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HAL Id: tel-01630261 https://tel.archives-ouvertes.fr/tel-01630261 Submitted on 7 Nov 2017 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Contribution to modelling of magnetoelectric composites for energy harvesting Gang Yang To cite this version: Gang Yang. Contribution to modelling of magnetoelectric composites for energy harvesting. Elec- tromagnetism. Université Pierre et Marie Curie - Paris VI, 2016. English. NNT : 2016PA066731. tel-01630261 Thèse de doctorat Université Pierre et Marie Curie Ecole Doctorale Science Mécanique Acoustique Electronique et Robotique Laboratoire d’Electronique et Electromagnétisme (L2E) Contribution to modelling of magnetoelectric composites for energy harvesting Présentée par Gang YANG soutenue le 05 décembre 2016 devant le jury composé de: M. Xavier Mininger Professeur à l’Université Paris Sud Rapporteur M. Abdelkader Benabou Maître de conférences, HDR à l’Université de Lille Rapporteur M. Nicolas Galopin Maître de conférences à l’Université de Grenoble 1 Examinateur M. Stéphane Holé Professeur à l’UPMC Examinateur M. Zhuoxiang Ren Professeur à l’UPMC Directeur de thèse M. Hakeim Talleb Maître de conférences à l’UPMC Co-encadrant Contents General introduction ....................................................................................................... 1 Chapter 1. General context - State of Art ........................................................................ 3 1.1 Magnetoelectric effect and materials .................................................................................. 3 1.1.1 Single-phase ME materials ..................................................................................................... 3 1.1.2 Two-phase ME composite materials ...................................................................................... 4 1.1.2.1 Bulk 0-3 composites ....................................................................................................................... 5 1.1.2.2 Laminated 2-2 composites ............................................................................................................. 6 1.1.2.3 Rod matrix 1-3 type composites .................................................................................................... 6 1.2 Magneto-mechanical effect and material ............................................................................. 6 1.2.1 Magneto-mechanical coupling ............................................................................................... 6 1.2.2 Magnetostrictive material ...................................................................................................... 8 1.3 Electro-mechanical effect and materials .............................................................................. 9 1.3.1 Electro-mechanical coupling .................................................................................................. 9 1.3.2 Piezoelectric material ........................................................................................................... 12 1.4 Magnetoelectric effect applications ................................................................................... 12 1.4.1 Magnetic field sensors .......................................................................................................... 12 1.4.1.1 Static magnetic field sensor ......................................................................................................... 13 1.4.1.2 Dynamic magnetic field sensor .................................................................................................... 13 1.4.2 Energy harvesting applications ............................................................................................. 13 1.5 Modelling and Characterizations of magnetoelectric materials and devices ........................ 15 1.5.1 Theoretical modelling methods ........................................................................................... 15 1.5.2 Experimental Characterization ............................................................................................. 16 1.6 Conclusion ........................................................................................................................ 17 Chapter 2. Analytical and Numerical Modelling of Magnetoelectric Composites ......... 18 2.1 Introduction ...................................................................................................................... 18 2.2 Electromagnetic and mechanical governing equations and constitutive laws ...................... 18 2.3 Analytical methods ........................................................................................................... 23 2.3.1 Simplified analytical method in static regime ...................................................................... 23 2.3.2 Equivalent circuit method .................................................................................................... 27 2.4 FEM modelling of the field problem in 2D .......................................................................... 33 2.4.1 Establishment of the 2D tensors .......................................................................................... 34 2.4.2 FEM formulation ................................................................................................................... 38 2.4.2.1 Fundamental formulations .......................................................................................................... 38 2.4.2.2 Boundary conditions .................................................................................................................... 40 2.4.2.3 FEM Simulation results ................................................................................................................ 41 2.4.3 Nonlinear static case ............................................................................................................ 44 2.4.3.1 Modelling of nonlinear piezomagnetic coupling .......................................................................... 44 2.4.3.1.1 Hirsinger model ......................................................................................................................... 45 2.4.3.2 Modelling of magnetic nonlinearity ............................................................................................. 48 2.4.4 Dynamic small signal regime ................................................................................................ 57 2.4.4.1.Coupling with the electric circuit load equation .......................................................................... 57 2.4.4.2 Effect of the complex impedance on the damping losses ........................................................... 58 2.4.4.3 Simulation results ........................................................................................................................ 59 2.5 Conclusion ........................................................................................................................ 61 Chapter 3. Assessment of ME composite performances ................................................ 62 3.1 Introduction ...................................................................................................................... 62 3.2 Performances of a ME composite as energy transducer ...................................................... 62 3.2.1 Output deliverable power under different modes ............................................................... 64 3.2.2 Electrical equivalent circuit model ....................................................................................... 65 3.2.3 Establishment of the optimal electrical load ........................................................................ 68 3.2.4 Transient dynamic response with a non-linear electrical load ............................................ 69 3.3 Multilayer ME composite materials ................................................................................... 72 3.3.1 Multilayer ME composite problems description and FEM modelling .................................. 73 3.3.2 Equivalent circuit method for multilayer ME composite problems ..................................... 74 3.3.3 Results and comparisons ...................................................................................................... 76 3.4 Conclusion ........................................................................................................................ 79 Chapter 4. Prospective application of ME composites as energy transducer ................. 80 4.1 Introduction ...................................................................................................................... 80 4.2 Potential application in biomedical domain ....................................................................... 80 4.2.1 Ferrite solenoid as external reader ...................................................................................... 81 4.2.2 Exposition limits of the magnetic field ................................................................................. 81 4.3 Measurement of a bilayer ME composite ........................................................................... 82 4.3.1 Measurement bench set-up ................................................................................................. 82 4.3.2 Static and dynamic measure responses ............................................................................... 84 4.3.3 Deliverable output power .................................................................................................... 86 4.4 Conclusion ........................................................................................................................ 86 General conclusion ........................................................................................................ 87 Appendix A. Characteristics of utilized materials ......................................................... 89 Appendix B. Different magnetostrictive nonlinear models ............................................ 91 Appendix C. Modified Newton-Raphson method .......................................................... 99 Appendix D. Multilayer analytical modelling ............................................................... 102 References .................................................................................................................... 108 1 General introduction Currently, the digital “nomads” wireless technologies have attracted significant researchers in the international scientific community, to the point that we now speak of "Internet of Everything" (IoE). The IoE is based on the idea that identifiable objects are located and controlled via the Internet. To achieve this goal, it is necessary to design embedded systems in millimeter/micrometer scales composed of wireless sensor nodes while overcoming a major drawback that is the excessive use of batteries, produced by the large number of power supply sensors. The problem is that the batteries must be changed or requires the use of chargers because their lifetimes are limited and that they are made with polluting component elements. To reduce this excessive use of pollutants and to obtain autonomy, each wireless sensor should be supplied by green energy harvesting techniques. Among the most proposed and studied solutions for micro-systems, we find essentially transducers based on mechanical vibrations using piezoelectric materials or electromagnetic energy from small coils or rectenna antennas. Use of mechanical vibrations as an exclusive excitation source is limited of ambient vibration areas and the recoverable electromagnetic energy for micro systems is often low to allow of a useful supply. One solution would be to get simultaneously both energies using materials sensitive to the electromagnetic field and the mechanical vibration such as magnetoelectric materials (ME) that combine the magnetostrictive (change of mechanical stress under an applied magnetic field and reciprocally) and piezoelectric (change of mechanical stress under an applied electric field and reciprocally) effects. Although early studies have started in the 1970s with notably the discovery of Terfenol-D ( Tb1−xDyxFe2 ), it was not until the early 2000s to see their interest arise in the international scientific community with the emergence of new magnetostrictive materials such as Metglas and piezoelectric materials including PMN-PT (Pb(Mg,Nb) O3 -PbTi O3 ), PZT-4/5/8 (Pb(Zr,Ti) O3), and BTO (BaTiO3). Homogenous analytical methods were developed to estimate ME bulk materials according to different polarizations (transverse-transverse and transverse-longitudinal) depending on the combination parameters (type, number, and thickness of layers). To validate the simulation results, bi- and tri- ME layer bulk composites were fabricated by sticking the magnetostrictive and piezoelectric materials with adhesive layers of Epoxy-type. Experimental results of ME coefficients have confirmed the possibility to obtain a few of V/(cm∙Oe) in no-resonant regime and few tens of V/(cm∙Oe) in resonant regime. In case of classical laminate bulk material (Terfenol- D/PZT/Terfenol-D), the delivered powers into optimal impedance are in the order of mW/ cm3. Nevertheless, it has been noticed that due to fatigue and inhomogeneous thicknesses of adhesive layers, the mechanical coupling can be degraded over time. This affects the magnetostrictive response and consequently the effective delivered power. Since 2010, many studies have been devoted to the design and the miniaturization of new ME composite materials coupling the giant magnetostrictive and piezoelectric effects. Thanks to thin film deposit processes, new robust combinations such as the new alloys CFO (CoFe2O4), FeONi, FeGa and FeCo can be created laying aside rare earth materials. At this scale level, the previous homogenous analytical methods do not allow of accurate modelling of the coupling phenomena and do not take into account the adhesive layers and the mechanical effects of electrodes. It is in this context that our research work at the Electronic and Electromagnetism Laboratory (L2E) propose a contribution to modelling of magnetoelectric composites for energy harvesting. This thesis is composed of four chapters. The first chapter reproduces in a general context properties on magnetoelectric composites. After a brief history, the magnetoelectric effect applications and the 2 modelling and characterizations of magnetoelectric materials and devices are presented. The second chapter presents the different numerical simulation tools to be used and developed in this thesis. Firstly, an analytical numerical method based on 0D-assumption modelling in static regime is presented. Secondly an analytical numerical method based on 1D-modelling using an equivalent electrical circuit is studied. Thirdly, a 2D multiphysics code based on the finite element method is presented. The third chapter investigates the deliverable output of a magnetoelectric laminate composites composed of Terfenol-D/PZT-5A/Terfenol-D materials in considering electrical load. The model has been developed for both harmonic and transient cases in considering a SSD technique. The fourth chapter presents a potential application in the biomedical domain and show measurement realization on a bilayer magnetoelectric laminate composites composed of Terfenol-D/PZT-5H. 3 Chapter 1. General context - State of Art 1.1 Magnetoelectric effect and materials Magnetoelectric (ME) effects exist in multifunctional active materials, they refer to the electric polarization induced by applied magnetic field, and the magnetization induced by applied uploads/Litterature/ 2016-pa-066731.pdf