3rd Seminar on Ferroic functional Materials

and

13th International Workshop on direct andinverse Problems in Piezoelectricity

October 4th – 6th, 2017

University of Kassel, Germany

Program and Book of Abstracts

Organized by:Andreas Ricoeur, Bjorn Kiefer and Stephan Lange

m terialsferroic

functional

FOR 1509: DFG Research Unit

PrefaceThe 3rd Seminar on Ferroic Functional Materials and the 13th International Workshopon Direct and Inverse Problems in Piezoelectricity will continue the successful seriesof conferences dedicated to the wide field of ferroelectric, ferromagnetic, multiferroic,and other coupled problems. Since their foundation, they have provided a platform forhighly topical talks and lively discussions, involving a wide range of researchers fromyoung academics to senior scientists and attracting participants from both academiaand industry with engineering, mathematical or physical backgrounds. Accordingly,the contributions nowadays cover various aspects of ferroic materials and coupledproblems including experimental work, material modeling and numerical approachesas well as industrial applications.

It is a great pleasure and honor for the local organizers, Andreas Ricoeur and StephanLange, to have the opportunity to host the combined seminar in Kassel this year. Weare particularly pleased that Bjorn Kiefer from TU Bergakademie Freiberg has joinedour organizing team. Our special thanks go to the DFG Research Unit FOR 1509“ferroic functional materials” and the Hessen State Ministry for Higher Education,Research and the Arts – Initiative for the Development of Scientific and EconomicExcellence (LOEWE–“Safer Materials”) for their financial support.

Kassel and Freiberg, October 2017 Andreas RicoeurBjorn Kiefer

Stephan Lange

i

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OrganizersProf. Dr.–Ing. habil. Andreas Ricoeur

Chair of Engineering Mechanics / Continuum MechanicsInstitute of MechanicsUniversity of KasselMonchebergstraße 734125 Kassel, Germanyricoeur@uni-kassel.de

Phone: +49 561 804 2820Fax: +49 561 804 2720

Prof. Dipl.–Ing. Bjorn Kiefer, Ph. D.

Chair of Applied Mechanics–Solid MechanicsInstitute of Mechanics and Fluid DynamicsTU Bergakademie FreibergLampadiusstraße 409596 Freiberg, GermanyBjoern.Kiefer@imfd.tu-freiberg.de

Phone: +49 3731 39 2075Fax: +49 3731 39 3455

Dr.–Ing. Stephan Lange

Chair of Engineering Mechanics / Continuum MechanicsInstitute of MechanicsUniversity of KasselMonchebergstraße 734125 Kassel, Germanystephan.lange@uni-kassel.de

Phone: +49 561 804 2823Fax: +49 561 804 2720

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Conference CommitteeThorsten Bartel (Dortmund University of Technology)Dominik Brands (University Duisburg – Essen)Marc–Andre Keip (University of Stuttgart)Doru C. Lupascu (University Duisburg – Essen)Andreas Menzel (Dortmund University of Technology)Ralf Muller (Kaiserslautern University of Technology)Jorg Schroder (University Duisburg – Essen)Paul Steinmann (Friedrich – Alexander – University Erlangen – Nuremberg)Bob Svendsen (RWTH Aachen University)Bai–Xiang Xu (Darmstadt University of Technology)

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Contents

1 General Information 11.1 Venue and traveling to Kassel . . . . . . . . . . . . . . . . . . . . . . 21.2 Accommodation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Social program and conference dinner . . . . . . . . . . . . . . . . . . 41.4 Access to the WiFi Network . . . . . . . . . . . . . . . . . . . . . . . 41.5 Informations for presenting authors and session chairs . . . . . . . . . 5

1.5.1 Time for each talk . . . . . . . . . . . . . . . . . . . . . . . . 51.5.2 Technical equipment in the lecture room . . . . . . . . . . . . 5

2 Program 72.1 Time schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Detailed program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Abstracts 15

Notes 49

List of Participants 51

v

vi Contents

1 General Information

1

2 General Information

1.1 Venue and traveling to KasselThe conference will be held at the “Campus Hollandischer Platz” at the Universityof Kassel, s. Fig. 1.1. Lectures take place at the building “Geistes- und Kulturwis-senschaften”, Kurt–Wolters–Straße 5, in room 0019/0020, s. Fig. 1.2.

Railway station Kassel–Wilhelmshohe

Detailed city maps. Fig. 1.2

Campus Hollandischer Platz

Fig. 1.1 Detail of the city map

Kassel is well connected to the national rail network. High speed trains, such as theInterCityExpress (ICE) and the InterCity (IC) stop at the railway station “Kassel–Wilhelmshohe”. Kassel central station is reduced to a regional station. There are nodirect connections to ICE or IC. Arriving by train at “Kassel–Wilhelmshohe”, the“Campus Hollandischer Platz” is directly connected by tram. Fastest connections aretram no. 1 (into the direction “Vellmar” – station “Hollandischer Platz/Universitat”)and tram no. 3 (into the direction “Ihringshauser Straße” – station “Katzensprung”),s. Fig. 1.2.Getting to Kassel by car is also possible, while Kassel is, via the motorways A7 andA44, directly connected to the German motorway network. Traveling by car, pleaseuse the following address:

Monchebergstraße 134125 Kassel

Next to this address there is a former gas station (“Esso”). In front of this, there isa parking spot. Further parking spots are along the Monchebergstraße, s. Fig. 1.2.For both a fee is required. The fee is up to e 7 per day. Free parking areas next tothe university are not available. Therefore traveling by train is highly recommended.

1.2 AccommodationThe accommodation is not included in the conference fee. A limited number of roomshas been reserved in the following two hotels, both located in a walking distance tothe conference venue, s. Fig. 1.2, with special rates for participants, until July 31,2017:

3

Hotel Renthof Kassel

Parking spot

Campus Hollandischer Platz

Station Katzensprung

Meeting point guided city tour

Tram No. 3/6/7

Station AltmarktTram No. 3/4/6/7/8

Tram No. 1/3/4/5/6/8 and RT No. 1/4

Hotel Deutscher Hof

Station Rathaus

Station LutherplatzTram No. 7

Station Hollandischer Platz/Universitat

Each Tram and RT No. 1/4Station Am Stern

Tram No. 1/5 and RT No. 1/4

Lectures

Restaurant Moritz

Fig. 1.2 Map of the center and the campus Hollandischer Platz

1. Hotel Renthof KasselRenthof 334117 KasselSingle Room: e 65,00 per night plus breakfast e 8,50Booking code: A2016-0051www.renthof-kassel.deTraveling by train, via railway station “Kassel–Wilhelmshohe”, the fastest con-nection to the Hotel Renthof Kassel is tram no. 3 (into the direction “Ihrings-hauser Straße”). Other possible tram connections are tram no. 4 (into the di-rection “Helsa” or “Hessisch Lichtenau”) and tram no. 7 (into the direction“Ihringshauser Straße”). But these connections last longer. For all connectionsuse the station “Altmarkt/Regierungsprasidum” to get to the Hotel RenthofKassel, s. Fig. 1.2.

4 General Information

2. Hotel Deutscher HofLutherstraße 3–534117 KasselSingle Room: e 60,00 per night incl. breakfastDouble Room (for single use): e 85,00 per night incl. breakfastBooking code: Piezo-Workshop, University of Kasselwww.deutscher-hof.de

Traveling by train, via railway station “Kassel–Wilhelmshohe”, the fastest con-nections to the Hotel Deutscher Hof are the tram no. 1 (into the direction“Vellmar”) and tram no. 3 (into the direction “Ihringshauser Straße”). Use sta-tion “Am Stern” to get to the Hotel Deutscher Hof. An other possibility, morecomfortable but it last longer, is tram no. 7 (into the direction “IhringshausserStraße”). Traveling with tram no. 7 use the station “Lutherplatz” directly infront of the Hotel Deutscher Hof, s. Fig 1.2.

For further hotel information please visit www.kassel-marketing.de

1.3 Social program and conference dinnerThe social program, a guided city tour under the topic “Kassel–Art–Culture”, andthe conference dinner on Thursday evening are included in the conference fee. Theguided city tour starts at 5 p.m. Meeting point is, s. Fig. 1.2:

Tourist informationWilhelmstraße 2334117 Kassel

Walking distance from both hotels to the meeting point is about 15 minutes. Fromthe “Campus Hollandischer Platz” there are different tram connections. Except tramno. 7, each tram stops at the station “Rathaus”, where the walking distance is abouttwo minutes to the meeting point, s. Fig. 1.2. The tour will end at the restaurant ofthe Hotel Renthof Kassel, where the conference dinner will take place. Approximateduration of the tour is two hours. Participants who do not join the city tour, pleasecome to the Hotel Renthof Kassel at 7 p.m.

1.4 Access to the WiFi NetworkIn the lecture room and on the campus the eduroam network is available. To connectwith this network, please use your private eduroam account.For participants who do not have an eduroam account, a special workshop account isoffered. Connect your device with the eduroam network and enter the following data:

Username: Piezo2017Password: Will be announced at the beginning of the seminar

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1.5 Informations for presenting authors and sessionchairs

1.5.1 Time for each talkThe presentation time of a regular talk is 30 minutes. A keynote lecture takes 45minutes. Both include five minutes of questions and answers. The chairman of asession is obliged to ensure the compliance of the presenting time.

1.5.2 Technical equipment in the lecture roomThe lecture room is equipped with a beamer and a laptop. A presenter is provided bythe organizers. On the laptop Microsoft PowerPoint 2010 as well as an actual versionof Adobe Acrobat Reader is installed. Due to well known problems with differentversions of Microsoft Office, the participants presenting their work with PowerPointare highly recommended to have a PDF version as a backup. It is also possible to usean own laptop. Available connections are VGA and HDMI. Any adapters to VGA orHDMI have to be organized by the presenting speaker, if necessary.Speakers of the upcoming session are asked to be in the lecture room ten minutesbefore the first talk to copy their presentation on the local laptop or to check theirown laptop with the technique of the lecture room.

6 General Information

2 Program

7

8 Program

2.1 Time schedule

Wednesday Thursday FridayOctober 4th October 5th October 6th

08:0008:30 Elten Polukhov Bai-Xaing Xu

08:3008:45 Robin Schulte Benjamin Jurgelucks

09:0009:15 Alexander Schlosser Eduard Rohan

09:3009:45 Bjorn Kiefer Eleni Agiasofitou

10:0010:15 Coffee Break Coffee Break

10:3010:45 Meinhard Kuna Vishal Boddu

11:0011:15 Wei–Lin Tan Franziska Wohler

11:3011:45 Sergii Kozinov Ananthan Vidyasagar

12:00

Registration

12:1512:30 Coffee Break

12:45 Welcome13:0013:15

Lunch BreakRestaurant Moritz

Lunch BreakRestaurant Moritz

13:30John Huber (invited)

13:45 Nicolas Michaelis

14:00 Doru Lupascu Jurgen Rodel (invited)

14:15 Thorsten Bartel

14:30 Harsh Trivedi Hans–Dieter Alber

14:45 Coffee Break

15:00 Soma Salamon Elisabeth Staudigl

15:15 Yangbin Ma

15:30 Coffee Break Florian Toth

15:45 Anna Grunebohm Closing16:00 Matthias Labusch

16:1516:30 Veronica Lemke

16:4517:00 Matthias Rambausek

17:1517:30 Min Yi

17:4518:0018:1518:3018:45

Guided City Tour

19:0019:1519:3019:45

FOR 1509

20:0020:15

Conference DinnerRenthof Kassel

(open end)

9

2.2 Detailed programThe title of a talk is linked to the appropriate abstract. For further contact informa-tion, the leading author is linked to the list of participants.

Wednesday, October 4th

Welcome 12:45 – 13:00Chair: Bjorn Kiefer R 0019, KW 512:45 Opening speech

Andreas Ricoeur

Session No. 1 13:00 – 15:15Chair: Bob Svendsen R 0019, KW 513:00 Some properties of laminates of coupled materials

John E. Huber – Yu Zhou

13:45 Measuring magnetoelectric coupling at different scalesDoru C. Lupascu – Heiko Wende – Vladimir V. Shvartsman – SomaSalamon – Samira Webers – Ahmadshah Nazrabi – Harsh Trivedi –Muhammad Naveed Ul–Haq – Joachim Landers – CarolinSchmitz–Antoniak

14:15 Experimentally probing magnetoelectric coupling at local scaleHarsh Trivedi – Vladimir V. Shvartsman – Doru C. Lupascu – Robert C.Pullar – Andrei Kholkin – Pavel Zelanovskiy – Vladimir Ya Shur

14:45 Study of Converse Magnetoelectric Effect inNiFe2O4-(Ba,Ca)(Zr,Ti)O3 multiferroicsMuhammad Naveed–Ul–Haq – Vladimir V. Shvartsman – Harsh Trivedi– Soma Salamon – Heiko Wende – Doru C. Lupascu

Coffee Break 15:15 – 15:45R 0020, KW 5

Session No. 2 15:45 – 17:45Chair: Doru C. Lupascu R 0019, KW 515:45 The magneto–electric coupling in multiferroic composites: A

two–scale homogenization approachMatthias Labusch – Jorg Schroder

16:15 Comparison of numerical simulation and experimental data ofmagneto–electric compositesVeronica Lemke – Matthias Labusch – Jorg Schroder – Heiko Wende

16:45 Magneto–electric coupling in soft–matter–based compositesMatthias Rambausek – Marc–Andre Keip

10 Program

17:15 Magnetoelastic coupling for magnetization switching withstochastic effectsMin Yi – Bai–Xiang Xu

Thursday, October 5th

Session No. 3 08:00 – 10:00Chair: Andreas Menzel R 0019, KW 508:00 Computational Multi-Scale Stability Analysis of Two-Phase

Periodic Electroactive Polymer Composites at Finite StrainsElten Polukhov – Daniel Vallicotti – Marc-Andre Keip

08:30 Towards a Variational Level Set Formulation forMicrostructure Evolution in FerroelectricsRobin Schulte – Andreas Menzel – Bob Svendsen

09:00 Influence of matrix and interface cracking on the effectiveconstitutive behaviour of multiferroic compositesAlexander Schlosser – Artjom Avakian – Andreas Ricoeur

09:30 Homogenization schemes for magnetic solids based on conceptsof energy relaxationBjorn Kiefer – Thorsten Bartel

Coffee Break 10:00 – 10:30R 0020, KW 5

Session No. 4 10:30 – 12:00Chair: Jorg Schroder R 0019, KW 510:30 An I–Integral for crack analysis in ferroelectric polycrystals

Hongjun Yu – Jie Wang – Sergii Kozinov – Meinhard Kuna

11:00 In situ observation of viscoelastic property evolution duringelectrical fatigue of PZTWei Lin Tan – Ananthan Vidyasagar – Katherine T. Faber – Dennis M.Kochmann

11:30 An I–Integral for extraction the intensity factors along acurved crack front in three–dimensional ferroelectricsHongjun Yu – Jie Wang – Sergii Kozinov – Meinhard Kuna

Lunch 12:00 – 13:30Restaurant Moritz, AB 13

11

Session No. 5 13:30 – 14:30Chair: Andreas Ricoeur R 0019, KW 513:30 Condition Monitoring of Shape Memory Material Stabilization

Nicolas Michaelis – Marvin Schmidt – Felix Welsch – Stefan Seelecke –Andreas Schutze

14:00 A Finite–Element–based macroscopic framework for themodelling of variant switching in MSMAThorsten Bartel – Bjorn Kiefer – Karsten Buckmann – Andreas Menzel

Coffee Break 14:30 – 15:00R 0020, KW 5

Session No. 6 15:00 – 16:00Chair: Thorsten Bartel R 0019, KW 515:00 Tailoring the Hysteresis and Electrocaloric Effect by Defect

EngineeringYang–Bin Ma – Karsten Albe – Bai–Xing Xu

15:30 Modeling the impact of domain walls on the electro calcoricresponseAnna Grunebohm – Madhura Marathe – Claude Ederer

Guided City Tour 17:00 – 19:00

17:00 Meeting point: Tourist informationWilhelmstraße 23, 34117 Kassel (s. Fig. 1.2)

Conference Dinner 19:00 – open end

19:00 Hotel Renthof KasselRenthof 3, 34117 Kassel (s. Fig. 1.2)

Friday, October 6th

Session No. 7 08:00 – 10:00Chair: Meinhard Kuna R 0019, KW 508:00 Phase field simulation of flexoelectricity in ferroelectric

materialsBai-Xiang Xu – Shuai Wang

08:30 Piezoelectric Material Characterization aided by AlgorithmicDifferentiationBenjamin Jurgelucks

12 Program

09:00 Shape sensitivity and homogenization for piezo–poroelasticmicrostructuresEduard Rohan – Vladimır Lukes

09:30 Mathematical modeling of piezoelectric quasicrystalsEleni Agiasofitou – Markus Lazar

Coffee Break 10:00 – 10:30R 0020, KW 5

Session No. 8 10:30 – 12:00Chair: Bjorn Kiefer R 0019, KW 510:30 A preliminary study on the emergence of ferroelectricity

Vishal Boddu – Paul Steinmann

11:00 Phase field simulation with leakage currents for nanogeneratorconceptsFranziska Wohler – Ingo Munch – Chad M. Landis – Werner Wagner

11:30 Understanding domain patterning and electromechanicalbehaviour in bulk ferroelekctrics using spectral phase fieldtechniquesAnanthan Vidyasagar – Wei Lin Tan – Dennis M. Kochmann

Lunch 12:00 – 13:30Restaurant Moritz, AB 13

Session No. 9 13:30 – 15:45Chair: Dominik Brands R 0019, KW 513:30 Lead–free Na1/2Bi1/2TiO3–based piezoelectric composites

Jurgen Rodel – Lukas M. Riemer – K. V. Lalitha – Jurij Koruza

14:15 A sharp interface model for phase interfaces without misfit ofthe crystal latticeHans–Dieter Alber

14:45 Charge–controlled actuation of dielectric elastomersElisabeth Staudigl – Michael Krommer

15:15 Non–Linear Dynamics of a Circular Piezoelectric Multi–LayerPlateFlorian Toth – Manuel Dorfmeister – Michael Schneider – Ulrich Schmid– Manfred Kaltenbacher

13

Closing 15:45 – 16:00Chair: Dominik Brands R 0019, KW 515:45 Closing words

Bjorn Kiefer

14 Program

3 AbstractsThe abstracts are arranged in alphabetical order of the presenting author.

15

16 Abstracts

Mathematical modeling of piezoelectric quasicrystalsEleni Agiasofitou1,∗ and Markus Lazar1

1Department of Physics, Darmstadt University of Technology,Hochschulstr. 6, 64289 Darmstadt, Germany

AbstractQuasicrystals were discovered by Shechtman in 1982. They belong to aperiodic crys-tals and possess long-range orientational order but no translational symmetry. Shecht-man was awarded the 2011 Nobel Prize in Chemistry for his great discovery. Dueto their structure, quasicrystals have some particular (mechanical, electronic, ther-modynamical, chemical, etc.) properties, which could be characterized as desirableproperties; such as low friction coefficient, high wear resistance, and low adhesion.These properties give to quasicrystals advantages in comparison to other conventionalmaterials used today. Nowadays, quasicrystals represent an interesting class of novelmaterials, which are expected to be applied to the coating for engines, solar cells,nuclear fuel containers, sensor and actuator devices, and heat converters.In this work, we start presenting the generalized linear piezoelectricity theory of qua-sicrystals with special focus on the constitutive modeling due to its special features.The basic equations governing one-dimensional piezoelectric quasicrystals are givenproviding also the classification of the phason piezoelectric moduli for all relevantLaue classes [1]. Using the hyperspace notation for piezoelectric quasicrystals, thethree-dimensional Green tensor for (arbitrary) piezoelectric quasicrystals is derived.Finally, piezoelectric quasicrystals are investigated for the first time in the frameworkof configurational or Eshelbian mechanics. Quasicrystalline materials with disloca-tions in the framework of Eshelbian mechanics have been investigated in [2]. Transla-tions, scaling transformations as well as rotations are examined. Important quantitiessuch as the Eshelby stress tensor, the scaling flux vector, the angular momentum ten-sor, configurational forces, configurational work, configurational vector moments aswell as the J-, M-, and L-integrals are derived for piezoelectric quasicrystals [3].

References[1] E. Agiasofitou and M. Lazar: On the constitutive modeling of piezoelectric

quasicrystals. Submitted (2017).[2] M. Lazar and E. Agiasofitou: Eshelbian mechanics of novel materials: Qua-

sicrystals. Journal of Micromechanics and Molecular Physics 1 (2016), 164008(39 pages).

[3] M. Lazar and E. Agiasofitou: Piezoelectricity in quasicrystals: Green tensorand Eshelbian mechanics. Submitted (2017).

∗Corresponding author: Eleni Agiasofitou (� agiasofitou@mechanik.tu-darmstadt.de)

References 17

A sharp interface model for phase interfaces withoutmisfit of the crystal lattice

Hans-Dieter Alber1,∗

1Fachbereich Mathematik, Technische Universitat Darmstadt, Schlossgartenstraße 7,64289 Darmstadt, Germany

AbstractThere is usually no misfit of the crystal lattice along interfaces between martensiticphases in solids. However, when in a sharp interface model the driving force forthe evolution of the interface is given by the jump of the Eshelby tensor, then suchforbidden interfaces with misfit can appear. To avoid this, we propose and discuss amodel where interfaces with misfit of the crystal lattice are penalized. We also showa simple numerical simulation based on this model.

∗Corresponding author: Hans-Dieter Alber (� alber@mathematik.tu-darmstadt.de)

18 Abstracts

A Finite-Element-based macroscopic framework forthe modelling of variant switching in MSMA

Thorsten Bartel1,∗, Bjorn Kiefer2 , Karsten Buckmann1 and Andreas Menzel1

1TU Dortmund, Institute of Mechanics, Leonhard-Euler-Str. 5, 44227 Dortmund, Germany2TU Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics,

Lampadiusstr. 4, 09599 Freiberg, Germany

AbstractThe macroscopic behaviour of ferroic functional materials such as magnetic shapememory alloys (MSMA) is highly affected by microscopic effects like the formationand further evolution of microstructures. Thus, the modelling of these effects is im-portant for establishing micromechanically well-motivated constitutive frameworkswith high physical plausiblity. On the basis of, e.g., [1], it has been shown that qua-siconvexification or, more generally speaking, relaxed energy potentials are promisingconcepts in the context of modelling magnetomechanically coupled material response.In this regard, the switching between different crystallographic variants of marten-site in MSMA as well as the formation and propagation of magnetic domains can betreated by the evolution of phase volume fractions as shown in, e.g., [2]. In addition tothese mechanisms, possible deviations of the local magnetisation vectors with respectto the easy axes is also taken into account by rotation angles in the aforementionedpublication. The current values for these internal state variables are obtained via(local) incremental energy minimisation and the effective quantities such as stresses,but also the magnetisation and magnetic induction are calculated in a post-processingstep. However, this framework was restricted to purely homogeneous problems so far,where, e.g., the influence of the demagnetisation field was captured by a demag-netisation tensor and the magnetisation itself. When inhomogeneous problems shallbe considered, the demagnetisation field has to be treated as an independent fieldvariable, for example in terms of a scalar-valued magnetic potential. The interme-diate conclusion arising from the current status of research activities states, that aconventional Finite-Element-based global implementation, where the external fieldsare discretised in space and determined via balance equations whereas internal statevariables are locally determined at the integration points in a condensed manner,is hardly if at all realisable. In this contribution, the implementation of energy re-laxation concepts for inhomogeneous magnetomechanically coupled problems will bediscussed.

References[1] A. DeSimone and R. D. James: A constrained theory of magnetoelasticity.

Journal of the Mechanics and Physics of Solids 50 (2002), 283–320.[2] B. Kiefer, K. Buckmann, and T. Bartel: Numerical energy relaxation to

model microstructure evolution in functional magnetic materials. GAMM-Mit-teilungen 38(1) (2015), 171–196.

∗Corresponding author: Thorsten Bartel (� thorsten.bartel@udo.edu)

References 19

A preliminary study on the emergence offerroelectricity

Vishal Boddu1,∗ and Paul Steinmann1

1Chair of Applied Mechanics, University of Erlangen-Nuremberg

AbstractThe enhancement of the ferroelectric properties of materials at reduced dimensions iscrucial for continuous advancements in nanoelectronic applications. A long-standingnotion that the ferroelectricity is suppressed at the scale of a few nanometers indicatesthe emergence of ferroelectricity at a scale slightly higher [1, 2]. Emergence is usedto describe a property, law, or phenomenon which occurs at (macroscopic) higherlength and time scales but not at (microscopic or nanoscopic) lower scales. Forinstance, small clusters do not exhibit sharp first order phase transitions such asmelting, and at the boundary it is not possible to completely categorize the cluster asa liquid or solid, since these concepts are (without extra definitions) only applicableto macroscopic systems. Temperature can be also seen as an example of an emergentmacroscopic behavior.In classical dynamics, a snapshot of the instantaneous momenta of a large numberof particles at equilibrium is sufficient to find the average kinetic energy per parti-cle which is proportional to the temperature. For a small number of particles theinstantaneous momenta at a given time are not statistically sufficient to determinethe temperature of the system. However, using the ergodic hypothesis, the temper-ature can still be obtained to arbitrary precision by further averaging the momentaover long enough time intervals. We sought to apply this to study the emergence offerroelectricity.We perform molecular dynamic simulations to investigate the emergence of ferroelec-tric property in BaTiO3 single crystals close to absolute zero under external electricloading using the core-shell model. In the core-shell model every ion is represented interms of a drude particle, consisting of a charged core and a charged electron shell,which introduces electronic polarizability in the ions. We study how the size andthe dimensionality effect the polarization-electric field hysteresis loops of the singlecrystals by obtaining the average electric polarization over long enough time intervals.

References[1] D Lee, H Lu, Y Gu, S.-Y. Choi, S.-D. Li, S Ryu, T. Paudel, K Song,

E Mikheev, S Lee, et al.: Emergence of room-temperature ferroelectricity atreduced dimensions. Science 349(6254) (2015), 1314–1317.

[2] C. Lichtensteiger, J.-M. Triscone, J. Junquera, and P. Ghosez: Ferro-electricity and Tetragonality in Ultrathin PbTiO3 Films. Physical review letters94(4) (2005), 047603.

∗Corresponding author: Vishal Boddu (� vishal.boddu@fau.de)

20 Abstracts

Modeling the impact of domain walls on the electrocaloric response

Anna Grunebohm1,∗, Madhura Marathe1 and Claude Ederer2

1Faculty of Physics and CENIDE, University of Duisburg-Essen, Germany2Materials Theory, ETH Zurich, Switzerland

AbstractThe electrocaloric effect (ECE) is the adiabatic temperature change of a materialin a varying external electrical field which is promising for novel cooling devices [3].However, a large ECE is restricted to a small temperature range in the vicinity of theferroelectric transition temperature, which is above room temperature for standardferroelectrics such as BaTiO3. Different ways to shift the operation temperature areepitaxial strain [1], the use ferroelectric to ferroelectric phase transitions [2], or theuse of solid solutions [4] and multilayers. In all cases, multi-domain ferroelectric phasemay be stabilized by the elastic boundary conditions or depolarization effects. Wediscuss the coupling between ferroelectric domains and the external electric field andits impact on the ECE by means of ab initio based simulations.

References[1] A. Grunebohm, M. Marathe, and C. Ederer: Tuning the caloric response

of BaTiO3 by tensile epitaxial strain. Euro. Phys. Lett. 115(4) (2016), 47002.[2] M. Marathe, D. Renggli, A. Grunebohm, M. Sanlialp, V. Shvartsman,

D. Lupascu, and C. Ederer: The electrocaloric effect in BaTiO3 at all threeferroelectric transitions: anisotropy and inverse caloric effects. Phys. Rev. B (ac-cepted). 2017. url: https://arxiv.org/pdf/1703.05515.pdf.

[3] X. Moya, S. Kar-Narayan, and N. D. Mathur: Caloric materials near ferroicphase transitions. Nature Mater. 13 (2014), 439.

[4] T. Nishimatsu, A. Grunebohm, U. Waghmare, and M. Kubo: MolecuarDynamics Simulations of Chemically Disordered Ferroelectrics (Ba,Sr)TiO3 witha semi-empirical effective Hamiltonian. J. Phys. Soc. Jap 85 (2016), 114714.

∗Corresponding author: Anna Grunebohm (� anna@thp.uni-due.de)

References 21

Some properties of laminates of coupled materialsJohn E. Huber1,∗ and Yu Zhou1

1University of Oxford, Department of Engineering Science

AbstractThe formation of a composite mixes together materials to give averaged materialproperties, but also allows the generation of new materials with properties that werenot present in any of the parent phases. In this talk we examine the linear prop-erties of laminates and explore some of the possibilities for forming materials withdesirable elastic or electromagnetically coupled properties. A significant practical in-terest in these materials now exists because of the development of methods for easymanufacture of complex composites. Micro- and nano-fabrication methods enable theconstruction of complex layered heterostructures, while additive manufacturing offersa potentially limitless combination of materials and the geometry of phases. Con-sidering first purely elastic laminates, we explore the formation of composites withdesirable elastic properties. Milton and Cherkaev showed [1] that, given sufficientlyextremal but isotropic starting materials, a homogenized composite could achieveany elastic tensor within the bounds imposed by thermodynamics. We explore theuse of isotropic and anisotropic starting materials combined with layering and ro-tation for the generation of materials with features such as auxeticity. We furtherexplore composites with tailored piezoelectric and magnetoelectric properties. It iswell-known that the magnetoelectric effect can be generated in composites where noneof the parent phases are themselves magnetoelectric [2]. We discuss combinations oflayered materials that can achieve enhanced performance and explore the limits ofperformance.

References[1] G. W. Milton and A. V.Cherkaev: Which elasticity tensors are realizable?

Journal of Engineering Materials and Technology 117 (1995), 483–493.[2] G. Srinivasan: Magnetoelectric composites. Annual Review of Materials Re-

search 40 (2010), 153–178.

∗Corresponding author: John E. Huber (� John.Huber@eng.ox.ac.uk)

22 Abstracts

Piezoelectric Material Characterization aided byAlgorithmic Differentiation

Benjamin Jurgelucks1,∗

1Mathematics and its Applications, Institute for Mathematics, Paderborn University

AbstractIn the last decades computer simulations have become a central element in the designprocess of piezoelectric devices. However, for physically correct computer simulationsprecise knowledge of the material properties is indispensable. One method of materialparameter characterization of a given piezoelectric specimen is based on an inverseproblem where the impedance curve computed in a computer simulation is fitted tophysical measurements thereof. However, the sensitivity of impedance with respectto some of the material parameters is usually low and close to zero and thus it is veryhard to find a solution to the inverse problem.In recent work [2, 3] it was shown that the sensitivity of impedance with respect tothe material parameters could be increased and optimized by introducing a triple-ringelectrode geometry on the surface of the ceramic. Introducing algorithmic differentia-tion to the computation of the sensitivities resulted [1] in an overall higher optimizedsensitivity.In this talk we will demonstrate how the use of algorithmic differentiation, the opti-mized electrode geometry and the optimized sensitivity of impedance can be exploitedfor the means of material parameter estimation problems in piezoelectricity.

References[1] B. Jurgelucks and L. Claes: “Optimisation of triple-ring-electrodes on piezo-

ceramic transducers using algorithmic differentiation”. In: AD2016 - 7th Inter-national Conference on Algorithmic Differentiation, Oxford, United Kingdom.2016.

[2] K. Kulshreshtha, B. Jurgelucks, F. Bause, J. Rautenberg, and C. Un-verzagt: Increasing the sensitivity of electrical impedance to piezoelectric ma-terial parameters with non-uniform electrical excitation. Journal of Sensors andSensor Systems 4 (2015), 217–227.

[3] C. Unverzagt, J. Rautenberg, and B. Henning: Sensitivitatssteigerung beider inversen Materialparameterbestimmung fur Piezokeramiken. tm-TechnischesMessen 82(2) (2015), 102–109.

∗Corresponding author: Benjamin Jurgelucks (� Benjamin.Jurgelucks@math.uni-paderborn.de)

References 23

Homogenization schemes for magnetic solidsbased on concepts of energy relaxation

Bjoern Kiefer1,∗ and Thorsten Bartel2

1TU Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics,Lampadiusstr. 4, 09599 Freiberg, Germany

2TU Dortmund, Institute of Mechanics, Leonhard-Euler-Str. 5, 44227 Dortmund, Germany

AbstractThe prediction of the effective behavior of a heterogeneous material—based on theknowledge of geometrical, distributional and constitutive properties of the involvedphases—by means of adequate homogenization concepts is a classical problem in solidmechanics. It is well-known that classical homogenization schemes in mechanics, suchas the Taylor/Voigt and Reuss/Sachs assumptions, can also be interpreted as ener-getic bounds. Furthermore, energy relaxation concepts have been established thatdetermine stable effective material responses based on appropriate (convex, quasi-convex, rank-one) energy hulls for multi-phase materials characterized by non-convexenergy landscapes, see [1–3] and references therein. In this contribution we pro-pose analogous relaxation-based homogenization approaches for magnetizable solids.In particular, we introduce novel scalar and vector-valued magnetic potential per-turbation schemes that yield relaxed effective free energy/enthalpy densities whichsimultaneously satisfy magnetic induction and magnetic field strength compatibil-ity requirements—i.e. the magnetostatic Maxwell equations—at the phase boundary.In this context, we also discuss adequate choices of thermodynamic potentials andtheir implications on the theoretical framework for constitutive modeling as well ascorresponding numerical treatments.

References[1] T. Bartel, B. Kiefer, K. Buckmann, and A. Menzel: A Kinematically-En-

hanced Relaxation Scheme for the Modeling of Displacive Phase Transforma-tions. Journal of Intelligent Material Systems and Structures 26(6) (2015), 701–717.

[2] B. Kiefer, K. Buckmann, and T. Bartel: Numerical Energy Relaxationto Model Microstructure Evolution in Functional Magnetic Materials. GAMM-Mitteilungen 38(1) (2015), 171–196.

[3] B. Kiefer, T. Furlan, and J. Mosler: A Numerical Convergence Study Re-garding Homogenization Assumptions in Phase Field Modeling. InternationalJournal for Numerical Methods in Engineering, in press (2017), DOI:10.1002/nme.5547.

∗Corresponding author: Bjoern Kiefer (� Bjoern.Kiefer@imfd.tu-freiberg.de)

24 Abstracts

An I-integral for extraction the intensity factors alonga curved crack front in three-dimensional ferroelectrics

Hongjun Yu1,3,∗, Jie Wang2 , Sergii Kozinov3 and Meinhard Kuna3

1Department of Astronautic Science and Mechanics, Harbin Institute of Technology,Harbin 150001, China

2Department of Engineering Mechanics, School of Aeronautics and Astronautics, ZhejiangUniversity, Hangzhou 310027, China

3Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg,Lampadiusstraße 4, Freiberg 09596, Germany

AbstractDomain switching causes nonlinear response of ferroelectrics, which makes it verydifficult to determine the fracture parameters for ferroelectrics under large-scale do-main switching. For large-scale switching problems, the spontaneous polarizationsnear the crack front can be assumed to be saturated. On the basis of this assump-tion, the authors established the I-integral method for two-dimensional ferroelectricsingle-crystals [2] and polycrystals [3]. This paper develops an I-integral to extractthe stress intensity factors and electric displacement intensity factors along a curvedcrack front in a three-dimensional ferroelectric single-crystal. The I-integral has manyadvantages over the switching toughening model. First, it is effective for large-scaleswitching. Second, it can decouple the stress intensity factors of different modes andthe electric displacement intensity factor. Third, it is independent of integration vol-ume size, regardless of the presence of domain walls. The phase field model [1] is firstemployed predict the polarization distributions of PbTiO3 ferroelectric single-crystalswith a semi-circular surface crack. Then, the I-integral method is used to study theinfluences of domain switching on the intensity factor values and their distributionsalong the crack front.

References[1] J. Wang and M. Kamlah: Three-dimensional finite element modeling of po-

larization switching in a ferroelectric single domain with an impermeable notch.Smart Mater. Struct. 18 (2009), 104008.

[2] H. J. Yu, J. Wang, T. Shimada, H. P. Wu, L. Z. Wu, M. Kuna, and T.Kitamura: An I-integral method for crack-tip intensity factor variation due todomain switching in ferroelectric single-crystals. J. Mech. Phys. Solids 94 (2016),207–229.

[3] H. J. Yu, J. Wang, S. Kozinov, and M. Kuna: An I-integral for crack analysisin ferroelectric polycrystals under large-scale switching. subnmitted to Eur. J.Mech. A-Solids (2017).

∗Corresponding author: Hongjun Yu (� yuhongjun@hit.edu.cn)

References 25

Charge-controlled actuation of dielectric elastomersElisabeth Staudigl1,∗ and Michael Krommer1

1Vienna University of Technology, Institute of Mechanics and Mechatronics Getreidemarkt9, A-1060 Vienna, Austria

AbstractIn this talk we study dielectric elastomer actuators in the form of a thin layer withtwo compliant electrodes. In such actuators two main sources of electro-mechanicalcoupling are present - electrostatic forces acting between the electric charges andelectrostriction due to intramolecular forces of the material, see [1]. In [2] we haveaccounted for electrostatic forces for the case of voltage-controlled actuators only. Involtage-controlled dielectric elastomer actuators the electric field is known to cause apull-in instability at a so-called breakdown voltage. This penomenen is not observedin charge-controlled actuators. However, a different instability, named charge local-ization instability has been reported in the literature for the case of electro-mechanicalcoupling by means of electrostatic forces, see [3]. In this talk we extend our formula-tion from [2] to electrostriction as well as to the case of charge-controlled actuatorsto study the necking instability in more detail. Basically, the free energy is additivelydecomposed into a purely mechanical part and an electrical part. The mechanicalfree energy, for which we use a neo-Hookean strain energy function, is a function ofthe mechanical right Cauchy-Green tensor, and the electrical free energy depends onthe material electric field and the total right Cauchy-Green tensor. Moreover, themechanical right Cauchy-Green tensor follows from a multiplicative decompositionof the deformation gradient tensor into an elastic deformation gradient tensor andan electric deformation gradient tensor; by means of the latter we account for elec-trostriction. Charge-controlled actuation is finally introduced through the Gauss lawof electrostatics.

Acknowledgement Support from the K2 area of the Linz Center of Mechatronics GmbH isgratefully acknowledged.

References[1] M. Mehnert, M. Hossain, and P. Steinmann: On nonlinear thermo-electro-

elasticity. Proceedings of the Royal Society A 472 (2016), 20160170.[2] E. Staudigl, M. Krommer, and Y. Vetyukov: Finite deformations of thin

plates made of dielectric elastomers: Modeling, Numerics and Stability. submittedto Journal of Intelligent Materials Systems and Structures 472 (), 20160170.

[3] E. Staudigl, M. Krommer, and Y. Vetyukov: Charge localization instabilityin a highly deformable dielectric elastomer. Applied Physics Letter 104 (2014),022905.

∗Corresponding author: Elisabeth Staudigl (� elisabeth.staudigl@tuwien.ac.at)

26 Abstracts

An I-integral for crack analysis in ferroelectricpolycrystals

Hongjun Yu1,3,∗, Jie Wang2 , Sergii Kozinov3 and Meinhard Kuna3

1Department of Astronautic Science and Mechanics, Harbin Institute of Technology,Harbin 150001, China

2Department of Engineering Mechanics, School of Aeronautics and Astronautics, ZhejiangUniversity, Hangzhou 310027, China

3Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg,Lampadiusstraße 4, Freiberg 09596, Germany

AbstractIt is a great challenge to extract the crack-tip fracture parameters of ferroelectricsdue to domain switching, especially for large-scale switching problems. This paperdevelops an area-independent I-integral, which has several merits over the switching-toughening model in determining the crack-tip stress intensity factors. First, restric-tion to small-scale switching is overcome. Second, the intensity factors of differentmodes are decoupled. Third, it is independent of integration area size, regardlessof the presence of grain boundaries and domain walls. These advantages ensure thesuccessful utility of the area-independent I-integral in ferroelectric polycrystals underlarge-scale domain switching. The phase field model is combined with the I-integralmethod to form an effective approach to predict the polarization distributions and toevaluate the crack-tip intensity factor. A tensile test of PbTiO3 ferroelectric poly-crystals with an impermeable crack is simulated through increasing the tensile strainstep by step. The I-integral shows good area-independence even when grain bound-aries and domain walls are included. For polycrystals, domain switching initiates notonly from the crack tip but also from the grain boundaries due to high polarizationgradient and stress concentration. Domain switching is triggered by a critical load,which greatly reduces the mode-I stress intensity factors. The critical load is muchlower for polycrystals than for single crystals and sometimes vanishes due to grainorientations. The mode-I stress intensity factor of the polycrystal is smaller than thatof the single crystal under the same applied load.

Fig. 3.1 Stable domain structures for (a) single-crystal, (b) polycrystal with grainsorient identically and (c) polycrystal with grains orient differently; (d) nor-malized KI vs applied tensile strain.

∗Corresponding author: Hongjun Yu (� yuhongjun@hit.edu.cn)

References 27

The magneto-electric coupling in multiferroiccomposites: A two-scale homogenization approach

Matthias Labusch1,∗ and Jorg Schroder1

1University Duisburg-Essen, Institute of Mechanics, Universitatsstr. 15, 45141 Essen

AbstractMultiferroic materials combine two or more ferroic characteristics and can exhibit aninteraction between electric and magnetic fields. This magneto-electric (ME) cou-pling can find applications in sensor technology or in magneto-electric data storagedevices [4]. Since most ME single-phase materials show such a coupling far belowroom temperature the manufacturing of two-phase composites, consisting of a fer-roelectric matrix with magnetostrictive inclusions, becomes important. Due to theinteraction of both constituents the composites generate a strain-induced ME cou-pling at room temperature, where we distinguish between the direct and converseME effect. The direct effect characterizes magnetically induced polarization, wherean applied magnetic field yields a deformation of the magnetostrictive phase, which istransferred to the ferroelectric phase. Due to the electro-mechanical properties of thematrix material the composite exhibit a change in polarization. On the other hand,the inverse ME effect characterizes electrically induced magnetization. The ME cou-pling significantly depends on the microscopic morphology and the ferroic propertiesof the individual constituents. In order to take both aspects into account, a finiteelement (FE2) homogenization approach is performed, which combines via a scalebridging the macro- and microscopic level [3]. Thereby, the microscopic morphologyis characterized be representative volume elements and the ferroic properties of thephases are described by suitable material models. The typical ferroelectric hysteresiscurves are modeled by considering the switching behavior of the spontaneous polar-izations of barium titanate unit cells [1], whereas the magnetic hysteresis loops aredescribed by a Preisach operator [2].

References[1] S. Hwang, C. Lynch, and R. McMeeking: Ferroelectric/Ferroelastic interac-

tion and a polarization switching model. Acta metall. mater. 43 (1995), 2073–2084.

[2] M. Kaltenbacher, B. Kaltenbacher, T. Hegewald, and R. Lerch: Fi-nite Element Formulation for Ferroelectric Hysteresis of Piezoelectric Materials.Journal of Intelligent Material Systems and Structures (2010).

[3] J. Schroder, M. Labusch, and M.-A. Keip: Algorithmic two-scale transitionfor magneto-electro-mechanically coupled problems - FE2-scheme: Localizationand Homogenization. Computer Methods in Applied Mechanics and Engineering302 (2016), 253–280.

[4] N. Spaldin and M. Fiebig: The Renaissance of Magnetoelectric Multiferroics.Science 309 (2005), 391–392.

∗Corresponding author: Matthias Labusch (� matthias.labusch@uni-due.de)

28 Abstracts

Comparison of numerical simulation and experimentaldata of magneto-electric composites

V. Lemke1,∗, M. Labusch1 , J. Schroder1 and H. Wende2

1Institute of Mechanics, Faculty of Engineering, University of Duisburg-Essen,Universitatsstraße 15, 45141 Essen, Germany

2Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE),University of Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany

AbstractIn technical applications, the combination of ferroic materials develop new opportu-nities to create better sensor technologies or data storages [4]. The reason for animprovement with magneto-electric (ME) materials can be explained by the fact thatcommonly they have the property of synergy between physical ferroic quantities. Incomposites constituted out of ferroelectric and ferromagnetic phases, a strain inducedmagneto-electric product property is recognized at room temperature [5]. One candifferentiate between the direct and the converse ME effect. The first characterizesa magnetically caused polarization, i.e. a magnetic field evokes a deformation ofthe magneto-active phase which is then transferred to the electro-active phase. Viceversa, the second ME effect is distinguished. In our work, we take a closer lookat a (1-3) composite, CoFe2O4 nanopillars embedded in a BaTiO3 matrix with thematerial coefficients taken from [1]. We compare our numerical simulations to theexperiments from [2] and [3]. In our calculations, we will investigate the direct MEeffect as well as the resulting polarization distribution over the whole body.

References[1] M. Labusch, M. Etier, D. C. Lupascu, J. Schroder, and M. A. Keip:

Product properties of a two-phase magneto-electric composite: Synthesis andnumerical modeling. Computational Mechanics 54 (2014), 71–83.

[2] C. Schmitz-Antoniak, D. Schmitz, P. Borisov, F. de Groot, S. Stienen,A. Warland, B. Krumme, R. Feyerherm, E. Dudzik, W. Kleemann,and H. Wende: Electric in-plane polarization in multiferroic CoFe2O4/BaTiO3nanocomposite tuned by magnetic fields. nature communications 4 (2013), 1–8.

[3] C. Schmitz-Antoniak, D. Schmitz, P. Borisov, F. de Groot, S. Stienen,A. Warland, B. Krumme, R. Feyerherm, E. Dudzik, W. Kleemann,and H. Wende: Electric in-plane polarization in multiferroic CoFe2O4/BaTiO3nanocomposite tuned by magnetic fields: Supplementary information. (2013).

[4] N. A. Spalding and M. Fiebig: The renaissance of magnetoelectric multifer-roics. Materials Science 309 (2005), 391–392.

[5] J. van Suchtelen: Product properties: a new application of composite materi-als. Philips Research Reports 27 (1972), 28–37.

∗Corresponding author: V. Lemke (� veronica.lemke@uni-due.de)

References 29

Measuring Magnetoelectric Coupling at DifferentScales

Doru C. Lupascu1,∗, Heiko Wende2 , Vladimir V. Shvartsman1 , Soma Salamon2 ,Samira Webers2 , Ahmadshah Nazrabi1 , Harsh Trivedi1 , Muhammad Naveed

Ul-Haq1 , Joachim Landers2 and Carolin Schmitz-Antoniak3

1Institute for Materials Science and Center for Nanointegration Duisburg-Essen(CENIDE), University of Duisburg-Essen, Universitatsstraße 15, 45141 Essen, Germany

2Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE),University of Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany

3Peter Grunberg Institute (PGI-6), Julich Research Centre, 52425 Julich, Germany

AbstractMagnetoelectric coupling is the material based coupling between electric and magneticfields without recurrence to electrodynamics. It can arise in intrinsic multiferroics aswell as in composites. Intrinsic multiferroics rely on atomistic coupling mechanisms,or coupled crystallographic order parameters, and even more complex mechanisms.They typically require operating temperatures much below T = 0◦C in order toexhibit their coupling effects. Room temperature applications are thus excluded.Consequently, composites have been designed to circumvent this limitation. Theyrely on field coupling between magnetostrictive and piezoelectric materials or in moreadvanced scenarios on quantum coupling in between both phases. This overview willdescribe experimental techniques and their particular limitations in accessing thesecoupling phenomena at different scales. Strain coupling is the dominant couplingmechanism at the macroscale as well as down to the micrometer. At the nanoscalemore subtle effects can arise and some care has to be taken when investigating localcoupling at interfaces using scanning probe techniques, e. g. due to semiconductoreffects, field screening, or gradient and surface effects. At the smallest length scaleatomic or molecular coupling can be tested using X-ray dichroism or probe atomslike 57Fe in Mossbauer spectroscopy. We display a selection of measuring techniquesat the different scales and outline possible pitfalls for experimentalists as well astheoreticians when using material parameters extracted from such experimental work[1]. Recent trends in the field will be displayed.

References[1] D. C. Lupascu, H. Wende, M. Etier, A. Nazrabi, I. Anusca, H. Trivedi,

V. V. Shvartsman, J. Landers, S. Salamon, and C. Schmitz-Antoniak:Measuring the Magnetoelectric Effect Across Scales. GAMM-Mitteilungen 38(2015), 25–74.

∗Corresponding author: Doru C. Lupascu (� doru.lupascu@uni-due.de)

30 Abstracts

Tailoring the Hysteresis and Electrocaloric Effect byDefect Engineering

Yang-Bin Ma1,∗, Karsten Albe1 and Bai-Xiang Xu1

1Technische Universitat Darmstadt

AbstractIn acceptor doped perovskite ferroelectrics, the A site or B site ions can be substi-tuted by ions with a lower valence, e.g., Ti ions in BaTiO3 are substituted by Mnor Cu. The associates of the acceptors and the compensating oxygen vacancies formnon-switchable or hardly switchable defect dipoles, which shift or pinch the dielectrichysteresis, and might affect or even enhance the electrocaloric effect (ECE) signifi-cantly. For studying this interest point, the lattice-based Monte-Carlo simulationswith the Ginzburg-Landau type Hamiltonian are applied to reveal the mechanism onthe domain structure level, which allows direct evaluation of the ECE by combiningthe canonical and microcanonical algorithm.In the case of anti-parallel defect dipoles, the hysteresis is shifted. When the inducedinternal field is stronger than the external field, there is transformation from thepositive ECE to the negative ECE. Other unexpected phenomena are additionallyunveiled, including the coexistence of the positive ECE and the negative ECE undermoderate field, and the double peak behavior of the ECE under high field. Finally thenegative electrocaloric effect in the presence of defect dipoles is utilized to modify theelectrocaloric cycle, and a significant enhancement of the ECE can be achieved. Ad-ditionally, the results from the Monte-Carlo simulations and the Molecular Dynamicsand compared, and show good qualitative agreement.In the case of the mixed defect dipoles a different type of hysteresis loop is shown.When the defect dipoles with two opposite directions are placed perpendicular to theexternal field, a perpendicular internal field is induced. In this fashion the character-istic pinched hysteresis loop appears below the Curie temperature TC, but disappearsabove TC. These simulated hysteresis loops are comparable with the experimentalobservations. Below TC, after field removal, the positive temperature change, i.e.,the negative ECE, is observed, due to the influence of the defect dipoles. However,above TC, the negative temperature change, i.e., the positive ECE still persists.

∗Corresponding author: Yang-Bin Ma (� y.ma@mfm.tu-darmstadt.de)

References 31

Condition Monitoring of Shape Memory MaterialStabilization

Nicolas Michaelis1,∗, Marvin Schmidt2,3 , Felix Welsch2 , Stefan Seelecke2 andAndreas Schutze1

1Lab for Measurement Technology, Dept.of Systems Engineering, Saarland University,Saarbrucken, Germany

2Intelligent Material Systems Laboratory, Dept.of Materials Science and Engineering,Dept.of Systems Engineering, Saarland University, Saarbrucken, Germany

3ZeMA Center for Mechatronics and Automation Technology, Saarbrucken, Germany

AbstractThis contribution presents a condition monitoring approach on shape memory mate-rial stabilization, especially for elastocaloric cooling applications. In addition to theknown applications of shape memory alloys (SMAs), another field of application hasrecently gained interest: elastocaloric cooling. It is currently being investigated as apart of the German Science Foundation (DFG) priority program SPP 1599 FerroicCooling [1].The main advantage of the elastocaloric cooling process consists in avoiding ozonedepleting refridgerants. Moreover, large latent heats and a small required work inputduring the application of elastocaloric materials (mostly Ni-Ti based SMAs) result inan efficient cooling process. The latent heats of the material become accessible undertensile loading and unloading of the SMA sample at high strain rates. This materialbehaviour is caused by the crystallographic phase transformation from austenite tomartensite and vice versa. Based on these material properties, elastocaloric coolingprocesses can be developed and implemented in SMA based cooling devices [3].Before the SMA can be used as heat transfer medium in cooling applications, the me-chanical and thermal material properties have to be stabilized. This can be achievedby an elastocaloric training process which basically consists in loading and unloadingthe SMA samples at very low strain rates (typically below 0.1 %·s−1). The mechani-cal material stabilization can be shown in stress-strain diagrams, whereas the thermalstabilization can be illustrated by cycle dependent temperature profiles of the sample[2].Analysing the self-sensing properties of the SMA concerning the material stabilizationis essential to create elastocaloric cooling devices, such as the cooling demonstratoraddressed in the priority program [3]. With an especially developed scientific testsetup different self-sensing parameters have been investigated, with the result that aresistance measurement of the SMA during the elastocaloric training process reflectsthe strain as well as the phase transformation and material stabilization. Further-more, impedance measurements might also allow a continuous condition monitoringduring operation to grant an early indication of impending material failure. These re-sults, will allow the implementation of SMA-based cooling devices without expensiveequipment like force and thermographic sensor technology.

∗Corresponding author: Nicolas Michaelis (� n.michaelis@lmt.uni-saarland.de)

32 Abstracts

References[1] S. Fahler et al.: Caloric Effects in Ferroic Materials: New Concepts for Cooling.

Advanced Engineering Materials 14(1-2) (2012), 10–19.[2] M. Schmidt et al.: Thermal Stabilization of NiTiCuV Shape Memory Alloys:

Observations During Elastocaloric Training. Shape Memory and Superelasticity(2015), 132–141.

[3] M. Schmidt, S.-M. Kirsch, S. Seelecke, and A. Schutze: Elastocaloric Cool-ing: from Fundamental Thermodynamics to Solid State Air Conditioning. Scienceand Technology for the Built Environment 22(5) (2016), 475–488.

References 33

Computational Multi-Scale Stability Analysisof Two-Phase Periodic Electroactive Polymer

Composites at Finite StrainsElten Polukhov1,∗, Daniel Vallicotti1 and Marc-Andre Keip1

1University of StuttgartInstitute of Applied Mechanics (CE), Chair of Material Theory,

Pfaffenwaldring 7, 70569 Stuttgart, Germany

AbstractDielectric electroactive polymers (dielectric EAPs) are functional materials whichexhibit coupled electrostrictive response to externally applied electrostatic loadings.The advantageous properties of these materials such as light weight, fast coupled re-sponse, high stretchability and easiness of fabrication give possibilities to apply themin advanced engineering designs. Nevertheless, optimal design of dielectric EAP com-posites requires to study the influence of the microscopic and macroscopic propertiesof these materials and to determine the stable loading ranges. Considering this, westudy multi-scale stability analysis of two-phase periodic EAP composites in the con-text of computational homogenization [2–4]. Particularly, the influence of the fibervolume fractions and aspect ratios to the onset of the localization-type macroscopicand bifurcation-type microscopic instabilities are investigated. The localization-typeinstabilities are determined as the loss of strong ellipticity of homogenized macroscopicmoduli at a certain finite deformation However, the bifurcation-type microscopic in-stabilities are treated by implementing Bloch-Floquet wave analysis in the context ofa finite element discretization [1, 4]. The critical periodicities and bifurcation modesdue to microscopic instabilities are demonstrated for selected representative boundaryvalue problems.

References[1] G. Geymonat, S. Muller, and N. Triantafyllidis: Homogenization of non-

linearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Archive for Rational Mechanics and Analysis 122(3) (1993), 231–290.

[2] M.-A. Keip, P. Steinmann, and J. Schroder: Two-scale computational ho-mogenization of electro-elasticity at finite strains. Computer Methods in AppliedMechanics and Engineering 278 (2014), 62–79.

[3] C. Miehe, D. Vallicotti, and S. Teichtmeister: Homogenization and mul-tiscale stability analysis in finite magneto-electro-elasticity. Application to softmatter EE, ME and MEE composites. Computer Methods in Applied Mechanicsand Engineering 300 (2016), 294–346.

[4] E. Polukhov, D. Vallicotti, and M.-A. Keip: Computational Stability Anal-ysis of Periodic Electroactive Polymer Composites across Scales. Submitted toComputer Methods in Applied Mechanics and Engineering (2017).

∗Corresponding author: Elten Polukhov (� polukhov@mechbau.uni-stuttgart.de)

34 Abstracts

Magneto-electric coupling in soft-matter-basedcomposites

Matthias Rambausek1,∗ and Marc-Andre Keip1

1University of Stuttgart, Institute of Applied Mechanics (CE), Chair of Material Theory,Pfaffenwaldring 7, 70569 Stuttgart, Germany

AbstractMagneto-electric coupling of solids can be realized by the construction of magneto-electric composites. Usually, these composites are made of hard materials [5]. Analternative route to magneto-electric coupling was proposed only recently by Liu andSharma [3]. Their approach is based on soft-matter magneto-electric composites.Such composites render an interesting class of materials that might be employed forthe design of novel magnetic-field sensors. Thus, in our contribution, we analyzethe magneto-electric coupling mechanisms in these materials. We present a seriesof multiscale simulations of soft magneto-electric bodies under physically reasonableboundary conditions [1, 4]. Thereby, we focus on the distinction between microstruc-tural and macrostructural coupling mechanisms. In detail, we compare the effec-tive macroscopic properties of magnetorheological elastomers under magneto-electricloading with the macroscopic shape-dependent [2] performance of a magneto-electrictransducer. In our analysis, we identify macroscopic effects to be crucial for, e.g., asensor’s performance. These effects are driven by magneto- and electro-mechanicalinteractions on both scales and clearly dominate the effective coupling moduli of thecomposite.

References[1] M.-A. Keip and M. Rambausek: A multiscale approach to the computational

characterization of magnetorheological elastomers. International Journal for Nu-merical Methods in Engineering 107(4) (2016), 338–360.

[2] M.-A. Keip and M. Rambausek: Computational and analytical investigationsof shape effects in the experimental characterization of magnetorheological elas-tomers. International Journal of Solids and Structures (2017). doi: 10.1016/j.ijsolstr.2017.04.012.

[3] L. Liu and P. Sharma: Giant and universal magnetoelectric coupling in soft ma-terials and concomitant ramifications for materials science and biology. PhysicalReview E 88(4) (2013), 040601.

[4] J.-P. Pelteret, D. Davydov, A. McBride, D. K. Vu, and P. Steinmann:Computational electro- and magneto-elasticity for quasi-incompressible mediaimmersed in free space. International Journal for Numerical Methods in Engi-neering 108(11) (2016), 1307–1342.

∗Corresponding author: Matthias Rambausek (� rambausek@mechbau.uni-stuttgart.de)

References 35

[5] J. Schroder, M. Labusch, and M.-A. Keip: Algorithmic two-scale transitionfor magneto-electro-mechanically coupled problems: FE2-scheme: Localizationand homogenization. Computer Methods in Applied Mechanics and Engineering302 (2016), 253–280.

36 Abstracts

Lead-free Na1/2Bi1/2TiO3-based piezoceramiccomposites

Jurgen Rodel1,∗, Lukas M. Riemer1 , K.V. Lalitha1 and Jurij Koruza1

1Institute of Materials Science, Technische Universitat Darmstadt, Alarich-Weiss-Str. 2,64287 Darmstadt, Germany

AbstractIn the past two decades, the environmental toxicity imposed by the use and disposalof lead-based piezoelectrics led to strong research efforts. The good piezoelectricproperties make (1-x)Na1/2Bi1/2TiO3-xBaTiO3 (NBT-xBT) solid solution a key can-didate as a low-cost lead-free alternative. In the recent research effort, the potentialdevelopment of composites including a hard second phase had not been considered,as this may hinder the development of large strains. We demonstrate in the followingtwo cases, where these composites lead to greatly improved properties.

The composites of NBT-xBT with ZnO inclusions had been demonstrated to increasethe depolarization temperature, Td [3]. The delayed thermal depolarization behav-ior of the composites is rationalized on the basis of two competing mechanisms -an increase in the transition temperature from ferroelectric to relaxor state (TF−R),thereby enhancing Td, and a stress induced shift in depolarization-temperature re-sulting in a broadened depolarization behavior [2].

The ZnO inclusions were also found to exert a clamping effect that elastically re-stricts the ability for domain wall movement. In applications, were so-called hardpiezoceramics are required, low losses, a high coercive field and a high electrome-chanical coupling factor Qm is required. A two-fold increase in Qm was observed forthe composites with NBT-6BT. Akin to other hard piezoelectrics, a decrease in thesaturation polarization and total strain was observed [1].

References[1] K. Lalitha, L. M. Riemer, J. Koruza, and J. Rodel: Hardening of elec-

tromechanical properties in piezoceramics using a composite approach. Appl.Phys. Let. accepted (2017).

[2] L. M. Riemer, L. K. Venkataraman, X. Jiang, N. Liu, C. Dietz, R. Stark,P. B. Groszewicz, G. Buntkowsky, J. Chen, S.-T. Zhang, J. Rodel, andJ. Koruza: Stress-Induced Phase Transition in Lead-Free Relaxor FerroelectricComposites. Acta Materialia submitted (2017).

[3] J. Zhang, Z. Pan, F.-F. Guo, W.-C. Liu, H. Ning, Y. B. Chen, M.-H. Lu,B. Yang, J. Chen, S.-T. Zhang, X. Xing, J. Rodel, W. Cao, and Y.-F.Chen: Semiconductor/relaxor 0-3 type composites without thermal depolariza-tion in Bi0.5Na0.5TiO3 –based lead-free piezoceramics. Nature Communications6 (2015), 6615.

∗Corresponding author: Jurgen Rodel (� roedel@ceramics.tu-darmstadt.de)

References 37

Shape sensitivity and homogenization forpiezo-poroelastic microstructures

Eduard Rohan1,∗ and Vladimır Lukes1

1European Centre of Excellence, NTIS – New Technologies for Information SocietyFaculty of Applied Sciences, University of West Bohemia, Univerzitnı 8, 30614 Pilsen,

Czech Republic

AbstractThe paper is devoted to the issues of homogenization and sensitivity analysis inmodelling of porous media constituted by piezoelectric porous skeleton with poressaturated by viscous fluid. Such materials can be generated as periodically distributedmicro-devices with many potential applications. Each microdevice is a copy of therepresentative volume element containing the piezoelectric solid part (the matrix) andthe viscous fluid saturated the pores (the channels).The macroscopic model was derived using the unfolding method of the periodic ho-mogenization [4], cf. [1]. The obtained model is an extension of the Biot modelcharacterized by the poroelastic coefficients modified by piezoelectric coupling effects.The present paper focuses on the shape sensitivity analysis (SSA) of the homogenizedcoefficients describing the effective medium properties. We extend the results of [3]for the porous medium. The SSA can be used in at least two different situations:1) the microstructure design to optimize desired effective properties, possibly leadingto function-graded metamaterials, 2) to extend the linear model beyond its scopefollowing the ideas of [2]. In the latter case, assuming the linear kinematics frame-work, the physical nonlinearity in the upscaled model is introduced in terms of thedeformation-dependent material coefficients which are approximated as linear func-tions of the macroscopic response expressed by the deformation, fluid pressure andthe electric field. Numerical illustrations will be given.

References[1] B. Miara, E. Rohan, M. Zidi, and B. Labat: Piezomaterials for bone regener-

ation design - homogenization approach. Jour. of the Mech. and Phys. of Solids(2005), 2529–2556.

[2] E. Rohan and V. Lukes: On modelling nonlinear phenomena in deforming het-erogeneous media using homogenization and sensitivity analysis concepts. Ap-plied Mathematics and Computation 267 (2015), 583–595.

[3] E. Rohan and B. Miara: Homogenization and shape sensitivity of microstruc-tures for design of piezoelectric bio-materials. Mechanics of Advanced Materialsand Structures 13 (2006), 473–485.

[4] E. Rohan, V. Lukes, and R. Cimrman: “Homogenization of the fluid-saturatedpiezoelectric porous metamaterials”. In: Coupled Problems in Science and En-gineering VII. Vol. 7. 2017, 1080–1091.

∗Corresponding author: Eduard Rohan (� rohan@kme.zcu.cz)

38 Abstracts

Influence of matrix and interface cracking on theeffective constitutive behaviour of multiferroic

compositesAlexander Schlosser1,∗, Artjom Avakian1 and Andreas Ricoeur1

1Chair of Engineering Mechanics/Continuum Mechanics, Institute of Mechanics,University of Kassel, Monchebergstraße 7, 34125 Kassel, Germany

AbstractThe coupling of magnetic and electric fields due to the constitutive behavior of amaterial is commonly denoted as magnetoelectric effect. The latter is only observedin a few crystal classes exhibiting a very weak coupling, mostly at low temperatures,which can hardly be exploited for technical applications. Much larger coupling coef-ficients are obtained at room temperature in composite materials with ferroelectricand ferromagnetic constituents. The magnetoelectric effect is then induced by thestrain field converting electrical and magnetic energies based on the piezoelectric andmagnetostrictive effects.The coupling of magnetic and electric fields due to the con-stitutive behavior of a material is commonly denoted as magnetoelectric effect. Thelatter is only observed in a few crystal classes exhibiting a very weak coupling, mostlyat low temperatures, which can hardly be exploited for technical applications. Muchlarger coupling coefficients are obtained at room temperature in composite materialswith ferroelectric and ferromagnetic constituents. The magnetoelectric effect is theninduced by the strain field converting electrical and magnetic energies based on thepiezoelectric and magnetostrictive effects.

The constitutive modeling of nonlinear multifield behavior as well as the finite ele-ment implementation are presented [1, 3]. Nonlinear material models describing themagneto-ferroelectric or electro-ferromagnetic behaviors are presented[1, 2]. Bothphysically and phenomenologically motivated constitutive models have been devel-oped for the numerical calculation of principally different nonlinear magnetostrictivebehaviors. On this basis, the polarization in the ferroelectric and magnetization inthe ferromagnetic constituents, respectively, are simulated and the resulting effectsare analyzed. Damaging processes are taken into account by models for micro crackgrowth in the ferroelectric constituent and cohesive zones at the boundary layers.The cohesive zone elements describe the degradation of mechanical, magnetic andelectrical features during delamination. Numerical simulations finally focus on theinvestigation of magnetoelectric coupling in particulate and laminated composites,revealing the essential role of damage going along with the poling process. Final goalof the research is to optimize magnetoelectric devices e.g. with respect to favorableelectric-magnetic poling sequences or geometric arrangements.

∗Corresponding author: Alexander Schlosser (� alexander.schlosser@uni-kassel.de)

References 39

References[1] A. Avakian and A. Ricoeur: Constitutive modeling of nonlinear reversible and

irreversible ferromagnetic behaviors and application to multiferroic composites.Journal of Intelligent Material Systems and Structures 27(18) (2016), 2536–2554.

[2] A. Avakian and A. Ricoeur: An extended constitutive model for nonlinearreversible ferromagnetic behaviour under magnetomechanical multiaxial loadingconditions. Journal of Applied Physics 121(5) (2017), 053901.

[3] A. Avakian, R. Gellmann, and A. Ricoeur: Nonlinear modeling and finiteelement simulation of magnetoelectric coupling and residual stress in multiferroiccomposites. Acta Mechanica 226(8) (2015), 2789–2806.

40 Abstracts

Towards a Variational Level Set Formulation forMicrostructure Evolution in Ferroelectrics

Robin Schulte1,∗, Andreas Menzel1,2 and Bob Svendsen3,4

1Institute of Mechanics, TU Dortmund, Leonhard-Euler-Strasse 5, 44227 Dortmund,Germany

2Division of Solid Mechanics, Lund University, P.O. Box 118, SE-22100 Lund, Sweden3Chair of Material Mechanics, RWTH Aachen University, Schinkelstrasse 2, 52062

Aachen, Germany4Department of Microstructure Physics and Alloy Design, Max Planck Institute for Iron

Research, Max-Planck Strasse 1, 40237 Dusseldorf, Germany

AbstractModelling frameworks such as level set formulations and phase field fomulations pro-vide more information about domain wall kinetics in ferroelectrics as compared to,e. g. , phenomenological models, since the microstructure is fully resolved in space andtime. In contrast to phase field models applied to the simulation of ferroelectrics, thatprovide a continuous transition between the domains, the classic level set approach isa sharp interface framework incorporating the jump conditions on the domain walls.In most cases, the level set function is defined as a signed distance function to theinterface. Due to numerical errors, additional methods are required to ensure thatthe level set function remains as a signed distance function. The most common ap-proach is the application of reinitialization algorithms, though these methods involvea high computational effort. In contrast, using a variational approach, the deviationfrom the signed distance function is penalised by an additional internal energy term.Hence, the level set function remains a priori a signed distance function.First examples are presented showing the domain wall kinetics for ferroelectric mate-rials under electromechanical loading. Furthermore, the visualisation of the level setfunction shows that the variational approach satisfies the constraint for the signeddistance function without reinitialization during the simulations.

References[1] V. K. Kalpakides and A. I. Arvanitakis: A level set approach to domain wall

kinetics and domain patterning in elastic ferroelectrics. Computer Methods inApplied Mechanics and Engineering 199 (2010), 2865–2875.

[2] C. Li, C. Xu, C. Gui, and M. D. Fox: Level Set Evolution Without Re-initialization: A New Variational Formulation. Proceedings of the 2005 IEEEComputer Society Conference on Computer Vision and Pattern Recognition (2005).

[3] S. Osher and R. Fedkiw: Level Set Methods and Dynamic Implicit Surfaces.New York: Springer, 2003.

∗Corresponding author: Robin Schulte (� robin.schulte@tu-dortmund.de)

References 41

In situ observations of viscoelastic property evolutionduring electrical fatigue of PZT

Wei Lin Tan1,∗, A. Vidyasagar1,2 , Katherine T. Faber1 andDennis M. Kochmann1,2

1Division of Engineering and Applied Science, California Institute of Technology,Pasadena, CA 91125, USA

2Mechanics and Materials, Department of Mechanical and Process Engineering, ETHZurich, 8092 Zurich, Switzerland

AbstractFerroelectrics are ubiquitous in our daily lives, in devices such as actuators, infrareddetectors and non-volatile memory. It has also recently been shown using BroadbandElectromechanical Spectroscopy (BES) that domain switching in ferroelectrics causeshigh damping at the coercive field [4]. The high stiffness of ferroelectric ceramics andthe ability to control damping in the material gives it great promise in engineeringapplications.However, it is also well known that extended bipolar electrical cycling causes decreasedpolarization magnitude as well as micro- and macro-cracking. To observe in situ theeffects of fatigue on the electrical and mechanical properties of bulk PZT ceramics,we employ BES to determine polarization, relative stiffness, and damping of sampleswith time. We further compare measured values with SEM micrographs of microcrackdensity at different numbers of cycles, and use existing models to relate the observedmicrostructure to the measured viscoelastic and electrical properties [1–3].

References[1] M. Kachanov: Effective Elastic Properties of Cracked Solids: Critical Review

of Some Basic Concepts. Applied Mechanics Reviews 45 (1992), 304–335.[2] S. J. Kim and Q. Jiang: Microcracking and electric fatigue of polycrystalline

ferroelectric ceramics. Smart Materials and Structures 5 (1996), 321–326.[3] K. Y. Sze and N. Sheng: Polygonal finite element method for nonlinear con-

stitutive modeling of polycrystalline ferroelectrics. Finite Elements in Analysisand Design 42 (2005), 107–129.

[4] C. S. Wojnar, J.-B. le Graverend, and D. M. Kochmann: Broadband controlof the viscoelasticity of ferroelectrics by electric fields. Applied Physics Letters.105(16) (2014), 162912–162916.

∗Corresponding author: Wei Lin Tan (� wtan@caltech.edu)

42 Abstracts

Non-Linear Dynamics of a Circular PiezoelectricMulti-Layer Plate

Florian Toth1,∗, Manuel Dorfmeister2 , Michael Schneider2 , Ulrich Schmid2 andManfred Kaltenbacher1

1Institute of Mechanics and Mechatronics, TU Wien,Getreidemarkt 9, 1060 Vienna, Austria

2Institute of Sensor and Actuator Systems, TU Wien,Gusshausstrasse 27-27, 1040 Vienna, Austria

AbstractIn digital sound reconstruction (DSR) the audiable sound is a superposition of shortsound pulses generated by set of acoustic transducers, a so called array of speaklets.Each transducer is a microelectromechanical systems (MEMS) consisting of circular,plate-like structure with several functional layers. The producible volume is propor-tional to the stroke level of the transducers. Therefore, the transducer is operatedwithin the post-buckling range.By a carefully controlled production process pre-stresses are introduced generating bi-stable structures. These show multiple possible equilibrium configurations with largedeflections. Piezoelectric actuation is then used to switch between the equilibriumconfigurations. We develop a modelling strategy suitable for the tailored design ofthe MEMS system.The pre-stress introduced by the production process is modelled by linear thermalexpansion. A plate model for the multi-layer structure is used to obtain a computa-tionally efficient formulation. The active piezoelectric layers are included by using anon-local constitutive relation [1]. The geometrical non-linearity arising from largetransverse displacements is taken into account by using von Karman theory. Ex-ploiting the rotational symmetry of the structure the governing partial differentialequations can be reduced to a set of coupled, non-linear ordinary differential equa-tions. Finally, we use the developed model to explore the non-linear dynamics of thesystem.

References[1] M. Krommer: The significance of non-local constitutive relations for composite

thin plates including piezoelastic layers with prescribed electric charge. SmartMaterials and Structures 12(3) (2003), 318–330. doi: 10.1088/0964-1726/12/3/302.

∗Corresponding author: Florian Toth (� florian.toth@tuwien.ac.at)

References 43

Experimentally probing magnetoelectric coupling atthe local scale

Harsh Trivedi1,∗, Vladimir V. Shvartsman1 , Doru C. Lupascu1 , Robert C. Pullar2 ,Andrei Kholkin2 , Pavel Zelanovskiy3 and Vladimir Ya Shur3

1Anstitute for Materials Science and Center for Nanointegration Duisburg-Essen(CENIDE), University of Duisburg-Essen, Universitatsstraße 15, 45141 Essen, Germany

2CICECO, University of Aveiro, 3810-193, Aveiro, Portugal3Center for Shared Use ”Modern Nanotechnology”, Institute of Natural Sciences, Ural

Federal University, 620000, Yekaterinburg, Russia

AbstractMultiferroic composites, which have emerged as an ideal solution for room tem- per-ature magnetoelectricity, involve a strain mediated effective coupling. Hence it be-comes evident to explore the coupling mechanism from a microscopic per- spective.Recently, attempts have been made to construct robust models for understandingthe strain mediated magnetoelectric effect in composites with var- ious morpholo-gies. Such models require experimental support. On the details of coupling, a properunderstanding about the behavior of the strain mediation in the vicinity of the in-terface between the constituent phases is still lacking. In this study we demon-strate the potential of various cantilever based microscopic tech- niques like Piezore-sponse Force Microscopy (PFM), Magnetic Force Microscopy (MFM), Kelvin ProbeForce Microscopy (KPFM), Micro-Raman, in studying the local manifestations ofthe strain mediated magnetoelectric effect in vari- ous classical composite systemslike Co/NiFe2O4 – BaTiO3 and Ba/SrFe12O19 – BaTiO3. The outcomes present anopportunity to gauge the magnitude of the effect locally.

∗Corresponding author: Harsh Trivedi (� harsh.trivedi@uni-due.de)

44 Abstracts

Study of Converse Magnetoelectric Effect inNiFe2O4-(Ba,Ca)(Zr,Ti)O3 multiferroics

M. Naveed-Ul-Haq1,∗, Vladimir V. Shvartsman1 , Harsh Trivedi1 , Soma Salamon2 ,Heiko Wende2 and Doru C. Lupascu1

1Institute for Materials Science and Center for Nanointegration Duisburg-Essen(CENIDE), University of Duisburg-Essen, Universitatsstraße 15, 45141 Essen, Germany

2Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE),University of Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany

AbstractMaterials exhibiting piezoelectricity and some form of magnetism simultaneously havebecome quite popular at the end of the 20th century. In this class of ma- terialsthe electric properties can be controlled via external magnetic field and conversely,magnetism can be induced or controlled via applied voltage/field. We in particu-lar consider the latter effect. It leads to a variety of applications in spintronics,memories, and tunnel junctions. Here we present the electrical con- trol of inducedmagnetization in bulk ceramic composites consisting of (Ba,Ca) (Zr,Ti)O3 as the fer-roelectric/piezoelectric phase and NiFe2O4 as the magnetic phase. The compositeshave been manufactured via solid state synthesis, and their structure has been verifiedvia x-ray diffraction combined with Rietveld analysis. We demonstrate that the sam-ples show an excellent converse magne- toelectric effect of 45 ps/m, which is almosttwice as large as it has been reported for samples prepared under similar conditions.

∗Corresponding author: M. Naveed-Ul-Haq (� naveed.ul-haq@uni-due.de)

References 45

Understanding domain patterning andelectromechanical behaviour in bulk ferroelectrics

using spectral phase field techniquesA. Vidyasagar1,2,∗, W. L. Tan2 and D.M. Kochmann1,2

1ETH Zurich, Ramistrasse 101, 8092 Zurich, Switzerland2GALCIT, California Institute of Technology, CA 91125, USA

AbstractKinetics of bulk polycrystalline ferroelectric ceramics such as barium titanate (Ba-TiO3) and lead zirconate titanate (PZT) are not well understood due to the rangeof length and time scales involved. Utilizing a spectral approach, the electrome-chanical problem is solved using diffuse interface phase field modeling. The insightsderived from this approach include prediction of patterns in polycrystalline ferro-electrics, understanding influences of grain size and misorientation and the motionof domain walls across grain boundaries and pinning sites. Computational predic-tions for electromechanical microstructure evolution, and macroscopic homogenisedpolarisation and strain hysteresis, show convincing agreement with our experimentalobservations. The coupling of a phase field damage model, as well as temperaturedependent effective physics will also be discussed during this presentation.

∗Corresponding author: A. Vidyasagar (� vvidyasa@caltech.edu)

46 Abstracts

Phase field simulation with leakage currents fornanogenerator concepts

Franziska Wohler1,∗, Ingo Munch1 , Chad M. Landis2 and Werner Wagner1

1Institute for Structural Analysis, Karlsruher Institute of Technology2Aerospace Engineering and Engineering Mechanics, University of Texas

AbstractWe design a nanogenerator on the base of ferroelectric thin films to transform para-sitic mechanical oscillations into usable electric energy. The conversion of mechanicalinto electrical energy is enabled by engineered electric polarization domain topology.Ambient vibrations deform the ferroelectric film such that electric polarization re-orders and causes electron flow between locally separated electrodes. Charging anelectric storage medium implies that a gradient of electric potential exists betweenelectrodes.Thus, leakage currents may appear between electroded surfaces if the fer-roelectric ceramic is not a perfect insulator. To optimize the nanogenerator concept,it is important to predict leakage currents. In literature, i.e. [1, 2], three mechanismsfor leakage currents J in ceramics are discussed: Ohm’s law, space-charge-limitedcurrent, and Schottky emission

J = σ 11 E , J = 98µκ0 εrE2 , J = A∗ T 2 exp

−e(φ0 −√

e E/4π εi κ0)kT

(3.1)

Therefore, we extend our formulation, which is based on the work of Su & Landis [3].We reformulate the terms in eq.(3.1) to bring into account that the electrical field Eis a vector out of R3 in our model. For instance, the space-charge-limited current isgiven by J = 9

8µκ0 εr‖E‖E .

References[1] H. Du, W. Liang, Y. Li, M. Gao, Y. Zhang, C. Chen, and Y. Lin: Leak-

age properties of BaTiO3 thin films on polycrystalline Ni substrates grownby polymer-assisted deposition with two-step annealing. J. Allo. Compds. 642(2015), 116–171.

[2] R. K. Pan, T. J. Zhang, J. Z. Wang, Z. J. Ma, J. Y. Eang, and D. F. Wang:Rectifying behavior and transport mechanisms of currents in Pt/ BaTiO3/Nb:SrTiO3 structure. J. Alloys Compd. 519 (2012), 140–143.

[3] Y. Su and C. M. Landis: Continuum thermodynamics of ferroelectric domainevolution: Theory, finite element implementation, and application to domain wallpinning. J. Mech. Phys. Solids 55 (2007), 280–305.

∗Corresponding author: Franziska Wohler (� franziska.woehler@kit.edu)

References 47

Phase field simulation of flexoelectricity inferroelectric materials

Bai-Xiang Xu1 and Shuai Wang1,∗

1Mechanics of Functional Materials Division, Department of Materials Science, TUDarmstadt

AbstractFlexoelectricity describes the linear coupling between the polarization and the straingradient or the coupling between the strain and the polarization gradient. [2] Unlikeother electromechanical coupling effects such as piezoelectricity, which require thenon-central symmetry of the structure, flexoelectricity applies to all crystal symme-tries. Due to the low theoretical values of flexocoupling coefficients, the study onflexoelectricity in solids had long been overlooked. In last decades, a series of experi-mental observations on large flexoelectric effect in ferroelectrics were reported by Maand Cross. [1] The flexoelectricity offers great opportunity to enhance the electrome-chanical coupling, and widen the choice of the materials. However, due to the highheterogeneity of strain and polarization in ferroelectrics, the interaction between theflexoelectric effect and the domain structure becomes complex, and effective modelingis required to reveal it and asisst the design.In this presentation, a continuum ferroelectric phase field model is coupled to flexo-electricity. For the ferroelectric properties, the polarization is regarded as the orderparameter in the phase field simulation. The evolution of the polarization is gov-erned by the time-dependent Ginzburg–Landau equation. By 2D simulation, thecomparison of domain patterns between samples with and without flexoelectric ef-fect is presented, which shows the importance of considering flexoelectric effect. Wealso observe that, the domain configuration in ferroelectrics is sensitive to differentcomponents of flexocoupling tensor. As one application example, the flexoelectricresponse of core-shell Bi1/2Na1/2TiO3-xSrTiO3 nanoparticles at high temperature ismodeled, along with comparison with the related Transmission Electron Microscopyobservations.

References[1] W. Ma and L. E. Cross: Flexoelectric polarization of barium strontium titanate

in the paraelectric state. Applied Physics Letters 81(18) (2002), 3440–3442.[2] P. Zubko, G. Catalan, and A. K. Tagantsev: Flexoelectric effect in solids.

Annual Review of Materials Research 43 (2013), 387–421.

∗Corresponding author: Shuai Wang (� wang@mfm.tu-darmstadt.de)

48 Abstracts

Magnetoelastic coupling for magnetization switchingwith stochastic effects

Min Yi1,∗ and Bai-Xiang Xu1

1Division of Mechanics of Functional Materials, Institute of Materials ScienceTechnical University of Darmstadt

Jovanka-Bontschits-Str. 2, Darmstadt 64287, Germany

AbstractSwitching dynamics plays a fundamental role in the application of nanomagnets inspintronic devices for information storage. In order to achieve low-power devices,the voltage control of magnetization without electric current is recently widely ex-plored. One way to realize the voltage control of magnetization is to use piezoelec-tric/ferromagnetic heterostructure, in which the voltage induced strain in piezoelec-tric layer is transferred to ferromagnetic layer and thus change the magnetic state dueto the magnetoelastic coupling. Therefore, as the intrinsic mechanism, magnetoelasticcoupling plays a critical role.In this work, we will study the magnetoelastic coupling and its application in strain-mediated magnetization switching with the consideration of stochastic effects bothin the atomic scale and microscale. The atomic-scale stochastic effect is originatedfrom the magnetic materials themselves. For example, in (CoxFe1−x)2B alloy whichis widely used in magnetic tunnel junctions, the disordered arrangement of Fe andCo atoms at the crystallographic sites results in compositional randomness. The mi-croscale stochastic effect comes from the finite temperature, which induces thermalfluctuations and thus random fields exerted on the magnetic moment. In order todeal with this tow-scale feature and the above-mentioned stochastic effects, we willadopt a multiscale simulation scheme by inputting density functional theory (DFT)calculation results to the switching dynamics in ferromagnetic materials. The mag-netoelastic coupling coefficients and other magnetic parameters will be predicted byDFT calculations. Then strain-induced magnetization switching by using magnetoe-lastic coupling will be studied and the associated results will be analyzed statistically.

∗Corresponding author: Min Yi (� yi@mfm.tu-darmstadt.de)

Notes

49

50 Notes

List of Participants

51

52

A

Agiasofitou, EleniDarmstadt University of TechnologyHochschulstraße 664289 DarmstadtGermanyagiasofitou@mechanik.tu-darmstadt.de

Alber, Hans–DieterDarmstadt University of TechnologySchloßgartenstraße 764289 DarmstadtGermanyalber@mathematik.tu-darmstadt.de

B

Bartel, ThorstenDortmund University of TechnologyLeonard–Euler–Straße 544227 DortmundGermanythorsten.bartel@tu-dortmund.de

Boddu, VishalUniversity of Erlangen–NurembergPaul–Gordan–Straße 391058 ErlangenGermanyvishal.boddur@fau.de

Brands, DominikUniversity of Duisburg–EssenUniversitatsstraße 1545141 EssenGermanydominik.brands@uni-due.de

E

El Khatib, OmarTU Bergakademie FreibergLampadiusstraße 409599 FreibergGermanyomar.el-khatib@student.tu-freiberg.de

G

Grunebohm, Anna

University of Duisburg–EssenLotharstraße. 147048 DuisburgGermanyanna@thp.uni-due.de

H

Huber, John E.University of OxfordParks RoadOxfordUnited Kingdomjohn.huber@eng.ox.ac.uk

J

Jurgelucks, BenjaminUniversity of PaderbornWarburger Straße 10033098 PaderbornGermanybenjamin.jurgelucks@math.uni-paderborn.de

K

Kiefer, BjornTU Bergakademie FreibergLampadiusstraße 409599 FreibergGermanyBjoern.Kiefer@imfd.tu-freiberg.de

Kozinov, SergiiTU Bergakademie FreibergLampadiusstraße 409599 FreibergGermanysergii.kozinov@imfd.tu-freiberg.de

Krommer, MichaelWien University of TechnologyGetreidemarkt 91060 ViennaAustriamichael.krommer@tuwien.ac.at

Kuna, MeinhardTU Bergakademie FreibergLampadiusstraße 4

53

09596 FreibergGermanymeinhard.kuna@imfd.tu-freiberg.de

L

Labusch, MatthiasUniversity of Duisburg–EssenUniversitatsstraße 1545141 EssenGermanymatthias.labusch@uni-due.de

Lange, StephanUniversity of KasselMonchebergstraße 734109 KasselGermanystephan.lange@uni-kassel.de

Lemke, VeronicaUniversity of Duisburg–EssenUniversitatsstraße 1545141 EssenGermanyveronica.lemke@uni-due.de

Lupascu, Doru C.University of Duisburg–EssenUniversitatsstraße 1545141 EssenGermanydoru.lupascu@uni-due.de

M

Ma, YangbinDarmstadt University of TechnologyJovanka–Bontschits–Straße 264287 DarmstadtGermanyy.ma@mfm.tu-darmstadt.de

Mahnken, RolfUniversity of PaderbornWarburger Straße 10033098 PaderbornGermanymahnken@ltm.upb.de

Medipour, FatemehDresden University of TechnologyGermanyfatemeh.mehdipour@mailbox.tu-dresden.de

Menzel, AndreasDortmund University of TechnologyLeonard–Euler–Straße 544227 DortmundGermanykerstin.walter@tu-dortmund.de

Michaelis, NicolasSaarland UniversityCampus A5.166123 SaarbruckenGermanyn.michaelis@lmt.uni-saarland.de

N

Naveed–Ul–Haq, MuhammadUniversity of Duisburg–EssenUniversitatsstraße 1545141 EssenGermanynaveed.ul-haq@uni-due.de

P

Polukhov, EltenUniversity of StuttgartPfaffenwaldring 770569 StuttgartGermanypolukhov@mechbau.uni-stuttgart.de

R

Rodel, JurgenDarmstadt University of TechnologyAlarich-Weiss-Straße 2364287 DarmstadtGermanyroedel@ceramics.tu-darmstadt.de

Rambausek, MatthiasUniversity of StuttgartPfaffenwaldring 770569 StuttgartGermanyrambausek@ist.uni-stuttgart.de

Ricoeur, AndreasUniversity of KasselMonchebergstraße 734109 KasselGermanyricoeur@uni-kassel.de

Rohan, Eduard

54

University of West BohemiaUniverzitnı 830614 PilsenCzech Republicrohan@kme.zcu.cz

S

Salomon, SomaUniversity of Duisburg–EssenLotharstraße 147057 DuisburgGermanysoma.salomon@uni-due.de

Schlosser, AlexanderUniversity of KasselMonchebergstraße 734109 KasselGermanyalexander.schlosser@uni-kassel.de

Schroder, JorgUniversity of Duisburg–EssenUniversitatsstraße 1545141 EssenGermanyj.schroeder@uni-due.de

Schulte, RobinDortmund University of TechnologyLeonard–Euler–Straße 544227 DortmundGermanyrobin.schulte@tu-dortmund.de

Schulze, VeronikaUniversity of PaderbornWarburger Straße 10033098 PaderbornGermanyschulzev@math.uni-paderborn.de

Staudigl, ElisabethVienna University of TechnologyGetreidemarkt 91060 ViennaAustriaelisabeth.staudigl@tuwien.ac.at

Svendsen, BobRWTH Aachen UniversitySchinkelstraße 252062 AachenGermanyanika.knops@cmm.rwth-aachen.de

T

Tan, Wei-LinCalifornia Institute of Technology1200 E. California Blvd. MC 138-78Pasadena, CA 91125United States of Americawtan@caltech.edu

Toth, FlorianVienna University of TechnologyGetreidemarkt 91060 ViennaAustriaflorian.toth@tuwien.ac.at

Trivedi, HarshUniversity of Duisburg–EssenUniversitatsstraße 1545141 EssenGermanyharsh.trivedi@uni-due.de

V

Vidyasagar, AnanthanETH ZurichTannenstrasse 38092 ZurichSwitzerlandvvidyasa@caltech.edu

W

Wohler, FranziskaKarlsruhe Institute of TechnologyKaiserstraße 1276131 KarlsruheGermanyfranziska.woehler@kit.edu

Webers, SamiraUniversity of Duisburg–EssenLotharstraße 147048 DuisburgGermanysamira.webers@uni-due.de

Wingen, MariusUniversity of KasselMonchebergstraße 734125 KasselGermanymarius.wingen@uni-kassel.de

X

55

Xu, Bai-XiangDarmstadt University of TechnologyJovanka–Bontschits–Straße 264287 DarmstadtGermanyxu@mfm.tu-darmstadt.de

Y

Yi, MinDarmstadt University of TechnologyJovanka–Bontschits–Straße 264287 DarmstadtGermanyyi@mfm.tu-darmstadt.de