soonas possible to help us scheduling the groups. (You can join us at 14:00 at theUniversity)

19:00-21:00 Banquet .. im Brezl Gwölb ..

19:00-21:00 The banquet will take place in Vienna's famous �Brezl Gwölb�, where romanticatmosphere meets the historical part of Vienna. Classical music and candlelight emphasizes Vienna's plain cocking, chosen wine and variations of culti-vated beers. A map and description can be found in the end of all workshopparticipants.


Wednesday, 24.09.2014

8:45-09:00 Opening

09:00-10:30 Session 7

09:00-09:45 B. Ayech: Sensing and blocked force experimental characterization of d15 shearmacro �bre composite transducers

09:45-10:30 D. Chen: Investigation of Deformation in PZT Ceramics under Uniaxial Load-ings by Digital Image Correlation

10:30-11:00 Co�ee break

11:00-12:30 Session 8

11:00-11:45 P. Mayrhofer: Piezoelectric constant determination of ScxAl1-xN via a com-bination of laser doppler vibrometry and FEM simulation: circular test

strucutres

11:45-12:30 K. Shaposhnikov: Complex frequency shifted PML application to problems ofwave propagation in periodic piezoelectric structures

12:30-12:45 Closing

12:45-13:30 Lunch

Suggestions for lunch

Naschmarkt

(cultural melting pot - every �avor)Between Rechte Wienzeile and Linke Wienzeile

***

Wieden Bräu

(typical Vienna food)Waaggasse 5

***

Santos

(Mexican theme)Favouritenstraÿe 4-6

***

Otto e Mezzo - Acht ein Halb

(Italian theme)Schleifmühlgasse 20

***

University Mensa

(no special food theme)Wiedner Hauptstraÿe 8-10

***


Your Host: Vienna University of Technology

Continuing with the successful series of the recent workshops in piezoelectricity, we want to inviteyou to Vienna University of Technology, where our workshop will take place in the wonderfulroom �Festsaal�.

The Vienna University of Technology (TU Vienna) is located in the heart of Europe, in acosmopolitan city of great cultural diversity. For nearly 200 years, it has been a place of research,teaching and learning in the service of progress. The TU Vienna has eight faculties lead bydeans: Architecture and Planning, Chemistry, Civil Engineering, computer Sciences, ElectricalEngineering and Information Technology, Mathematics and Geoinformation, Mechanical andIndustrial Engineering, and Physics. The TU Vienna is among the most successful technicaluniversities in Europe and is Austria's largest scienti�c-technical research and educationalinstitution. Through our research we �develop scienti�c excellence�, through our teaching we�enhance comprehensive competence�.

More Information visit: www.tuwien.ac.at

10 th Workshop on Direct and Inverse Problems in Piezoelectricity 1

Molecular static simulations of domain wall

behaviour of ferroelectric barium titanat in the

rhombohedral phase

Florian Endres1 and Paul Steinmann1

1Chair of Applied Mechanics, Department of Mechanical Engineering, University ofErlangen - Nuremberg, Egerlandstrasse 5, 91058 Erlangen, Germany,

[email protected]

Abstract. Ferroelectric functional materials are used widely in all kinds of technicalapplications. Therefore ferroelectric materials like e.g. barium titanate are modelledand simulated on all length scales [1]. Thereby continuum mechanics are used to modelmaterial on the macro scale using phenomenological observations [2]. On the other sideatomistic simulations are used to simulate material behaviour more detailed but sufferfrom the significant computational costs of such simulations. Nevertheless some ferro-electric phenomena like e.g. domain walls are occurring at length scales of only severalangstrom and atomistic simulations are indispensable for a better physical understandingof the material behaviour.

Our proposed molecular static algorithm is capable of atomistic simulations with thebenefit of a reduction of the computational costs compared to molecular dynamics. Thusa variety of domain wall configurations can be simulated efficiently and draws inferencesabout ferroelectric phenomena at the atomistic level [3].

The focus of this talk is to present a molecular static algorithm for the simulation of ferro-electric barium titanate and the used core-shell model which is widely used in moleculardynamics simulations of ferroelectric materials [4]. Moreover we present several numericalexamples of different domain wall configurations and discuss the results including domainwall energies and stability.

References

[1] Ellad B. Tadmor and Ronald E. Miller. Continuum, Atomistic and Multiscale Tech-niques. Modeling Materials, Cambridge University Press, New York, 2011.

[2] M. Kamlah. Ferroelectric and ferroelastic piezoceramics - modeling of electrome-chanical hysteresis phenomena. Continuum Mechanics and Thermodynamics 13,219-268, 2001.

[3] F. Endres, P. Steinmann. A molecular statics algorithm for the simulation of ferro-electric materials, submitted, 2014.

[4] S. Tinte, M. Stachiotty, M. Sepliarsky, R. Migoni and C.O. Rodriguez. Atomisticmodelling of BaTiO3 based on first-principle calculations, Journal of Physics: Con-densed Matter 11, 9679, 1999.



Phase field simulations of domain evolution

in ferroelectric single and polycrystals

David Schrade1, R. Müller1, and D. Gross2

1Institute of Applied Mechanics, Department of Mechanical and Process Engineering,TU Kaiserslautern, Gottlieb-Daimler-Str. Postfach 3049, D-67653 Kaiserslautern,

Germany, [email protected] Festkörpermechanik, Fachbereich Bau- und Umweltingenieurwissenschaften,

TU Darmstadt, Franziska-Braun-Straße 7, D-64287 Darmstadt, Germany

Abstract. An electro-mechanically coupled phase field model for ferroelectric domainevolution is presented. The thermodynamical framework of the phase field model isbased on Gurtin’s notion of a microstress system [1] from which a Ginzburg-Landau typeevolution equation is derived. The thermodynamic potential is formulated by employingan invariant formulation for transverse isotropy [2], which allows for a consistent derivationof the material tensors. The model is implemented in a 2d finite element framework [3]by using linear ansatz functions and quadrilateral elements with four point Gauss andimplicit time integration. The numerical simulations focus on size effects with regard todomain formation in single and polycrystals; furthermore the domain evolution duringferroelectric switching in polycrystals is investigated.

References

[1] M. E. Gurtin. Generalized Ginzburg-Landau and Cahn-Hilliard equations based ona microforce balance, Physica D, 92: 178–192, 1996.

[2] D. Schrade, R. Müller, D. Gross, M.-A. Keip, H. Thai, and J. Schröder. An invariantformulation for phase field models in ferroelectrics, IJSS, 51: 2144–2156, 2014.

[3] D. Schrade, R. Mueller, B. X. Xu, and D. Gross. Domain evolution in ferroelec-tric materials: A continuum phase field model and finite element implementation,Comput. Meth. Appl. Mech. Eng., 196: 4365–4374, 2014.



Product properties of magneto-electric composites

in consideration of ferroelectric switching

Matthias Labusch1, Marc-André Keip2, Doru C. Lupascu3 & Jörg Schröder1

1Institute of Mechanics, Department of Civil Engineering, University of Duisburg-Essen,Universtitätsstr. 15, 45141 Essen, Germany, {matthias.labusch,j.schroeder}@uni-due.de

2Institute of Applied Mechanics (CE), University of Stuttgart, Pfaffenwaldring 7,70569 Stuttgart, Germany, [email protected]

1Institute for Materials Science, University of Duisburg-Essen, Universtitätsstr. 15,45141 Essen, Germany, [email protected]

Abstract. Materials that combine two or more ferroic states are termed multiferroics. Ifa material exhibits ferroelectric and ferromagnetic behavior it is termed a magneto-electric(ME) multiferroic. Such materials could enable new smart devices in the area of electric-field controlled magnetic data storage or highly sensitive magnetic-field sensors [1]. Infact, there exist some natural ME multiferroics that possess ME coupling properties, butthey are not appropriate for technical applications due to their extremely low ME effectat room temperature. Thus, in the present contribution, we focus on the simulation ofcomposite ME multiferroics, which generate the desired coupling as a product property :due to the interaction between electroactive and magnetoactive phases these solids show achange in magnetization as a result of an applied electric field and, vice versa, a change inpolarization through an applied magnetic field. Of course, their overall effective propertiesstrongly depend on their microstructure. In order to analyze the associated phenomena,we embed the underlying microscopic morphology into a two-scale finite-element (FE2)homogenization framework [2,3]. Furthermore, we will take into account experimentalmicrostructures measured in [4]. Since the overall ME properties significantly depend onthe polarization state of the ferroelectric phase, a material model is implemented thatconsiders the switching behavior of the spontaneous polarization [5].

References

[1] N. A. Spalding and M. Fiebig. The renaissance of magnetoelectric multiferroics,Materials Science, 309: 391–392, 2005.

[2] J. Schröder and M.-A. Keip. Two-scale homogenization of electro-mechanicallycoupled boundary value problems, Computational Mechanics, 50: 229–244, 2012.

[3] M. Labusch, M. Etier, D. C. Lupascu, J. Schröder, and M.-A. Keip. Product proper-ties of a two-phase magneto-electric composite: Synthesis and numerical modeling,Computational Mechanics, 54: 71–83, 2014.

[4] M. Etier, V.V. Shvartsman, Y. Gao, J. Landers, H. Wende, and D.C. Lupascu. Mag-netoelectric effect in (0-3) CoFe2O4-BaTiO3 (20/80) composite ceramics preparedby the organosol route, Ferroelectrics, 448: 77–85, 2013.

[5] S. C. Hwang, C. S. Lynch, and R. M. McMeeking. Ferroelectric/ferroelastic interac-tions and a polarization switching model, Acta Metall. Mater., 43: 2073–2084, 1995.



Modelling Ferroelectric and Ferroelastic Hysteresis:

Thermodynamical Consistency by Hysteresis

Potentials

Barbara Kaltenbacher1 and Pavel Krejci2

1Institute of Mathematics , Alpen Adria University Klagenfurt Universittsstr. 65-67A-9020 Klagenfurt, Austria, [email protected]

2Institute of Mathematics of the Academy of Sciences of the Czech Republic CZ-11567Praha 1, Czech Republic, [email protected]

Abstract. After a short overview on hysteresis modelling in piezoelectricity we willdwell on phenomenological hysteresis models based on Preisach operators. Here a keyopen question has been thermodynamic consistency, which can now be answered in asatisfactory manner by using hysteresis potentials. For this purpose we rely on a modelthat has been originally proposed by Daniele Davino, Pavel Krejci, and Ciro Visone(Smart Materials and Structures, 2013) in the context of magnetostriction. This modelincorporates not only ferroelectricity but also ferroelasticity and, due to its very generalform, is highly flexible and can very well be fit to experimental data.



A new measurement setup for an increased

sensitivity of electrical impedance to all piezoelectic

material parameters with one piezoelectric disk

Jens Rautenberg1, Carsten Unverzagt1, Benjamin Jurgelucks2, and KshitijKulshreshtha2

1Measurement Engineering Group, 2Research group Mathematics and its Applications,University of Paderborn, Warburger Str. 100, D-33098 Paderborn,

[email protected]

Abstract. The measuring of piezoelectric material properties begins in the 1940’s, whereMason starts studying piezoelectric resonators, that could be modeled with 1D-equations.The outcome of this research was the 176-1987 IEEE Standard on Piezoelectricity. Butthe suggested measurements with 5 different specimens do not necessarily lead to selfconsistent data-sets, as they are produced in different ways and frequency dependentbehavior must be considered as well [1]. This is why there has been a lot of researchin finding measurement setups with less specimens. But therewith another problem, thecoupling of modes, emerged and the simple 1D-equations were not satisfactory any longer.It was only after the arising of efficient FEM-tools and inverse solution schemes that thisproblem could be resolved [2]. But there is still need for two specimens if only impedancemeasurements should be used, or for an additional measurement with a laser scanningvibrometer if only one specimen is available [3].

The latest approach to characterize a whole data-set on the basis of one impedance mea-surement with a single piezoelectric disk has again shown that there is only little sen-sitivity to cE12 and e31 [4]. So we tried to increase these sensitivities by modifying theelectrode topology and using an additional electrical network during impedance measure-ment. Therewith the technical effort is again low, and we are still working with the samematerial. Apart from the measurement setup and the suggested electrode topology wewill show that the sensitivities could be increased in an overlapped frequency band. Thisis important as we try to find consistent material data for a defined operating frequency.

References

[1] J. Smits. Iterative Method for Accurate Determination of the Real and ImaginaryParts of the Materials Coefficients of Piezoelectric Ceramics, In IEEE Transactionson Sonics and Ultrasonics, 23(6): 393–401, 1976.

[2] T. Lahmer,et al. FEM-Based Determination of Real and Complex Elastic, Dielec-tric, and Piezoelectric Moduli in Piezoceramic Materials, In IEEE Transactions onUltrasonics, Ferroelectrics, and Frequency Control, 55(2): 465–475, 2008.

[3] S. J. Rupitsch, and R. Lerch. Inverse Method to estimate material parameters forpiezoceramic disc actuators, In Applied Physics A, 97(4): 735–740, 2009.

[4] N. Perez, et al. Identification of elastic, dielectric, and piezoelectric constants inpiezoceramic disks, In IEEE Transactions on Ultrasonics, Ferroelectrics and Fre-quency Control, 57(12): 2772–2783, 2010.



Characterization of the Mechanical and

Piezoelectrical Properties of Aluminum Nitride Thin

Films at Varying Film Thickness

Michael Schneider1, Achim Bittner1, and Ulrich Schmid1

1Institute for Sensor and Actuator Systems, Microsystems Technology, ViennaUniversity of Technology, Floragasse 7/2, 1040 Vienna, Austria,

[email protected]

Abstract. In micro-/nanomachined devices and systems, aluminum nitride (AlN) thinfilms are widely used due to their piezoelectric properties. In order to design AlN basedsensors and actuators, a good understanding of the mechanical and piezoelectrical prop-erties is of the utmost importance.

This work presents a novel approach of modifying the interface between the AlN thin filmand the silicon substrate by an in-situ sputter etching step prior to thin film deposition.The achieved optimization of the crystallographic orientation and, hence, improvement ofthe electrical and piezoelectrical properties is discussed. Additionally it is shown, that byutilizing this approach, good piezoelectric coefficients can be achieved over a film thicknessrange of 70 - 400 nm. The piezoelectric coefficients are measured using both a piezometerand a laser doppler vibrometer [1].

The mechanical properties such as Young’s modulus and film stress are characterized usinga load-deflection (LD) method. In order to extract the mechanical film parameters fromthe measured LD-relationship, a novel mathematical model is applied [2]. We show, thatthe Young’s modulus is largely independent of film thickness in the investigated range of100 - 1000 nm.

References

[1] J. Hernando, J. L. Sanchez-Rojas, S. Gonzalez-Castilla, E. Iborra, A. Ababneh andU. Schmid. Simulation and laser vibrometry characterization of piezoelectric AlNthin films, Applied Physics, 104: 053502–053509, 2008.

[2] J. Schalko, R. Beigelbeck, M. Stifter, M. Schneider, A. Bittner, and U. Schmid.Improved load-deflection method for the extraction of elastomechanical propertiesof circularly shaped thin-film diaphragms, Proc. SPIE 8066, Smart Sensors, Actu-ators, and MEMS V, (May 05, 2011)



Piezoelectric Constant Determination of ScxAl1−xNvia a combination of Laser Doppler Vibrometry and

FEM Simulation: Circular test structures

P. M. Mayrhofer1, A. Bittner1, and U. Schmid1

1 Institute of Sensor and Actuator Systems, Vienna University of Technology, Vienna,Austria, [email protected]

Abstract

Piezoelectric thin films based on AlN are implemented into a large variety of Si-basedMEMS devices for actuation or sensing purposes.[1] Upon doping AlN with Sc the piezo-electric constants d33 and d31 are increased, accompanied by a pronounced softening ofthe material, decreasing C33, while only a weak increase of �r is observed. Recently,Hernando et al. introduced the FEM based evaluation of interferometrically determineddeflection curves from quadratic electrodes on AlN thin films. This approach accountsfor the inherent substrate bending by a complete simulation of a structure consistingof substrate/bottom-electrode/thin film/ top-electrode.[2] Our work extends the above-mentioned approach and uses simple circular and bulls eye shaped platinum electrodesdeposited on ScxAl1−xN with x = 0.27. ScxAl1−xN thin films were deposited on n-dopedSi(100) via DC magnetron sputtering from an alloy target at a constant back pressure,but varying substrate self-bias as well as Ar/N2 ratios, respectively. Based on rotationalsymmetric test structure design, the computational effort of FEM deflection simulationswith Comsol is significantly reduced. Hence, the piezoelectric constants d31 and d33 canbe simultaneously swept within a large range with a resolution of 0.1 pm/V to find thebest match between simulation and measurement. For simple circular electrodes the kHzrange frequency voltage is applied on the top electrode while for bulls-eye electrodes theinner disc and the outer ring exhibit a 180 phase shifted excitation, whereas the substrateacting as ground for both electrode types. The newly introduced electrodes with phaseshifted excitation enable a more precise determination of d31 and d33 due to enhanceddifferences in the displacement curve shapes. The evaluation of piezoelectric constantsshows values for d33 up to 14 pm/V.

References

[1] G. Piazza, et al., Piezoelectric aluminum nitride thin films for microelectromechan-ical systems. Mrs Bull, 2012. 37(11): p. 1051-1061.

[2] J. Hernando, et al., Simulation and laser vibrometry characterization of piezoelectricAIN thin films. J Appl Phys, 2008. 104(5).



Inverse Method for characterizing material

parameters of active and passive components

Manuel Weiß1,∗, Jürgen Ilg1, Stefan J. Rupitsch1, and Reinhard Lerch1

1Department of Sensor Technology, Friedrich-Alexander-University ofErlangen-Nuremberg, Paul-Gordan-Str. 3/5, 91052 Erlangen, Germany,

*[email protected]

Abstract. In order to achieve reliable finite element (FE) based simulation results foractuator and sensor applications, precise material parameters of all involved componentsare required. Common characterization methods [1] lead to inaccurate simulation results,usually far from satisfactory. The presented Inverse Method ensures adequate parametervalues for active (piezoelectric ceramics) as well as passive (e.g., plastics) materials.

The Inverse Method is based on the minimization of the deviation between measurements(electrical impedance, mechanical displacement) and simulation results by an optimizationalgorithm (e.g., Levenberg-Marquard algorithm). The material parameters of piezoelectricceramics are identified via an iterative adjustment of the simulation parameters [2]. TheInverse Method is also qualified to determine the frequency dependence of mechanicalmaterial parameters, like elasticity modulus, of passive materials [3].

In the talk, we give an insight into the fundamentals and capabilities of the adaptedInverse Method and show selected results of characterized materials.

References

[1] IEEE Standard on Piezoelectricity, ANSI/IEEE Standard 176–1987.

[2] S. J. Rupitsch, A. Sutor, J. Ilg and R. Lerch. Identification Procedure for Realand Imaginary Material Parameters of Piezoceramic Materials, IEEE InternationalUltrasonics Symposium Proceedings, 1214–1217, 2010.

[3] J. Ilg, S. J. Rupitsch and R. Lerch. Determination of frequency and temperaturedependent mechanical material properties by means of an Inverse Method, In Ma-terials Characterisation, Transactions on Engineering Sciences, 77, 2013. Siena,Italien, 04.-06.06.2013.



Modeling and inverse identification of a high

bandwidth ultrasonic measurement setup based on

piezoelectric 1-3 composites

Fabian Bause1, Manuel Webersen1, Jens Rautenberg1, and Bernd Henning1

1Measurement Engineering Group, Faculty of Electrical Engineering, Computer Scienceand Mathematics, University of Paderborn, Warburger Str. 100, 33098 Paderborn,

Germany, [email protected]

Abstract. This contribution deals with the modeling and inverse identification of a highbandwidth ultrasonic measurement setup, consisting of an ultrasonic transmitting andreceiving transducer as well as a power amplifier and a receiving amplifier. The exactknowledge about the dynamic behavior of the complete measurement setup is a crucialaspect if one intends to characterize unknown media with respect to their acoustic prop-erties. This is especially true if an inverse approach is used for the characterization ofthe media under consideration. For the modeling part, we focus on a one-dimensionalmodel, i.e. the Mason model [1]. An essential limitation of this model is, that it is onlyadequate if the transducer under consideration oscillates in only one oscillation mode, e.g.pure thickness mode oscillation. This is true if one uses a quartz crystal, a piezo-ceramicwith large diameter-thickness-ratio or piezoelectric 1-3 composites. Due to performanceand impedance matching purposes, we focus on piezoelectric 1-3 composites. For inverseidentification of the transducer’s model parameters we utilize the AD (algorithmic dif-ferentiation) tool ADiMAT [2], which provides exact gradient information, i.e. Jacobianmatrix. This information can be used for detailed sensitivity studies of certain modelparameters to a measurable information, e.g. electrical impedance or dynamic behav-ior. The inverse identification of the measurement setup is carried out in multiple steps.First we identify the temperature dependent properties of the piezoelectric composite diskbased on its electrical impedance. After adhering a front plate and a backing material thetransducer is characterized again, once more based on its electrical impedance [3]. Theidentification of the amplifiers is based on standard routines for identification of dynamicsystems. Finally, a test setup is designed, i.e. a small water channel, which is used toevaluate the conformance of the simulated received signals and the experimental signals.

References

[1] R. Lerch, G. Sessler, and D. Wolf. Technische Akustik. Grundlagen und Anwen-dungen. Springer, Berlin, 2009.

[2] C.H. Bischof, H.M. Bücker, B. Lang, A. Rasch, A. Vehreschild. Combining SourceTransformation and Operator Overloading Techniques to Compute Derivatives forMATLAB Programs. In Proc. IEEE Int. Workshop SCAM, 2002.

[3] F. Bause, J. Rautenberg, B. Henning. Design, modeling and identification of anultrasonic composite transducer for target impedance independent short pulse gen-eration. In Processings Sensor Conferences, Nuremberg, 68–73, 2013.


10th Workshop on Direct and Inverse Problems in Piezoelectricity

Piezoelectric d15 shear sensing mechanism experimental

evaluations under parallel and series connections

P. Berik1, A. Benjeddou

2, 3, M. Krommer

1

1 Institute of Technical Mechanics, Johannes Kepler University, Linz, Austria

2 Structures, Institut Supérieur de Mécanique de Paris, 3 rue Fernand Hainaut, Saint Ouen CEDEX, France

3 E-mail: [email protected]

Abstract

The piezoelectric d15 shear sensing mechanism was rarely investigated either numerically or

experimentally as attested by the latest state of the art of shear-mode piezoceramic advanced materials and

structures [1]; therefore, in continuation of the recent effort [2] on this topic, we report here on the sensor

response experiments of piezoceramic shear d15 patches which are integrated in a composite sandwich

structure and connected in parallel and series configurations. The core of the smart structure is formed

from four piezoceramic shear d15 patches arranged in the same polarization direction and sandwiched

between two identical glass fiber reinforced polymer composite layers. The dynamic (harmonic at 20 Hz)

response of the composite structure was monitored using these four piezoceramic shear d15 patches acting

as sensors in parallel and series configurations, and the data were evaluated by a pulse-multi-analyser

system. A charge amplifier was used as a signal conditioning circuit between the piezoceramic shear d15

patches and the pulse multi-analyser system so that the outputs of the piezoceramic shear sensor are in a

short-circuit state. The induced open-circuit voltage outputs are post-processed from the measured parallel

and series short-circuit electric charges and capacitances. The benchmark was simulated in parallel and

series sensor connections using three dimensional finite elements with ABAQUS® code in order to

validate the performed experiments in terms of produced electric charge and voltage outputs.

Experimental and numerical results show good correlations in all cases.

Keywords: piezoceramic, d15 shear-mode, sensing, charge amplifier, short-circuit, open-circuit

References:

[1] Benjeddou A. “shear-mode piezoceramic advanced materials and structures: a state of the art”,

Mechanics of Advanced Materials and Structures, 2007, 14 (4): 263-275.

[2] Berik, P., Benjeddou, A., Krommer M. “Experimental assessment of the piezoelectric transverse d15

shear sensing mechanism”, Smart Structures and Systems, 2014, 13(4):567-585.

Aknowledgments:

The authors are thankfull for this research’s support from the Linz Center of Mechatronics (LCM) in the

framework of the Austrian COMET-K2 programme.



On the modeling of nonlinear electro-mechanical

response in ferroelectrics

Nataliya Kraynyukova

Department of Mathematics, Darmstadt University of Technology, Schlossgartenstr. 7,Darmstadt, Germany, e-mail: [email protected]

Abstract. We consider a simple geometric case, when the ferroelectric sample has aconstant cross section perpendicular to one axis. Electro-mechanical forces applied tothe entire top and bottom surfaces of the material body are supposed to be constantwith respect to the spatial variable and depend only on time. Numerous experimentalresults for the considered 1D process gave rise to the development of mathematical models,which had to incorporate many observed material properties. One class of rate-dependentmodels is based on the plasticity theory for metals and uses remanent strain and remanentpolarisation as internal variables. Although 3D generalisations of such models are difficultto treat within the mathematical existence theory, 1D models can be reduced to the systemof ordinary differential equations, which has the unique solution. We discuss the modelingof nonlinear relations in the corresponding system of differential equations, which describeselectro-mechanical response of internal variables.



Regularity properties of solutions to mixed interface

crack problems of thermo-electro-magneto-elasticity

David Natroshvili

Department of Mathematics, Georgian Technical University, 77 M.Kostava str., 0175Tbilisi, Georgia, [email protected]

Abstract. We investigate regularity properties of solutions to mixed boundary valueproblems of thermo-electro-magneto-elasticity for homogeneous and piece wise homoge-neous anisotropic elastic solid structures with interior and interface cracks. Using thepotential method and theory of pseudodifferential equations on manifolds with boundarywe prove the existence and uniqueness of solutions. The singularities and asymptotic be-haviour of the thermo-mechanical and electro-magnetic fields are analyzed near the crackedges and near the curves, where different types of boundary conditions collide. In partic-ular, for some important classes of anisotropic media we derive explicit expressions for thecorresponding stress singularity exponents and demonstrate their essential dependence onthe material parameters. The questions related to the so called oscillating singularitiesare treated in detail as well.

The contribution extends the results obtained in the reference [1] to more complex prob-lems.

References

[1] T. Buchukuri, O. Chkadua, D. Natroshvili, Mixed boundary value problems of ther-mopiezoelectricity for solids with interior cracks, Integral Equations and OperatorTheory, 64(4): 495-537, 2009.



Mixed type Interaction Problem of Acoustic Waves

and Piezoelectric Structures

George Chkadua1

1 King’s College London, Department of Mathematics, Strand, London, UK,[email protected]

Abstract.

We investigate the mixed type transmission problem arising in the model of fluid-solid acoustic interaction when a piezo-ceramic elastic body (Ω+) is embedded inan unbounded fluid domain (Ω−). The corresponding physical process is describedby boundary-transmission problem for second order partial differential equations. Inparticular, in the bounded domain Ω+ we have 4 × 4 dimensional matrix strongly ellipticsecond order partial differential equation, while in the unbounded complement domainΩ− we have a scalar Helmholtz equation describing acoustic wave propagation. Thephysical kinematic and dynamic relations mathematically are described by appropriateboundary and transmission conditions. With the help of the potential method andtheory of pseudodifferential equations based on the Wiener-Hopf factorization methodthe uniqueness and existence theorems are proved in Sobolev-Slobodetskii spaces.Such type of interaction problems of different dimensional fields appear in the mathemat-ical model of piezoelectric transducers. Further examples of similar models are relatedto phased array microphones, ultrasound equipment, inkjet droplet actuators, drugdiscovery, sonar transducers, bioimaging, immunochemistry and acousto-biotherapeutics(see [1-3] ).In the paper [4] main theorems of mixed type interaction problem of acoustic waves andpiezoelectric structures are stated without proof. The Dirichlet type and Neumann typeinteraction problems of acoustic waves and piezoelectric structures are studied in [5].

References

[1] T.R. Gururaja. Piezoelectric transducers for medical ultrasonic imaging, Proceed-ings of the Eighth IEEE International Symposium on applications of Ferroelectrics,259-265, 1992.

[2] F. Josse, Z.A. Shana, D.E. Radtke and D.T. Haworth. Analysis of piezoelectric bulk-acoustic-wave resonators as detectors in viscous conductive liquids, IEEE Transac-tions on Ultrasonics, Ferroelectrics and Frequency Control, 37 (5), 1990.

[3] M. Thompson, C. L. Arthur and G. K. Dhaliwal. Liquid-phase piezoelectric andacoustic transmission studies of interfacial immunochemistry, Anal. Chem., 58 (6),1206-1209, 1986.

[4] G.Chkadua. Mathematical problems of interaction of different dimensional physicalfields Journal of Physics: Conference Series, 451: 012025, 2013.

[5] G.Chkadua and D. Natroshvili. Interaction of Acoustic Waves and PiezoelectricStructures, Math.Meth. Appl.Sci., (Accepted for publication).



Nonlinear modeling of thin piezoelectric shells using

an extended multiplicative decomposition of the

deformation gradient

Alexander Humer1, Michael Krommer2, and Yury Vetyukov2

1Linz Center of Mechatronics GmbH, Altenbergerstr. 69, A-4040 Linz, Austria,[email protected]

2Institute for Technical Mechanics, Johannes Kepler University Linz, Altenbergerstr. 69,A-4040 Linz, Austria, {michael.krommer,yury.vetyukov}@jku.at

Abstract. Nonlinear modeling of the inelastic behavior of materials by a multiplicativedecomposition of the deformation gradient tensor is quite common for finite strains. Ina three-dimensional formulation the deformation gradient is decomposed as F = Fe · Fi.Here, Fi is the inelastic part and Fe the elastic part. In addition the specific free energyis additively composed of two parts Ψ = Ψe + Ψi; Ψe is the elastic part of the specific freeenergy, and the inelastic part Ψi together with the specific form of the inelastic part of de-formation gradient relates to the specific physical nature of the considered inelasticity. Themultiplicative decomposition of the deformation gradient has successfully been applied inthe modeling of different kinds of inelastic material behavior [1]. Among the various fieldsof finite strain problems, this concept has proven applicable in thermoelasticity, elasto-plasticity, as well as for the description of residual stresses arising in growth processes ofbiological tissues. In the context of advanced materials, electro-elastic elastomers havebeen investigated in [2], shape-memory alloys in [3] and piezoelastic materials in [4], inwhich reversible piezoelectric processes were considered within a three-dimensional con-tinuum theory.

In the present paper we intend to translate this formulation to thin piezoelectric struc-tures; in particular, to thin piezoelectric shells. We model such shells as a materialsurfaces, for which material points have translational and rotational degrees of freedom;the latter are further constrained to the case, for which transverse shear is negligible.Two strain measures C and K on the structural level are used, which are related to thecorresponding differential geometry of the surface; namely, to the first and second metrictensor of the surface in the reference configuration and in the actual configuration. Inparticular, we address the following aspects in detail:

• Geometry: From the three-dimensional formulation we know that the multiplicativedecomposition of the deformation gradient tensor results into an additive decompo-sition of total Green strain tensor into a Green-type elastic part and an Almansi-typepiezoelectric part. This can be directly translated to the two strain measures on theshell level. We show that this is equivalent to a hybrid decomposition at the shelllevel - multiplicative for the deformation gradient and additive for the curvaturetensor.

• Thermodynamics: We introduce a 2D specific free energy as an additive decompo-sition according to Ψ̄ = Ψ̄e + Ψ̄i, from which the strain measures can be computedfrom the partial derivatives of the elastic specific free energy Ψ̄e(Ce,Ke) with respect



Sensing and blocked force experimental

characterization of d15 shear macro fibre composite

transducers

A. Benjeddou1, R. Midol1, B. Kranz2

1Institut Supérieur de Mécanique de Paris - SUPMECA, 3 rue Fernand Hainaut, 93400Saint Ouen, France, [email protected]

2Fraunhofer Institute for Machine Tools and Forming Technology – IWU, NöthnitzerStraße 44, 01187 Dresden, Germany

Abstract. The d15 shear macro-fibre composite (MFC) transducer is a new type thatuses the shear-mode response of piezoelectric rectangular cross-section fibres (polarizedalong their length), separated with epoxy and forming an active core that is sandwichedbetween electrode and encapsulating layers [1]; therefore, in continuation of the authors’previous effort [1] on the numerical and experimental characterizations of these new (pro-totypes) shear MFCs, we report here, for the first time, on the sensing and blocked forceexperimental dynamic (under varying excitation frequency) characterizations of differentshear MFC samples using new experimental setups. It was found that the shear MFCsensing response is linear when epoxy adhesive, instead of the earlier used wax, is usedfor fixing the patch to the device support, while the blocking force under 45 V voltageactuation was found to be 1.677 N. These new experimental results will be used later forfurther validating the developed enthalpy [2] and average quantities [3] based numericalhomogenization procedures in order to obtain shear MFC electromechanical properties.

Keywords: Macro-fibre composites, piezoelectric d15 shear-mode, sensing, blocked force,experiments

References

[1] B. Kranz, A. Benjeddou, W.-G. Drossel. Numerical and experimental character-izations of longitudinally polarized piezoelectric d15 shear macro-fiber composites.Acta Mechanica, 224 (11): 2471-2487, 2013.

[2] B. Kranz, A. Benjeddou, W.-G. Drossel. Enthalpybased homogenization procedurefor composite piezoelectric modules with integrated electrodes. Smart Structuresand Systems, 12 (5): 579-594, 2013.

[3] M. A. Trindade, A. Benjeddou. Finite element characterization and parametricanalysis of the nonlinear behaviour of an actual d15 shear MFC. Acta Mechanica,224 (11): 2489-2503, 2013.

Acknowledgments: The first author thanks the support from the Linz Center of Mecha-tronics (LCM) in the framework of the Austrian COMET-K2 programme, while the secondauthor thanks the support from the Fraunhofer IWU – Dresden.


10th Workshop on Direct and Inverse Problems in Piezoelectricity

Investigation of Deformation in PZT Ceramics under Uniaxial Loadings by Digital Image Correlation

Di Chen†, Marc Kamlah‡

Institute for Applied Materials (IAM-WBM),

Karlsruhe Institute of Technology (KIT),

Hermann-von-Helmholtz-Platz 1,

76344, Eggenstein-Leopoldshafen, Germany †[email protected], ‡[email protected]

Abstract. Digital image correlation (DIC) is a noncontact method which was employed to monitor

the deformation at the surface of piezoelectric ceramic specimens. It is a powerful method to

investigate the local deformation of any part of the observed surface as the ROI (region of interest) on

the surface of a sample can be selected correspondingly.

First, we present the validation of our implementation of the DIC method by comparing to results from

measurement with a linear variable displacement transducer (LVDT) under uniaxial electric field.

Second, we will discuss the homogeneity of the deformation in a slender bulk specimen under

mechanical compression. Because of friction at both the top and bottom surfaces of the PZT ceramic

specimen, the distribution of deformation under uniaxial compressive stress usually shows a barreling

shape. By focusing on correspondingly selected ROIs and calculating the values of strain components

there, the barreling behavior was proved. This finding is the experimental justification for the selection

of an aspect ratio of 3:1 for our specimens, where only the central cubic region of the specimen

represents the desired purely uniaxial stress and strain state. Only from this region, true uniaxial stress-

strain results can be obtained to be used in the development of constitutive models.


Stiffness constants determination (and optimisation) up to 800°C, using

simultaneous BAW and SAW measurements.

P. Nicolay

Carinthian Tech Research (CTR AG), Villach, Austria

[email protected]

To develop high temperature SAW sensors, accurate sets of material constants and temperature coefficients (TCs) are

required. Unfortunately, the determination of accurate TCs requires a lot of investment. In 2013, Nicolay and Aubert

suggested to ease the procedure by using a Simulated Annealing optimization algorithm (SA) to fine-tune the TCs [1-2].

Three SAW Fractional Frequency Curves (FFCs) and SA were used to compute a new set of TCs for Langasite (LGS) and predict with good accuracy the FFC of two other cuts. However, several TC values were not optimized at all. To

solve this issue, the use of additional BAW FFCs was suggested. Besides, there was a need for validation of the whole

method as a simple and cheap way to determine accurate sets of TCs.

The goal of this work was to tackle these two issues. A simple solution was found to measure BAW and SAW FFCs

simultaneously. Then, the method was used to derive TCC (first and second order) of LGS stiffness constants (TCC) from a whole new set of FFCs obtained up to 700°C using an innovative and easy-to-use test chamber. The chamber is

20×20×15 cm3 in size. It is connected to a vacuum pump and comprises a small suspended sample holder, equipped

with a resistive heater and connected via feed-through to a Network Analyzer. Each FFC was acquired in less than 30

minutes.

The new set of TCC was used to compute the FFC on two test cuts, with good agreement. This seems to confirm the

practical interest of the method that will be presented in details. An estimation of the overall costs and time required for

the whole procedure will be provided, as complementary information for further assessment of the method’s economic

viability.

References

[1] P. Nicolay, T. Aubert, A numerical method to derive accurate temperature coefficients of material constants from

high-temperature SAW measurements: application to Langasite, IEEE Trans. Ultrason. Ferroelect. Freq. Contr. 60 (10)

(2013)

[2] P. Nicolay, T. Aubert, An optimized set of temperature coefficients for LGS, Proceedings of the 2013 IEEE

International Ultrasonics Symposium, pp. 271-274



Complex Frequency Shifted Perfectly Matched

Layers Application for Wave Propagation Problems

in Periodic Piezoelectric Structures

Kirill Shaposhnikov1, Manfred Kaltenbacher1, and Pascal Nicolay2

1Institute of Mechanics and Mechatronics, Faculty of Mechanical and IndustrialEngineering, Vienna University of Technology, Karlsplatz 13, 1040 Vienna, Austria,

[email protected] 2CTR Carinthian Tech Research AG,Europastrasse 4/1, 9524 Villach, Austria, [email protected]

Abstract. The periodic piezoelectric structure approach usually finds an applicationfor simulations of surface acoustic wave (SAW) sensors based on piezoelectric interdigitaltransducers (IDT). It allows of considering only a unit cell with periodic boundary condi-tions instead of modelling the whole device. Another extensively used simplification liesin a truncation of the computation domain, for example, imposing absorbing boundaryconditions at the bottom of the substrate.

Here a periodic boundary value problem for the equation of motion coupled with Gauss’slaw is considered. A complex frequency shifted perfectly matched layer (CFS-PML) isutilized as the absorbing condition. Such a perfectly matched layer differs from theclassical one in the stretched-coordinate metrics

s (x) = κ (x) +σ (x)

α (x) + iω,

where κ, σ and α are real-valued non-negative functions, κ ≥ 1. CFS-PML has beenknown to be efficient to solve wave propagation problems in anisotropic elastic [1, 2]and piezoelectric media [3]. The fine quality of such a PML is its ability to absorb notonly propagating but also evanescent waves. This advantage makes it possible to applyCFS-PML for modelling both Rayleigh and leaky type SAW devices.

A pure FEM scheme with periodic boundary conditions imposed through Lagrange multi-pliers has been used for numerical computations. The influence of CFS-PML parameterson wave solutions of various types has been studied. The results have been comparedwith those obtained utilizing the classical PML model.

References

[1] D. Komatitsch and R. Martin. An unsplit convolutional perfectly matched layerimproved at grazing incidence for the seismic wave equation, Geophysics, 72(5):SM155–SM167, 2007.

[2] Y. F. Li and O. Bou Matar. Convolutional perfectly matched layer for elasticsecond-order wave equation, J. Acoust. Soc. Am., 127(3): 1318–1326, 2010.

[3] O. Bou Matar, E. Galopin, Y. Li and O. Ducloux. An Optimized Convolutional-Perfectly Matched Layer (C-PML) Absorbing Boundary Condition for Second-orderElastic Wave Equations, Proceedings of the COMSOL Users Conference, Grenoble,France, 2007.



SPACE

List of Participants

Benjeddou AyechInstitut of Technical Mechanics

(p.15,20) Johannes Kepler [email protected]

Fabian BauseElektrische Messtechnik, EIM-E

(p.14) Universität [email protected]

Achim BittnerInstiute for Sensor- and Actuator SystemsVienna University of [email protected]

Di ChenInsititute for Applied Materials

(p.21) Karlsruhe Institute of Technology (KIT)[email protected]

George ChkaduaDepartment of Mathematics

(p.18) King's College [email protected]

Srujana DusariCTR AGCarithian Tech Research [email protected]

Florian EndresLehrstuhl für Technische Mechanik

(p.6) Universität Erlangen-Nürnberg�[email protected]

Benjamin JurgelucksInstitut für MathematikUniversität [email protected]

Barbara KaltenbacherInstitute of Mathematics

(p.9) Alpen-Adria Universität [email protected]

Manfred KaltenbacherInstiute of Mechanics and MechatronicsVienna University of [email protected]

Nataliya KraynyukovaFachbereich Mathematik

(p.16) TU [email protected]

Michael KrommerInstitute of Technical Mechanics

(p.19) Johannes Kepler University [email protected]

Matthias LabuschInstitut für Mechanik


Patrick MayrhoferInstiute for Sensor- and Actuator Systems

(p.12) Vienna University of [email protected]


David NatroshviliDepartment of Mathematics

(p.17) Georgian Technical [email protected]

Pascal NicolayCTR AG

(p.22) Carithian Tech Research [email protected]

Jens RautenbergerElektrische Messtechnik, EIM-E


Ulrich SchmidInstiute for Sensor- and Actuator SystemsVienna University of [email protected]

Michael SchneiderInstitute of Sensor and Actuator Systems

(p.11) Vienna University of [email protected]

David SchradeLehrstuhl für Technische Mechanik

(p.7) TU [email protected]

Kirill ShaposhnikovInstitut für Mechanik und Mechatronik

(p.23) Technische Universität [email protected]

David TumpoldInstiute of Mechanics and MechatronicsVienna University of [email protected]

Manuel WeiÿLehrstuhl für Sensorik


U3U1

U1

U4

Herrengasse

Ledererhof 9

1010 Wien

~ 10 min .

U4

U2

U2

Schottentor Schottenring

Stephansplatz

Schwedenplatz

U3
