The book provides an overview of the physical phenomena in ferromagnetic and ferroelectric materials on the micro-scale, including the origin of domain structures, domain wall motion and magnetisation or polarization rotation. This discussion leads to multiscale and phenomenological macroscopic models which account for the hysteretic behaviour, followed by a detailed derivation of variational inequalities as the main mathematical tool in hysteresis modelling, hysteresis energy balance and continuous data dependence. Classical elasto-plasticity is used as an example application where thermodynamic potentials and dissipation functions are defined and their relationship to commonly used yield conditions and associated flow rules is shown. The concepts developed there provide the basis for modelling the ferroelectric material behaviour that occurs in piezoelectric ceramics, as well as ferromagnetic behaviour through scalar and vector hysteresis models. These models are complemented by efficient finite element strategies, and identification methods to determine the necessary material parameters in the hysteresis models based on measurements.
An introduction to mathematical modeling of hysteresis.- Thermodynamically consistent modeling of ferroelectricity and finite element formulations.- Multiscale approach for the electro-mechanical behaviour of ferroelectric ceramics.- Energy-based hysteresis model for ferromagnetic materials and efficient finite element formulation.- Multiscale approach for the magneto-mechanical behaviour of ferromagnetic materials.
Manfred Kaltenbacher is Professor of Measurement and Actuator Technology at TU Graz, Austria, where he also served as Head of the Institute of Fundamentals and Theory of Electrical Engineering. His main research interests are advanced finite element methods for multi-physics (magneto-mechanics, vibro- and aero-acoustics, and piezoelectrics) and combined experimental and simulation-based methods for material parameter determination (magnetics, acoustics, piezoelectrics). He serves as Editor-in-Chief of Acta Acustica, and member of the editorial advisory board of Acta Mechanica. He is a member of the Austrian Academy of Sciences, the IEEE Society, the AIAA Society, and the European Acoustics Association.
Astrid Pechstein is Associate Professor at the Institute of Technical Mechanics in the Mechatronics Department at JKU Linz, Austria. She is member of the editorial advisory board of Acta Mechanica journal. Her main interests lie in interdisciplinary research, where she tries to combine theoretical results from computational mathematics with problem-specific approaches from mechanical engineering. Her focus is on the derivation of novel finite element methods.
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