3 Seminar on Ferroic Functional Materials and 13

Home , Darmstadt, Kassel, University of Kassel

3rd Seminar on Ferroic functional Materials

and

13th International Workshop on direct and inverse 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

ferroic m terials functional

FOR 1509: DFG Research Unit

Preface

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

It is a great pleasure and honor for the local organizers, Andreas Ricoeur and Stephan Lange, to have the opportunity to host the combined seminar in Kassel this year. We are particularly pleased that BjörnKiefer from TU Bergakademie Freiberg has joined our 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 Economic Excellence (LOEWE–“Safer Materials”) for their financial support.

Kassel and Freiberg, October 2017 Andreas Ricoeur Bjorn¨ Kiefer Stephan Lange

i ii

Organizers

Prof. Dr.–Ing. habil. Andreas Ricoeur Chair of Engineering Mechanics / Continuum Mechanics Institute of Mechanics University of Kassel M¨onchebergstraße 7 34125 Kassel, Germany [email protected]

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

Prof. Dipl.–Ing. Bj¨ornKiefer, Ph. D. Chair of Applied Mechanics–Solid Mechanics Institute of Mechanics and Fluid Dynamics TU Bergakademie Freiberg Lampadiusstraße 4 09596 Freiberg, Germany [email protected]

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

Dr.–Ing. Stephan Lange Chair of Engineering Mechanics / Continuum Mechanics Institute of Mechanics University of Kassel M¨onchebergstraße 7 34125 Kassel, Germany [email protected]

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

Conference Committee

Thorsten Bartel (Dortmund University of Technology) Dominik Brands (University Duisburg – Essen) Marc–AndréKeip (University of Stuttgart) Doru C. Lupascu (University Duisburg – Essen) Andreas Menzel (Dortmund University of Technology) Ralf Müller(Kaiserslautern University of Technology) JörgSchröder(University Duisburg – Essen) Paul Steinmann (Friedrich – Alexander – University Erlangen – Nuremberg) Bob Svendsen (RWTH Aachen University) Bai–Xiang Xu (Darmstadt University of Technology) iv Contents

1 General Information1 1.1 Venue and traveling to Kassel...... 2 1.2 Accommodation...... 2 1.3 Social program and conference dinner...... 4 1.4 Access to the WiFi Network...... 4 1.5 Informations for presenting authors and session chairs...... 5 1.5.1 Time for each talk...... 5 1.5.2 Technical equipment in the lecture room...... 5

2 Program7 2.1 Time schedule...... 8 2.2 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 Kassel

The conference will be held at the “Campus Holl¨andischer Platz” at the University of 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.

Campus Holl¨andischer Platz Detailed city map s. Fig. 1.2

Railway station Kassel–Wilhelmsh¨ohe

Fig. 1.1 Detail of the city map

Kassel is well connected to the national rail network. High speed trains, such as the InterCityExpress (ICE) and the InterCity (IC) stop at the railway station “Kassel– Wilhelmshöhe”. Kassel central station is reduced to a regional station. There are no direct connections to ICE or IC. Arriving by train at “Kassel–Wilhelmshöhe”,the “Campus Holländischer Platz” is directly connected by tram. Fastest connections are tram no. 1 (into the direction “Vellmar” – station “Holländischer Platz/Universität”) and tram no. 3 (into the direction “IhringshäuserStraße” – station “Katzensprung”), s. Fig. 1.2. Getting to Kassel by car is also possible, while Kassel is, via the motorways A7 and A44, directly connected to the German motorway network. Traveling by car, please use the following address:

M¨onchebergstraße 1 34125 Kassel

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

1.2 Accommodation

The accommodation is not included in the conference fee. A limited number of rooms has been reserved in the following two hotels, both located in a walking distance to the conference venue, s. Fig. 1.2, with special rates for participants, until July 31, 2017: 3

Restaurant Moritz Campus Holl¨andischer Platz

Station Holl¨andischer Platz/Universit¨at Tram No. 1/5 and RT No. 1/4

Hotel Deutscher Hof Lectures

Station Lutherplatz Parking spot Tram No. 7

Station Katzensprung Tram No. 3/6/7 Station Am Stern Each Tram and RT No. 1/4

Station Altmarkt Tram No. 3/4/6/7/8

Meeting point guided city tour Hotel Renthof Kassel

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

Fig. 1.2 Map of the center and the campus Holl¨andischer Platz

1. Hotel Renthof Kassel Renthof 3 34117 Kassel Single Room: e 65,00 per night plus breakfast e 8,50 Booking code: A2016-0051 www.renthof-kassel.de Traveling by train, via railway station “Kassel–Wilhelmshöhe”,the fastest con- nection to the Hotel Renthof Kassel is tram no. 3 (into the direction “Ihrings- häuserStraße”). Other possible tram connections are tram no. 4 (into the direction “Helsa” or “Hessisch Lichtenau”) and tram no. 7 (into the direction “IhringshäuserStraße”). But these connections last longer. For all connections use the station “Altmarkt/Regierungspräsidum”to get to the Hotel Renthof Kassel, s. Fig. 1.2. 4 General Information

2. Hotel Deutscher Hof Lutherstraße 3–5 34117 Kassel Single Room: e 60,00 per night incl. breakfast Double Room (for single use): e 85,00 per night incl. breakfast Booking code: Piezo-Workshop, University of Kassel www.deutscher-hof.de Traveling by train, via railway station “Kassel–Wilhelmshöhe”,the fastest connections to the Hotel Deutscher Hof are the tram no. 1 (into the direction “Vellmar”) and tram no. 3 (into the direction “IhringshäuserStraße”). Use station “Am Stern” to get to the Hotel Deutscher Hof. An other possibility, more comfortable but it last longer, is tram no. 7 (into the direction “Ihringshäusser Straße”). Traveling with tram no. 7 use the station “Lutherplatz” directly in front 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 dinner

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

Tourist information Wilhelmstraße 23 34117 Kassel

Walking distance from both hotels to the meeting point is about 15 minutes. From the “Campus Holl¨andischer Platz” there are diﬀerent tram connections. Except tram no. 7, each tram stops at the station “Rathaus”, where the walking distance is about two minutes to the meeting point, s. Fig. 1.2. The tour will end at the restaurant of the Hotel Renthof Kassel, where the conference dinner will take place. Approximate duration of the tour is two hours. Participants who do not join the city tour, please come to the Hotel Renthof Kassel at 7 p.m.

1.4 Access to the WiFi Network

In the lecture room and on the campus the eduroam network is available. To connect with this network, please use your private eduroam account. For participants who do not have an eduroam account, a special workshop account is oﬀered. Connect your device with the eduroam network and enter the following data:

Username: Piezo2017 Password: Will be announced at the beginning of the seminar 5

1.5 Informations for presenting authors and session chairs

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

1.5.2 Technical equipment in the lecture room The lecture room is equipped with a beamer and a laptop. A presenter is provided by the organizers. On the laptop Microsoft PowerPoint 2010 as well as an actual version of Adobe Acrobat Reader is installed. Due to well known problems with different versions of Microsoft Office, the participants presenting their work with PowerPoint are highly recommended to have a PDF version as a backup. It is also possible to use an own laptop. Available connections are VGA and HDMI. Any adapters to VGA or HDMI have to be organized by the presenting speaker, if necessary. Speakers of the upcoming session are asked to be in the lecture room ten minutes before the first talk to copy their presentation on the local laptop or to check their own laptop with the technique of the lecture room. 6 General Information 2 Program

7 8 Program

2.1 Time schedule

Wednesday Thursday Friday October 4th October 5th October 6th 08:00 Elten Polukhov Bai-Xaing Xu 08:30 08:30 Robin Schulte Benjamin Jurgelucks 08:45 09:00 Alexander Schlosser Eduard Rohan 09:15 09:30 BjörnKiefer Eleni Agiasofitou 09:45 10:00 Coffee Break Coffee Break 10:15 10:30 Meinhard Kuna Vishal Boddu 10:45 11:00 Wei–Lin Tan Franziska Wöhler 11:15 11:30 Registration Sergii Kozinov Ananthan Vidyasagar 11:45 12:00 12:15 Coffee Break 12:30 Lunch Break Lunch Break 12:45 Welcome Restaurant Moritz Restaurant Moritz 13:00 13:15 John Huber (invited) 13:30 Nicolas Michaelis 13:45 JürgenRödel(invited) Doru Lupascu 14:00 Thorsten Bartel 14:15 Harsh Trivedi Hans–Dieter Alber 14:30 Coffee Break 14:45 Soma Salamon Elisabeth Staudigl 15:00 Yangbin Ma 15:15 Coffee Break Florian Toth 15:30 Anna Grünebohm 15:45 Closing Matthias Labusch 16:00 16:15 Veronica Lemke 16:30 16:45 Matthias Rambausek 17:00 17:15 Min Yi 17:30 17:45 Guided City Tour 18:00 18:15 18:30 18:45 FOR 1509 19:00 19:15 Conference Dinner 19:30 Renthof Kassel 19:45 (open end) 20:00 20:15 9

2.2 Detailed program

The title of a talk is linked to the appropriate abstract. For further contact information, the leading author is linked to the list of participants.

Wednesday, October 4th

Welcome 12:45 – 13:00 Chair: Bj¨ornKiefer R 0019, KW 5 12:45 Opening speech Andreas Ricoeur

Session No. 1 13:00 – 15:15 Chair: Bob Svendsen R 0019, KW 5 13:00 Some properties of laminates of coupled materials John E. Huber – Yu Zhou

13:45 Measuring magnetoelectric coupling at diﬀerent scales Doru C. Lupascu – Heiko Wende – Vladimir V. Shvartsman – Soma Salamon – Samira Webers – Ahmadshah Nazrabi – Harsh Trivedi – Muhammad Naveed Ul–Haq – Joachim Landers – Carolin Schmitz–Antoniak

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

14:45 Study of Converse Magnetoelectric Eﬀect in NiFe2O4-(Ba,Ca)(Zr,Ti)O3 multiferroics Muhammad Naveed–Ul–Haq – Vladimir V. Shvartsman – Harsh Trivedi – Soma Salamon – Heiko Wende – Doru C. Lupascu

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

Session No. 2 15:45 – 17:45 Chair: Doru C. Lupascu R 0019, KW 5 15:45 The magneto–electric coupling in multiferroic composites: A two–scale homogenization approach Matthias Labusch – J¨orgSchr¨oder

16:15 Comparison of numerical simulation and experimental data of magneto–electric composites Veronica Lemke – Matthias Labusch – J¨orgSchr¨oder– Heiko Wende

16:45 Magneto–electric coupling in soft–matter–based composites Matthias Rambausek – Marc–Andr´eKeip 10 Program

17:15 Magnetoelastic coupling for magnetization switching with stochastic eﬀects Min Yi – Bai–Xiang Xu

Thursday, October 5th

Session No. 3 08:00 – 10:00 Chair: Andreas Menzel R 0019, KW 5 08:00 Computational Multi-Scale Stability Analysis of Two-Phase Periodic Electroactive Polymer Composites at Finite Strains Elten Polukhov – Daniel Vallicotti – Marc-Andr´eKeip

08:30 Towards a Variational Level Set Formulation for Microstructure Evolution in Ferroelectrics Robin Schulte – Andreas Menzel – Bob Svendsen

09:00 Inﬂuence of matrix and interface cracking on the eﬀective constitutive behaviour of multiferroic composites Alexander Schlosser – Artjom Avakian – Andreas Ricoeur

09:30 Homogenization schemes for magnetic solids based on concepts of energy relaxation Bj¨ornKiefer – Thorsten Bartel

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

Session No. 4 10:30 – 12:00 Chair: J¨org Schr¨oder R 0019, KW 5 10:30 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 during electrical fatigue of PZT Wei Lin Tan – Ananthan Vidyasagar – Katherine T. Faber – Dennis M. Kochmann

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

Lunch 12:00 – 13:30 Restaurant Moritz, AB 13 11

Session No. 5 13:30 – 14:30 Chair: Andreas Ricoeur R 0019, KW 5 13:30 Condition Monitoring of Shape Memory Material Stabilization Nicolas Michaelis – Marvin Schmidt – Felix Welsch – Stefan Seelecke – Andreas Sch¨utze

14:00 A Finite–Element–based macroscopic framework for the modelling of variant switching in MSMA Thorsten Bartel – Bj¨ornKiefer – Karsten Buckmann – Andreas Menzel

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

Session No. 6 15:00 – 16:00 Chair: Thorsten Bartel R 0019, KW 5 15:00 Tailoring the Hysteresis and Electrocaloric Eﬀect by Defect Engineering Yang–Bin Ma – Karsten Albe – Bai–Xing Xu

15:30 Modeling the impact of domain walls on the electro calcoric response Anna Gr¨unebohm – Madhura Marathe – Claude Ederer

Guided City Tour 17:00 – 19:00

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

Conference Dinner 19:00 – open end

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

Friday, October 6th

Session No. 7 08:00 – 10:00 Chair: Meinhard Kuna R 0019, KW 5 08:00 Phase ﬁeld simulation of ﬂexoelectricity in ferroelectric materials Bai-Xiang Xu – Shuai Wang

08:30 Piezoelectric Material Characterization aided by Algorithmic Diﬀerentiation Benjamin Jurgelucks 12 Program

09:00 Shape sensitivity and homogenization for piezo–poroelastic microstructures Eduard Rohan – Vladim´ırLuke˘s

09:30 Mathematical modeling of piezoelectric quasicrystals Eleni Agiasoﬁtou – Markus Lazar

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

Session No. 8 10:30 – 12:00 Chair: Bj¨orn Kiefer R 0019, KW 5 10:30 A preliminary study on the emergence of ferroelectricity Vishal Boddu – Paul Steinmann

11:00 Phase field simulation with leakage currents for nanogenerator concepts Franziska Wöhler – Ingo Münch – Chad M. Landis – Werner Wagner

11:30 Understanding domain patterning and electromechanical behaviour in bulk ferroelekctrics using spectral phase ﬁeld techniques Ananthan Vidyasagar – Wei Lin Tan – Dennis M. Kochmann

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

Session No. 9 13:30 – 15:45 Chair: Dominik Brands R 0019, KW 5 13:30 Lead–free Na1/2Bi1/2TiO3–based piezoelectric composites J¨urgenR¨odel – Lukas M. Riemer – K. V. Lalitha – Jurij Koruza

14:15 A sharp interface model for phase interfaces without misﬁt of the crystal lattice Hans–Dieter Alber

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

15:15 Non–Linear Dynamics of a Circular Piezoelectric Multi–Layer Plate Florian Toth – Manuel Dorfmeister – Michael Schneider – Ulrich Schmid – Manfred Kaltenbacher 13

Closing 15:45 – 16:00 Chair: Dominik Brands R 0019, KW 5 15:45 Closing words Bj¨ornKiefer 14 Program 3 Abstracts

The abstracts are arranged in alphabetical order of the presenting author.

15 16 Abstracts

Mathematical modeling of piezoelectric quasicrystals

Eleni Agiasoﬁtou1,∗ and Markus Lazar1

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

Abstract

Quasicrystals were discovered by Shechtman in 1982. They belong to aperiodic crystals and possess long-range orientational order but no translational symmetry. Shecht- man was awarded the 2011 Nobel Prize in Chemistry for his great discovery. Due to their structure, quasicrystals have some particular (mechanical, electronic, ther- modynamical, chemical, etc.) properties, which could be characterized as desirable properties; such as low friction coefficient, high wear resistance, and low adhesion. These properties give to quasicrystals advantages in comparison to other conventional materials used today. Nowadays, quasicrystals represent an interesting class of novel materials, 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 quasicrystals with special focus on the constitutive modeling due to its special features. The basic equations governing one-dimensional piezoelectric quasicrystals are given providing also the classification of the phason piezoelectric moduli for all relevant Laue classes [1]. Using the hyperspace notation for piezoelectric quasicrystals, the three-dimensional Green tensor for (arbitrary) piezoelectric quasicrystals is derived. Finally, piezoelectric quasicrystals are investigated for the first time in the framework of 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 quantities such as the Eshelby stress tensor, the scaling flux vector, the angular momentum tensor, configurational forces, configurational work, configurational vector moments as well 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 tensor and Eshelbian mechanics. Submitted (2017).

∗Corresponding author: Eleni Agiasoﬁtou ( agiasoﬁ[email protected]) References 17

A sharp interface model for phase interfaces without misﬁt of the crystal lattice

Hans-Dieter Alber1,∗

1Fachbereich Mathematik, Technische Universit¨atDarmstadt, Schlossgartenstraße 7, 64289 Darmstadt, Germany

Abstract

There is usually no misfit of the crystal lattice along interfaces between martensitic phases in solids. However, when in a sharp interface model the driving force for the evolution of the interface is given by the jump of the Eshelby tensor, then such forbidden interfaces with misfit can appear. To avoid this, we propose and discuss a model where interfaces with misfit of the crystal lattice are penalized. We also show a simple numerical simulation based on this model.

∗Corresponding author: Hans-Dieter Alber ( [email protected]) 18 Abstracts

A Finite-Element-based macroscopic framework for the modelling of variant switching in MSMA Thorsten Bartel1,∗, Bj¨ornKiefer2 , Karsten Buckmann1 and Andreas Menzel1

1TU Dortmund, Institute of Mechanics, Leonhard-Euler-Str. 5, 44227 Dortmund, Germany 2TU Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics, Lampadiusstr. 4, 09599 Freiberg, Germany

Abstract

The macroscopic behaviour of ferroic functional materials such as magnetic shape memory alloys (MSMA) is highly affected by microscopic effects like the formation and further evolution of microstructures. Thus, the modelling of these effects is important for establishing micromechanically well-motivated constitutive frameworks with 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 promising concepts in the context of modelling magnetomechanically coupled material response. In this regard, the switching between different crystallographic variants of martensite in MSMA as well as the formation and propagation of magnetic domains can be treated by the evolution of phase volume fractions as shown in, e.g., [2]. In addition to these mechanisms, possible deviations of the local magnetisation vectors with respect to the easy axes is also taken into account by rotation angles in the aforementioned publication. 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-processing step. However, this framework was restricted to purely homogeneous problems so far, where, e.g., the influence of the demagnetisation field was captured by a demagnetisation tensor and the magnetisation itself. When inhomogeneous problems shall be considered, the demagnetisation field has to be treated as an independent field variable, for example in terms of a scalar-valued magnetic potential. The interme- diate conclusion arising from the current status of research activities states, that a conventional Finite-Element-based global implementation, where the external fields are discretised in space and determined via balance equations whereas internal state variables are locally determined at the integration points in a condensed manner, is hardly if at all realisable. In this contribution, the implementation of energy relaxation concepts for inhomogeneous magnetomechanically coupled problems will be discussed.

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 ( [email protected]) References 19

A preliminary study on the emergence of ferroelectricity

Vishal Boddu1,∗ and Paul Steinmann1

1Chair of Applied Mechanics, University of Erlangen-Nuremberg

Abstract

The enhancement of the ferroelectric properties of materials at reduced dimensions is crucial for continuous advancements in nanoelectronic applications. A long-standing notion that the ferroelectricity is suppressed at the scale of a few nanometers indicates the emergence of ferroelectricity at a scale slightly higher [1,2]. Emergence is used to describe a property, law, or phenomenon which occurs at (macroscopic) higher length and time scales but not at (microscopic or nanoscopic) lower scales. For instance, small clusters do not exhibit sharp first order phase transitions such as melting, and at the boundary it is not possible to completely categorize the cluster as a liquid or solid, since these concepts are (without extra definitions) only applicable to macroscopic systems. Temperature can be also seen as an example of an emergent macroscopic behavior. In classical dynamics, a snapshot of the instantaneous momenta of a large number of particles at equilibrium is sufficient to find the average kinetic energy per particle which is proportional to the temperature. For a small number of particles the instantaneous momenta at a given time are not statistically sufficient to determine the temperature of the system. However, using the ergodic hypothesis, the temperature can still be obtained to arbitrary precision by further averaging the momenta over long enough time intervals. We sought to apply this to study the emergence of ferroelectricity. We perform molecular dynamic simulations to investigate the emergence of ferroelectric property in BaTiO3 single crystals close to absolute zero under external electric loading using the core-shell model. In the core-shell model every ion is represented in terms 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 and the dimensionality effect the polarization-electric field hysteresis loops of the single crystals 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 at reduced 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 letters 94(4) (2005), 047603.

∗Corresponding author: Vishal Boddu ( [email protected]) 20 Abstracts

Modeling the impact of domain walls on the electro caloric response

Anna Gr¨unebohm1,∗, Madhura Marathe1 and Claude Ederer2

1Faculty of Physics and CENIDE, University of Duisburg-Essen, Germany 2Materials Theory, ETH Z¨urich, Switzerland

Abstract

The electrocaloric effect (ECE) is the adiabatic temperature change of a material in 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 the ferroelectric transition temperature, which is above room temperature for standard ferroelectrics such as BaTiO3. Different ways to shift the operation temperature are epitaxial strain [1], the use ferroelectric to ferroelectric phase transitions [2], or the use of solid solutions [4] and multilayers. In all cases, multi-domain ferroelectric phase may be stabilized by the elastic boundary conditions or depolarization effects. We discuss the coupling between ferroelectric domains and the external electric field and its 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 three ferroelectric transitions: anisotropy and inverse caloric effects. Phys. Rev. B (accepted). 2017. url: https://arxiv.org/pdf/1703.05515.pdf. [3]X. Moya, S. Kar-Narayan, and N. D. Mathur: Caloric materials near ferroic phase transitions. Nature Mater. 13 (2014), 439. [4]T. Nishimatsu, A. Grunebohm¨ , U. Waghmare, and M. Kubo: Molecuar Dynamics Simulations of Chemically Disordered Ferroelectrics (Ba,Sr)TiO3 with a semi-empirical effective Hamiltonian. J. Phys. Soc. Jap 85 (2016), 114714.

∗Corresponding author: Anna Gr¨unebohm ( [email protected]) References 21

Some properties of laminates of coupled materials

John E. Huber1,∗ and Yu Zhou1

1University of Oxford, Department of Engineering Science

Abstract

The formation of a composite mixes together materials to give averaged material properties, but also allows the generation of new materials with properties that were not present in any of the parent phases. In this talk we examine the linear properties of laminates and explore some of the possibilities for forming materials with desirable elastic or electromagnetically coupled properties. A significant practical interest in these materials now exists because of the development of methods for easy manufacture of complex composites. Micro- and nano-fabrication methods enable the construction of complex layered heterostructures, while additive manufacturing offers a potentially limitless combination of materials and the geometry of phases. Con- sidering first purely elastic laminates, we explore the formation of composites with desirable elastic properties. Milton and Cherkaev showed [1] that, given sufficiently extremal but isotropic starting materials, a homogenized composite could achieve any elastic tensor within the bounds imposed by thermodynamics. We explore the use of isotropic and anisotropic starting materials combined with layering and rotation for the generation of materials with features such as auxeticity. We further explore composites with tailored piezoelectric and magnetoelectric properties. It is well-known that the magnetoelectric effect can be generated in composites where none of the parent phases are themselves magnetoelectric [2]. We discuss combinations of layered materials that can achieve enhanced performance and explore the limits of performance.

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 ( [email protected]) 22 Abstracts

Piezoelectric Material Characterization aided by Algorithmic Diﬀerentiation

Benjamin Jurgelucks1,∗

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

Abstract

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

References

[1]B. Jurgelucks and L. Claes: “Optimisation of triple-ring-electrodes on piezoceramic 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 material parameters with non-uniform electrical excitation. Journal of Sensors and Sensor Systems 4 (2015), 217–227. [3]C. Unverzagt, J. Rautenberg, and B. Henning: Sensitivitätssteigerungbei der inversen Materialparameterbestimmung fürPiezokeramiken. tm-Technisches Messen 82(2) (2015), 102–109.

∗Corresponding author: Benjamin Jurgelucks ( [email protected] paderborn.de) References 23

Homogenization schemes for magnetic solids based 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

Abstract

The prediction of the effective behavior of a heterogeneous material—based on the knowledge of geometrical, distributional and constitutive properties of the involved phases—by means of adequate homogenization concepts is a classical problem in solid mechanics. It is well-known that classical homogenization schemes in mechanics, such as the Taylor/Voigt and Reuss/Sachs assumptions, can also be interpreted as ener- getic bounds. Furthermore, energy relaxation concepts have been established that determine stable effective material responses based on appropriate (convex, quasi- convex, rank-one) energy hulls for multi-phase materials characterized by non-convex energy landscapes, see [1–3] and references therein. In this contribution we propose 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 which simultaneously 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 and their implications on the theoretical framework for constitutive modeling as well as corresponding 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 Relaxation to 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. International Journal for Numerical Methods in Engineering, in press (2017), DOI: 10.1002/nme.5547.

∗Corresponding author: Bjoern Kiefer ( [email protected]) 24 Abstracts

An I-integral for extraction the intensity factors along a 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, Zhejiang University, Hangzhou 310027, China 3Institute of Mechanics and Fluid Dynamics, TU Bergakademie Freiberg, Lampadiusstraße 4, Freiberg 09596, Germany

Abstract

Domain switching causes nonlinear response of ferroelectrics, which makes it very difficult to determine the fracture parameters for ferroelectrics under large-scale domain switching. For large-scale switching problems, the spontaneous polarizations near 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 ferroelectric single-crystals [2] and polycrystals [3]. This paper develops an I-integral to extract the stress intensity factors and electric displacement intensity factors along a curved crack front in a three-dimensional ferroelectric single-crystal. The I-integral has many advantages over the switching toughening model. First, it is effective for large-scale switching. Second, it can decouple the stress intensity factors of different modes and the electric displacement intensity factor. Third, it is independent of integration volume size, regardless of the presence of domain walls. The phase field model [1] is first employed predict the polarization distributions of PbTiO3 ferroelectric single-crystals with a semi-circular surface crack. Then, the I-integral method is used to study the influences of domain switching on the intensity factor values and their distributions along the crack front.

References

[1]J. Wang and M. Kamlah: Three-dimensional ﬁnite element modeling of polarization 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 to domain 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 analysis in ferroelectric polycrystals under large-scale switching. subnmitted to Eur. J. Mech. A-Solids (2017).

∗Corresponding author: Hongjun Yu ( [email protected]) References 25

Charge-controlled actuation of dielectric elastomers

Elisabeth Staudigl1,∗ and Michael Krommer1

1Vienna University of Technology, Institute of Mechanics and Mechatronics Getreidemarkt 9, A-1060 Vienna, Austria

Abstract

In this talk we study dielectric elastomer actuators in the form of a thin layer with two compliant electrodes. In such actuators two main sources of electro-mechanical coupling are present - electrostatic forces acting between the electric charges and electrostriction due to intramolecular forces of the material, see [1]. In [2] we have accounted for electrostatic forces for the case of voltage-controlled actuators only. In voltage-controlled dielectric elastomer actuators the electric field is known to cause a pull-in instability at a so-called breakdown voltage. This penomenen is not observed in charge-controlled actuators. However, a different instability, named charge localization instability has been reported in the literature for the case of electro-mechanical coupling by means of electrostatic forces, see [3]. In this talk we extend our formulation from [2] to electrostriction as well as to the case of charge-controlled actuators to study the necking instability in more detail. Basically, the free energy is additively decomposed into a purely mechanical part and an electrical part. The mechanical free energy, for which we use a neo-Hookean strain energy function, is a function of the mechanical right Cauchy-Green tensor, and the electrical free energy depends on the material electric field and the total right Cauchy-Green tensor. Moreover, the mechanical right Cauchy-Green tensor follows from a multiplicative decomposition of the deformation gradient tensor into an elastic deformation gradient tensor and an electric deformation gradient tensor; by means of the latter we account for electrostriction. Charge-controlled actuation is finally introduced through the Gauss law of electrostatics.

Acknowledgement Support from the K2 area of the Linz Center of Mechatronics GmbH is gratefully 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. submitted to Journal of Intelligent Materials Systems and Structures 472 (), 20160170. [3]E. Staudigl, M. Krommer, and Y. Vetyukov: Charge localization instability in a highly deformable dielectric elastomer. Applied Physics Letter 104 (2014), 022905.

∗Corresponding author: Elisabeth Staudigl ( [email protected]) 26 Abstracts

An I-integral for crack analysis in ferroelectric polycrystals

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

Abstract

It is a great challenge to extract the crack-tip fracture parameters of ferroelectrics due to domain switching, especially for large-scale switching problems. This paper develops 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 different modes are decoupled. Third, it is independent of integration area size, regardless of the presence of grain boundaries and domain walls. These advantages ensure the successful utility of the area-independent I-integral in ferroelectric polycrystals under large-scale domain switching. The phase field model is combined with the I-integral method to form an effective approach to predict the polarization distributions and to evaluate the crack-tip intensity factor. A tensile test of PbTiO3 ferroelectric polycrystals with an impermeable crack is simulated through increasing the tensile strain step by step. The I-integral shows good area-independence even when grain boundaries and domain walls are included. For polycrystals, domain switching initiates not only from the crack tip but also from the grain boundaries due to high polarization gradient and stress concentration. Domain switching is triggered by a critical load, which greatly reduces the mode-I stress intensity factors. The critical load is much lower for polycrystals than for single crystals and sometimes vanishes due to grain orientations. The mode-I stress intensity factor of the polycrystal is smaller than that of the single crystal under the same applied load.

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

∗Corresponding author: Hongjun Yu ( [email protected]) References 27

The magneto-electric coupling in multiferroic composites: A two-scale homogenization approach Matthias Labusch1,∗ and J¨orgSchr¨oder1

1University Duisburg-Essen, Institute of Mechanics, Universit¨atsstr.15, 45141 Essen

Abstract

Multiferroic materials combine two or more ferroic characteristics and can exhibit an interaction between electric and magnetic fields. This magneto-electric (ME) coupling can find applications in sensor technology or in magneto-electric data storage devices [4]. Since most ME single-phase materials show such a coupling far below room temperature the manufacturing of two-phase composites, consisting of a ferroelectric matrix with magnetostrictive inclusions, becomes important. Due to the interaction of both constituents the composites generate a strain-induced ME coupling at room temperature, where we distinguish between the direct and converse ME effect. The direct effect characterizes magnetically induced polarization, where an applied magnetic field yields a deformation of the magnetostrictive phase, which is transferred to the ferroelectric phase. Due to the electro-mechanical properties of the matrix material the composite exhibit a change in polarization. On the other hand, the inverse ME effect characterizes electrically induced magnetization. The ME coupling significantly depends on the microscopic morphology and the ferroic properties of the individual constituents. In order to take both aspects into account, a finite element (FE2) homogenization approach is performed, which combines via a scale bridging the macro- and microscopic level [3]. Thereby, the microscopic morphology is characterized be representative volume elements and the ferroic properties of the phases are described by suitable material models. The typical ferroelectric hysteresis curves are modeled by considering the switching behavior of the spontaneous polarizations of barium titanate unit cells [1], whereas the magnetic hysteresis loops are described by a Preisach operator [2].

References

[1]S. Hwang, C. Lynch, and R. McMeeking: Ferroelectric/Ferroelastic interaction 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 transition for magneto-electro-mechanically coupled problems - FE2-scheme: Localization and Homogenization. Computer Methods in Applied Mechanics and Engineering 302 (2016), 253–280. [4]N. Spaldin and M. Fiebig: The Renaissance of Magnetoelectric Multiferroics. Science 309 (2005), 391–392.

∗Corresponding author: Matthias Labusch ( [email protected]) 28 Abstracts

Comparison of numerical simulation and experimental data of magneto-electric composites

V. Lemke1,∗, M. Labusch1 , J. Schr¨oder1 and H. Wende2

1Institute of Mechanics, Faculty of Engineering, University of Duisburg-Essen, Universit¨atsstraße15, 45141 Essen, Germany 2Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, Lotharstraße 1, 47048 Duisburg, Germany

Abstract

In technical applications, the combination of ferroic materials develop new opportu- nities to create better sensor technologies or data storages [4]. The reason for an improvement with magneto-electric (ME) materials can be explained by the fact that commonly they have the property of synergy between physical ferroic quantities. In composites constituted out of ferroelectric and ferromagnetic phases, a strain induced magneto-electric product property is recognized at room temperature [5]. One can differentiate between the direct and the converse ME effect. The first characterizes a magnetically caused polarization, i.e. a magnetic field evokes a deformation of the magneto-active phase which is then transferred to the electro-active phase. Vice versa, the second ME effect is distinguished. In our work, we take a closer look at a (1-3) composite, CoFe2O4 nanopillars embedded in a BaTiO3 matrix with the material coefficients taken from [1]. We compare our numerical simulations to the experiments from [2] and [3]. In our calculations, we will investigate the direct ME effect 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 and numerical 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/BaTiO3 nanocomposite 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/BaTiO3 nanocomposite tuned by magnetic ﬁelds: Supplementary information. (2013). [4] N. A. Spalding and M. Fiebig: The renaissance of magnetoelectric multiferroics. Materials Science 309 (2005), 391–392. [5] J. van Suchtelen: Product properties: a new application of composite materials. Philips Research Reports 27 (1972), 28–37.

∗Corresponding author: V. Lemke ( [email protected]) References 29

Measuring Magnetoelectric Coupling at Diﬀerent Scales

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, Universitätsstraße15, 45141 Essen, Germany 2Faculty of Physics and Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen, Lotharstraße 1, 47057 Duisburg, Germany 3Peter Grünberg Institute (PGI-6), Jülich Research Centre, 52425 Jülich, Germany

Abstract

Magnetoelectric coupling is the material based coupling between electric and magnetic fields without recurrence to electrodynamics. It can arise in intrinsic multiferroics as well 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 to exhibit their coupling effects. Room temperature applications are thus excluded. Consequently, composites have been designed to circumvent this limitation. They rely on field coupling between magnetostrictive and piezoelectric materials or in more advanced scenarios on quantum coupling in between both phases. This overview will describe experimental techniques and their particular limitations in accessing these coupling phenomena at different scales. Strain coupling is the dominant coupling mechanism at the macroscale as well as down to the micrometer. At the nanoscale more subtle effects can arise and some care has to be taken when investigating local coupling at interfaces using scanning probe techniques, e. g. due to semiconductor effects, field screening, or gradient and surface effects. At the smallest length scale atomic or molecular coupling can be tested using X-ray dichroism or probe atoms like 57Fe in Mössbauerspectroscopy. We display a selection of measuring techniques at the different scales and outline possible pitfalls for experimentalists as well as theoreticians 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 ( [email protected]) 30 Abstracts

Tailoring the Hysteresis and Electrocaloric Eﬀect by Defect Engineering

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

1Technische Universit¨atDarmstadt

Abstract

In acceptor doped perovskite ferroelectrics, the A site or B site ions can be substituted by ions with a lower valence, e.g., Ti ions in BaTiO3 are substituted by Mn or Cu. The associates of the acceptors and the compensating oxygen vacancies form non-switchable or hardly switchable defect dipoles, which shift or pinch the dielectric hysteresis, and might affect or even enhance the electrocaloric effect (ECE) significantly. For studying this interest point, the lattice-based Monte-Carlo simulations with the Ginzburg-Landau type Hamiltonian are applied to reveal the mechanism on the domain structure level, which allows direct evaluation of the ECE by combining the canonical and microcanonical algorithm. In the case of anti-parallel defect dipoles, the hysteresis is shifted. When the induced internal field is stronger than the external field, there is transformation from the positive ECE to the negative ECE. Other unexpected phenomena are additionally unveiled, including the coexistence of the positive ECE and the negative ECE under moderate field, and the double peak behavior of the ECE under high field. Finally the negative electrocaloric effect in the presence of defect dipoles is utilized to modify the electrocaloric cycle, and a significant enhancement of the ECE can be achieved. Ad- ditionally, the results from the Monte-Carlo simulations and the Molecular Dynamics and 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 the external field, a perpendicular internal field is induced. In this fashion the character- istic pinched hysteresis loop appears below the Curie temperature TC, but disappears above TC. These simulated hysteresis loops are comparable with the experimental observations. 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 ( [email protected]) References 31

Condition Monitoring of Shape Memory Material Stabilization

Nicolas Michaelis1,∗, Marvin Schmidt2,3 , Felix Welsch2 , Stefan Seelecke2 and Andreas Sch¨utze1

1Lab for Measurement Technology, Dept.of Systems Engineering, Saarland University, Saarbrücken, Germany 2Intelligent Material Systems Laboratory, Dept.of Materials Science and Engineering, Dept.of Systems Engineering, Saarland University, Saarbrücken, Germany 3ZeMA Center for Mechatronics and Automation Technology, Saarbrücken, Germany

Abstract

This contribution presents a condition monitoring approach on shape memory material stabilization, especially for elastocaloric cooling applications. In addition to the known applications of shape memory alloys (SMAs), another field of application has recently gained interest: elastocaloric cooling. It is currently being investigated as a part of the German Science Foundation (DFG) priority program SPP 1599 Ferroic Cooling [1]. The main advantage of the elastocaloric cooling process consists in avoiding ozone depleting refridgerants. Moreover, large latent heats and a small required work input during the application of elastocaloric materials (mostly Ni-Ti based SMAs) result in an efficient cooling process. The latent heats of the material become accessible under tensile loading and unloading of the SMA sample at high strain rates. This material behaviour is caused by the crystallographic phase transformation from austenite to martensite and vice versa. Based on these material properties, elastocaloric cooling processes 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 mechanical and thermal material properties have to be stabilized. This can be achieved by an elastocaloric training process which basically consists in loading and unloading the SMA samples at very low strain rates (typically below 0.1 %·s−1). The mechanical material stabilization can be shown in stress-strain diagrams, whereas the thermal stabilization can be illustrated by cycle dependent temperature profiles of the sample [2]. Analysing the self-sensing properties of the SMA concerning the material stabilization is essential to create elastocaloric cooling devices, such as the cooling demonstrator addressed in the priority program [3]. With an especially developed scientific test setup different self-sensing parameters have been investigated, with the result that a resistance measurement of the SMA during the elastocaloric training process reflects the strain as well as the phase transformation and material stabilization. Further- more, impedance measurements might also allow a continuous condition monitoring during operation to grant an early indication of impending material failure. These results, will allow the implementation of SMA-based cooling devices without expensive equipment like force and thermographic sensor technology.

∗Corresponding author: Nicolas Michaelis ( [email protected]) 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. Science and Technology for the Built Environment 22(5) (2016), 475–488. References 33

Computational Multi-Scale Stability Analysis of Two-Phase Periodic Electroactive Polymer Composites at Finite Strains Elten Polukhov1,∗, Daniel Vallicotti1 and Marc-Andr´eKeip1

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

Abstract

Dielectric electroactive polymers (dielectric EAPs) are functional materials which exhibit coupled electrostrictive response to externally applied electrostatic loadings. The advantageous properties of these materials such as light weight, fast coupled response, high stretchability and easiness of fabrication give possibilities to apply them in advanced engineering designs. Nevertheless, optimal design of dielectric EAP composites requires to study the influence of the microscopic and macroscopic properties of these materials and to determine the stable loading ranges. Considering this, we study multi-scale stability analysis of two-phase periodic EAP composites in the context of computational homogenization [2–4]. Particularly, the influence of the fiber volume fractions and aspect ratios to the onset of the localization-type macroscopic and bifurcation-type microscopic instabilities are investigated. The localization-type instabilities are determined as the loss of strong ellipticity of homogenized macroscopic moduli at a certain finite deformation However, the bifurcation-type microscopic instabilities are treated by implementing Bloch-Floquet wave analysis in the context of a finite element discretization [1,4]. The critical periodicities and bifurcation modes due to microscopic instabilities are demonstrated for selected representative boundary value 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 homogenization of electro-elasticity at ﬁnite strains. Computer Methods in Applied Mechanics and Engineering 278 (2014), 62–79. [3]C. Miehe, D. Vallicotti, and S. Teichtmeister: Homogenization and multiscale stability analysis in ﬁnite magneto-electro-elasticity. Application to soft matter EE, ME and MEE composites. Computer Methods in Applied Mechanics and 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 to Computer Methods in Applied Mechanics and Engineering (2017).

∗Corresponding author: Elten Polukhov ( [email protected]) 34 Abstracts

Magneto-electric coupling in soft-matter-based composites

Matthias Rambausek1,∗ and Marc-Andr´eKeip1

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

Abstract

Magneto-electric coupling of solids can be realized by the construction of magnetoelectric composites. Usually, these composites are made of hard materials [5]. An alternative route to magneto-electric coupling was proposed only recently by Liu and Sharma [3]. Their approach is based on soft-matter magneto-electric composites. Such composites render an interesting class of materials that might be employed for the design of novel magnetic-field sensors. Thus, in our contribution, we analyze the magneto-electric coupling mechanisms in these materials. We present a series of multiscale simulations of soft magneto-electric bodies under physically reasonable boundary conditions [1,4]. Thereby, we focus on the distinction between microstruc- tural and macrostructural coupling mechanisms. In detail, we compare the effective macroscopic properties of magnetorheological elastomers under magneto-electric loading with the macroscopic shape-dependent [2] performance of a magneto-electric transducer. In our analysis, we identify macroscopic effects to be crucial for, e.g., a sensor’s performance. These effects are driven by magneto- and electro-mechanical interactions on both scales and clearly dominate the effective coupling moduli of the composite.

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 investigations of shape eﬀects in the experimental characterization of magnetorheological elastomers. 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 materials and concomitant ramiﬁcations for materials science and biology. Physical Review 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 media immersed in free space. International Journal for Numerical Methods in Engi- neering 108(11) (2016), 1307–1342.

∗Corresponding author: Matthias Rambausek ( [email protected]) References 35

[5]J. Schroder¨ , M. Labusch, and M.-A. Keip: Algorithmic two-scale transition for magneto-electro-mechanically coupled problems: FE2-scheme: Localization and homogenization. Computer Methods in Applied Mechanics and Engineering 302 (2016), 253–280. 36 Abstracts

Lead-free Na1/2Bi1/2TiO3-based piezoceramic composites J¨urgenR¨odel1,∗, Lukas M. Riemer1 , K.V. Lalitha1 and Jurij Koruza1

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

Abstract

In the past two decades, the environmental toxicity imposed by the use and disposal of lead-based piezoelectrics led to strong research eﬀorts. The good piezoelectric properties 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 potential development of composites including a hard second phase had not been considered, as this may hinder the development of large strains. We demonstrate in the following two cases, where these composites lead to greatly improved properties.

The composites of NBT-xBT with ZnO inclusions had been demonstrated to increase the depolarization temperature, Td [3]. The delayed thermal depolarization behavior 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 resulting 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 hard piezoceramics are required, low losses, a high coercive ﬁeld and a high electromechanical coupling factor Qm is required. A two-fold increase in Qm was observed for the composites with NBT-6BT. Akin to other hard piezoelectrics, a decrease in the saturation polarization and total strain was observed [1].

References

[1]K. Lalitha, L. M. Riemer, J. Koruza, and J. Rodel¨ : Hardening of electromechanical 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¨ , and J. Koruza: Stress-Induced Phase Transition in Lead-Free Relaxor Ferroelectric Composites. 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 depolarization in Bi0.5Na0.5TiO3 –based lead-free piezoceramics. Nature Communications 6 (2015), 6615.

∗Corresponding author: J¨urgenR¨odel( [email protected]) References 37

Shape sensitivity and homogenization for piezo-poroelastic microstructures

Eduard Rohan1,∗ and Vladim´ırLukeˇs1

1European Centre of Excellence, NTIS – New Technologies for Information Society Faculty of Applied Sciences, University of West Bohemia, Univerzitn´ı8, 30614 Pilsen, Czech Republic

Abstract

The paper is devoted to the issues of homogenization and sensitivity analysis in modelling of porous media constituted by piezoelectric porous skeleton with pores saturated by viscous fluid. Such materials can be generated as periodically distributed micro-devices with many potential applications. Each microdevice is a copy of the representative volume element containing the piezoelectric solid part (the matrix) and the viscous fluid saturated the pores (the channels). The macroscopic model was derived using the unfolding method of the periodic homogenization [4], cf. [1]. The obtained model is an extension of the Biot model characterized by the poroelastic coefficients modified by piezoelectric coupling effects. The present paper focuses on the shape sensitivity analysis (SSA) of the homogenized coefficients 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 leading to function-graded metamaterials, 2) to extend the linear model beyond its scope following the ideas of [2]. In the latter case, assuming the linear kinematics framework, the physical nonlinearity in the upscaled model is introduced in terms of the deformation-dependent material coefficients which are approximated as linear func- tions of the macroscopic response expressed by the deformation, fluid pressure and the 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. Lukeˇs: On modelling nonlinear phenomena in deforming heterogeneous 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 microstructures for design of piezoelectric bio-materials. Mechanics of Advanced Materials and Structures 13 (2006), 473–485. [4]E. Rohan, V. Lukeˇs, and R. Cimrman: “Homogenization of the ﬂuid-saturated piezoelectric porous metamaterials”. In: Coupled Problems in Science and En- gineering VII. Vol. 7. 2017, 1080–1091.

∗Corresponding author: Eduard Rohan ( [email protected]) 38 Abstracts

Inﬂuence of matrix and interface cracking on the eﬀective constitutive behaviour of multiferroic composites

Alexander Schlosser1,∗, Artjom Avakian1 and Andreas Ricoeur1

1Chair of Engineering Mechanics/Continuum Mechanics, Institute of Mechanics, University of Kassel, M¨onchebergstraße 7, 34125 Kassel, Germany

Abstract

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

The constitutive modeling of nonlinear multifield behavior as well as the finite element implementation are presented [1,3]. Nonlinear material models describing the magneto-ferroelectric or electro-ferromagnetic behaviors are presented[1,2]. Both physically and phenomenologically motivated constitutive models have been developed for the numerical calculation of principally different nonlinear magnetostrictive behaviors. On this basis, the polarization in the ferroelectric and magnetization in the ferromagnetic constituents, respectively, are simulated and the resulting effects are analyzed. Damaging processes are taken into account by models for micro crack growth in the ferroelectric constituent and cohesive zones at the boundary layers. The cohesive zone elements describe the degradation of mechanical, magnetic and electrical features during delamination. Numerical simulations finally focus on the investigation of magnetoelectric coupling in particulate and laminated composites, revealing the essential role of damage going along with the poling process. Final goal of the research is to optimize magnetoelectric devices e.g. with respect to favorable electric-magnetic poling sequences or geometric arrangements.

∗Corresponding author: Alexander Schlosser ( [email protected]) 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 nonlinear reversible ferromagnetic behaviour under magnetomechanical multiaxial loading conditions. Journal of Applied Physics 121(5) (2017), 053901. [3]A. Avakian, R. Gellmann, and A. Ricoeur: Nonlinear modeling and ﬁnite element simulation of magnetoelectric coupling and residual stress in multiferroic composites. Acta Mechanica 226(8) (2015), 2789–2806. 40 Abstracts

Towards a Variational Level Set Formulation for Microstructure 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, Sweden 3Chair of Material Mechanics, RWTH Aachen University, Schinkelstrasse 2, 52062 Aachen, Germany 4Department of Microstructure Physics and Alloy Design, Max Planck Institute for Iron Research, Max-Planck Strasse 1, 40237 D¨usseldorf,Germany

Abstract

Modelling frameworks such as level set formulations and phase field fomulations provide more information about domain wall kinetics in ferroelectrics as compared to, e. g. , phenomenological models, since the microstructure is fully resolved in space and time. In contrast to phase field models applied to the simulation of ferroelectrics, that provide a continuous transition between the domains, the classic level set approach is a 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 the interface. Due to numerical errors, additional methods are required to ensure that the level set function remains as a signed distance function. The most common approach is the application of reinitialization algorithms, though these methods involve a high computational effort. In contrast, using a variational approach, the deviation from 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 materials under electromechanical loading. Furthermore, the visualisation of the level set function shows that the variational approach satisfies the constraint for the signed distance 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 in Applied 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 IEEE Computer 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 ( [email protected]) References 41

In situ observations of viscoelastic property evolution during electrical fatigue of PZT

Wei Lin Tan1,∗, A. Vidyasagar1,2 , Katherine T. Faber1 and Dennis 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, ETH Z¨urich, 8092 Z¨urich, Switzerland

Abstract

Ferroelectrics are ubiquitous in our daily lives, in devices such as actuators, infrared detectors and non-volatile memory. It has also recently been shown using Broadband Electromechanical Spectroscopy (BES) that domain switching in ferroelectrics causes high damping at the coercive field [4]. The high stiffness of ferroelectric ceramics and the ability to control damping in the material gives it great promise in engineering applications. However, it is also well known that extended bipolar electrical cycling causes decreased polarization magnitude as well as micro- and macro-cracking. To observe in situ the effects of fatigue on the electrical and mechanical properties of bulk PZT ceramics, we employ BES to determine polarization, relative stiffness, and damping of samples with time. We further compare measured values with SEM micrographs of microcrack density at different numbers of cycles, and use existing models to relate the observed microstructure 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 constitutive modeling of polycrystalline ferroelectrics. Finite Elements in Analysis and Design 42 (2005), 107–129. [4] C. S. Wojnar, J.-B. le Graverend, and D. M. Kochmann: Broadband control of the viscoelasticity of ferroelectrics by electric fields. Applied Physics Letters. 105(16) (2014), 162912–162916.

∗Corresponding author: Wei Lin Tan ( [email protected]) 42 Abstracts

Non-Linear Dynamics of a Circular Piezoelectric Multi-Layer Plate

Florian Toth1,∗, Manuel Dorfmeister2 , Michael Schneider2 , Ulrich Schmid2 and Manfred 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

Abstract

In digital sound reconstruction (DSR) the audiable sound is a superposition of short sound 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 proportional to the stroke level of the transducers. Therefore, the transducer is operated within 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 large deflections. Piezoelectric actuation is then used to switch between the equilibrium configurations. We develop a modelling strategy suitable for the tailored design of the MEMS system. The pre-stress introduced by the production process is modelled by linear thermal expansion. 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 a non-local constitutive relation [1]. The geometrical non-linearity arising from large transverse displacements is taken into account by using von Karman theory. Ex- ploiting the rotational symmetry of the structure the governing partial differential equations can be reduced to a set of coupled, non-linear ordinary differential equations. Finally, we use the developed model to explore the non-linear dynamics of the system.

References

[1]M. Krommer: The signiﬁcance of non-local constitutive relations for composite thin plates including piezoelastic layers with prescribed electric charge. Smart Materials and Structures 12(3) (2003), 318–330. doi: 10.1088/0964-1726/12/ 3/302.

∗Corresponding author: Florian Toth ( ﬂ[email protected]) References 43

Experimentally probing magnetoelectric coupling at the 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, Universit¨atsstraße15, 45141 Essen, Germany 2CICECO, University of Aveiro, 3810-193, Aveiro, Portugal 3Center for Shared Use ”Modern Nanotechnology”, Institute of Natural Sciences, Ural Federal University, 620000, Yekaterinburg, Russia

Abstract

Multiferroic composites, which have emerged as an ideal solution for room temper- ature magnetoelectricity, involve a strain mediated effective coupling. Hence it becomes evident to explore the coupling mechanism from a microscopic per- spective. Recently, attempts have been made to construct robust models for understanding the strain mediated magnetoelectric effect in composites with various morpholo- gies. Such models require experimental support. On the details of coupling, a proper understanding about the behavior of the strain mediation in the vicinity of the interface between the constituent phases is still lacking. In this study we demonstrate the potential of various cantilever based microscopic techniques like Piezore- sponse Force Microscopy (PFM), Magnetic Force Microscopy (MFM), Kelvin Probe Force Microscopy (KPFM), Micro-Raman, in studying the local manifestations of the strain mediated magnetoelectric effect in various classical composite systems like Co/NiFe2O4 – BaTiO3 and Ba/SrFe12O19 – BaTiO3. The outcomes present an opportunity to gauge the magnitude of the effect locally.

∗Corresponding author: Harsh Trivedi ( [email protected]) 44 Abstracts

Study of Converse Magnetoelectric Eﬀect in NiFe2O4-(Ba,Ca)(Zr,Ti)O3 multiferroics M. Naveed-Ul-Haq1,∗, Vladimir V. Shvartsman1 , Harsh Trivedi1 , Soma Salamon2 , Heiko Wende2 and Doru C. Lupascu1

Abstract

Materials exhibiting piezoelectricity and some form of magnetism simultaneously have become quite popular at the end of the 20th century. In this class of materials the electric properties can be controlled via external magnetic field and conversely, magnetism can be induced or controlled via applied voltage/field. We in particular consider the latter effect. It leads to a variety of applications in spintronics, memories, and tunnel junctions. Here we present the electrical control of induced magnetization in bulk ceramic composites consisting of (Ba,Ca) (Zr,Ti)O3 as the ferroelectric/piezoelectric phase and NiFe2O4 as the magnetic phase. The composites have been manufactured via solid state synthesis, and their structure has been verified via x-ray diffraction combined with Rietveld analysis. We demonstrate that the samples show an excellent converse magnetoelectric effect of 45 ps/m, which is almost twice as large as it has been reported for samples prepared under similar conditions.

∗Corresponding author: M. Naveed-Ul-Haq ( [email protected]) References 45

Understanding domain patterning and electromechanical behaviour in bulk ferroelectrics using spectral phase ﬁeld techniques

A. Vidyasagar1,2,∗, W. L. Tan2 and D.M. Kochmann1,2

1ETH Zürich, Rämistrasse101, 8092 Zürich, Switzerland 2GALCIT, California Institute of Technology, CA 91125, USA

Abstract

Kinetics of bulk polycrystalline ferroelectric ceramics such as barium titanate (Ba- TiO3) and lead zirconate titanate (PZT) are not well understood due to the range of length and time scales involved. Utilizing a spectral approach, the electromechanical problem is solved using diffuse interface phase field modeling. The insights derived from this approach include prediction of patterns in polycrystalline ferroelectrics, understanding influences of grain size and misorientation and the motion of domain walls across grain boundaries and pinning sites. Computational predic- tions for electromechanical microstructure evolution, and macroscopic homogenised polarisation and strain hysteresis, show convincing agreement with our experimental observations. The coupling of a phase field damage model, as well as temperature dependent effective physics will also be discussed during this presentation.

∗Corresponding author: A. Vidyasagar ( [email protected]) 46 Abstracts

Phase ﬁeld simulation with leakage currents for nanogenerator concepts

Franziska W¨ohler1,∗, Ingo M¨unch1 , Chad M. Landis2 and Werner Wagner1

1Institute for Structural Analysis, Karlsruher Institute of Technology 2Aerospace Engineering and Engineering Mechanics, University of Texas

Abstract

We design a nanogenerator on the base of ferroelectric thin films to transform para- sitic mechanical oscillations into usable electric energy. The conversion of mechanical into 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 an electric storage medium implies that a gradient of electric potential exists between electrodes.Thus, leakage currents may appear between electroded surfaces if the ferroelectric 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 mechanisms for leakage currents J in ceramics are discussed: Ohm’s law, space-charge-limited current, and Schottky emission q −e(φ − e E/4π ε κ ) 9 2 ∗ 2 0 i 0 J = σ 11 E , J = µ κ0 εr E , J = A T exp   (3.1) 8 kT

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 E is a vector out of R3 in our model. For instance, the space-charge-limited current is 9 given by J = 8 µ κ0 εr kEkE.

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 grown by 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 domain evolution: Theory, ﬁnite element implementation, and application to domain wall pinning. J. Mech. Phys. Solids 55 (2007), 280–305.

∗Corresponding author: Franziska W¨ohler( [email protected]) References 47

Phase ﬁeld simulation of ﬂexoelectricity in ferroelectric materials

Bai-Xiang Xu1 and Shuai Wang1,∗

1Mechanics of Functional Materials Division, Department of Materials Science, TU Darmstadt

Abstract

Flexoelectricity describes the linear coupling between the polarization and the strain gradient or the coupling between the strain and the polarization gradient. [2] Unlike other electromechanical coupling effects such as piezoelectricity, which require the non-central symmetry of the structure, flexoelectricity applies to all crystal symme- tries. Due to the low theoretical values of flexocoupling coefficients, the study on flexoelectricity in solids had long been overlooked. In last decades, a series of experimental observations on large flexoelectric effect in ferroelectrics were reported by Ma and Cross. [1] The flexoelectricity offers great opportunity to enhance the electromechanical coupling, and widen the choice of the materials. However, due to the high heterogeneity of strain and polarization in ferroelectrics, the interaction between the flexoelectric effect and the domain structure becomes complex, and effective modeling is required to reveal it and asisst the design. In this presentation, a continuum ferroelectric phase field model is coupled to flexoelectricity. For the ferroelectric properties, the polarization is regarded as the order parameter in the phase field simulation. The evolution of the polarization is gov- erned by the time-dependent Ginzburg–Landau equation. By 2D simulation, the comparison of domain patterns between samples with and without flexoelectric effect is presented, which shows the importance of considering flexoelectric effect. We also observe that, the domain configuration in ferroelectrics is sensitive to different components of flexocoupling tensor. As one application example, the flexoelectric response of core-shell Bi1/2Na1/2TiO3-xSrTiO3 nanoparticles at high temperature is modeled, along with comparison with the related Transmission Electron Microscopy observations.

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 ( [email protected]) 48 Abstracts

Magnetoelastic coupling for magnetization switching with stochastic eﬀects

Min Yi1,∗ and Bai-Xiang Xu1

1Division of Mechanics of Functional Materials, Institute of Materials Science Technical University of Darmstadt Jovanka-Bontschits-Str. 2, Darmstadt 64287, Germany

Abstract

Switching dynamics plays a fundamental role in the application of nanomagnets in spintronic 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 piezoelectric/ferromagnetic heterostructure, in which the voltage induced strain in piezoelectric layer is transferred to ferromagnetic layer and thus change the magnetic state due to the magnetoelastic coupling. Therefore, as the intrinsic mechanism, magnetoelastic coupling 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 both in the atomic scale and microscale. The atomic-scale stochastic effect is originated from the magnetic materials themselves. For example, in (Cox Fe1−x )2B alloy which is widely used in magnetic tunnel junctions, the disordered arrangement of Fe and Co atoms at the crystallographic sites results in compositional randomness. The microscale stochastic effect comes from the finite temperature, which induces thermal fluctuations and thus random fields exerted on the magnetic moment. In order to deal with this tow-scale feature and the above-mentioned stochastic effects, we will adopt a multiscale simulation scheme by inputting density functional theory (DFT) calculation results to the switching dynamics in ferromagnetic materials. The magnetoelastic coupling coefficients and other magnetic parameters will be predicted by DFT calculations. Then strain-induced magnetization switching by using magnetoelastic coupling will be studied and the associated results will be analyzed statistically.

∗Corresponding author: Min Yi ( [email protected]) Notes

49 50 Notes List of Participants

51 52

A University of Duisburg–Essen Lotharstraße. 1 Agiasoﬁtou, Eleni 47048 Duisburg Darmstadt University of Technology Germany Hochschulstraße 6 [email protected] 64289 Darmstadt Germany H agiasoﬁ[email protected] Alber, Hans–Dieter Huber, John E. Darmstadt University of Technology University of Oxford Schloßgartenstraße 7 Parks Road 64289 Darmstadt Oxford Germany United Kingdom [email protected] [email protected]

B J

Bartel, Thorsten Jurgelucks, Benjamin Dortmund University of Technology University of Paderborn Leonard–Euler–Straße 5 Warburger Straße 100 44227 Dortmund 33098 Paderborn Germany Germany [email protected] [email protected] Boddu, Vishal paderborn.de University of Erlangen–Nuremberg K Paul–Gordan–Straße 3 91058 Erlangen Kiefer, Björn Germany TU Bergakademie Freiberg [email protected] Lampadiusstraße 4 Brands, Dominik 09599 Freiberg University of Duisburg–Essen Germany Universitätsstraße15 [email protected] 45141 Essen Kozinov, Sergii Germany TU Bergakademie Freiberg [email protected] Lampadiusstraße 4 09599 Freiberg E Germany [email protected] El Khatib, Omar Krommer, Michael TU Bergakademie Freiberg Wien University of Technology Lampadiusstraße 4 Getreidemarkt 9 09599 Freiberg 1060 Vienna Germany Austria [email protected] [email protected] G Kuna, Meinhard TU Bergakademie Freiberg Grünebohm, Anna Lampadiusstraße 4 53

09596 Freiberg Menzel, Andreas Germany Dortmund University of Technology [email protected] Leonard–Euler–Straße 5 44227 Dortmund L Germany [email protected] Labusch, Matthias Michaelis, Nicolas University of Duisburg–Essen Saarland University Universitätsstraße15 Campus A5.1 45141 Essen 66123 Saarbrücken Germany Germany [email protected] [email protected] Lange, Stephan University of Kassel N Mönchebergstraße 7 Naveed–Ul–Haq, Muhammad 34109 Kassel University of Duisburg–Essen Germany Universitätsstraße15 [email protected] 45141 Essen Lemke, Veronica Germany University of Duisburg–Essen [email protected] Universitätsstraße15 45141 Essen P Germany Polukhov, Elten [email protected] University of Stuttgart Lupascu, Doru C. Pfaffenwaldring 7 University of Duisburg–Essen 70569 Stuttgart Universitätsstraße15 Germany 45141 Essen [email protected] Germany [email protected] R

M Rödel, Jürgen Darmstadt University of Technology Ma, Yangbin Alarich-Weiss-Straße 2 Darmstadt University of Technology 364287 Darmstadt Jovanka–Bontschits–Straße 2 Germany 64287 Darmstadt [email protected] Germany Rambausek, Matthias [email protected] University of Stuttgart Mahnken, Rolf Pfaffenwaldring 7 University of Paderborn 70569 Stuttgart Warburger Straße 100 Germany 33098 Paderborn [email protected] Germany Ricoeur, Andreas [email protected] University of Kassel Medipour, Fatemeh Mönchebergstraße 7 Dresden University of Technology 34109 Kassel Germany Germany [email protected] [email protected] dresden.de Rohan, Eduard 54

University of West Bohemia T Univerzitn´ı8 Tan, Wei-Lin 30614 Pilsen California Institute of Technology Czech Republic 1200 E. California Blvd. MC 138-78 [email protected] Pasadena, CA 91125 S United States of America [email protected] Salomon, Soma Toth, Florian University of Duisburg–Essen Vienna University of Technology Lotharstraße 1 Getreidemarkt 9 47057 Duisburg 1060 Vienna Germany Austria [email protected] fl[email protected] Schlosser, Alexander Trivedi, Harsh University of Kassel University of Duisburg–Essen Mönchebergstraße 7 Universitätsstraße15 34109 Kassel 45141 Essen Germany Germany [email protected] [email protected] Schröder,Jörg University of Duisburg–Essen V Universitätsstraße15 Vidyasagar, Ananthan 45141 Essen ETH Zurich Germany Tannenstrasse 3 [email protected] 8092 Zurich Schulte, Robin Switzerland Dortmund University of Technology [email protected] Leonard–Euler–Straße 5 44227 Dortmund W Germany Wöhler, Franziska [email protected] Karlsruhe Institute of Technology Schulze, Veronika Kaiserstraße 12 University of Paderborn 76131 Karlsruhe Warburger Straße 100 Germany 33098 Paderborn [email protected] Germany Webers, Samira [email protected] University of Duisburg–Essen Staudigl, Elisabeth Lotharstraße 1 Vienna University of Technology 47048 Duisburg Getreidemarkt 9 Germany 1060 Vienna [email protected] Austria Wingen, Marius [email protected] University of Kassel Svendsen, Bob Mönchebergstraße 7 RWTH Aachen University 34125 Kassel Schinkelstraße 2 Germany 52062 Aachen [email protected] Germany [email protected] X 55

Xu, Bai-Xiang Yi, Min Darmstadt University of Technology Darmstadt University of Technology Jovanka–Bontschits–Straße 2 Jovanka–Bontschits–Straße 2 64287 Darmstadt 64287 Darmstadt Germany Germany [email protected] [email protected] Y