The hysteretic behavior of certain materials provides the basis for the design of many of today’s “smart” systems. Prominent example are ferroelectric and ferromagnetic materials, which have been adopted as sensors and actuators in diverse fields of applications, ranging from microelectromechanical systems (MEMS) for high-precision positioning to vibrational and structural noise control as well as hearing aids. As these materials are taken to their limits by increasing incident fields, frequencies, decreasing size, reaction times as well as transition to large deformation applications, a detailed knowledge on the underlying physics is necessary to enable accurate multi-physics simulations.
The response of ferroelectric or ferromagnetic materials depends on their state of remanent polarization or magnetization and the presence of external electric or magnetic fields. In classical applications, the remanent polarization or magnetization state is assumed as uni-directional and constant. As the operational range of sensors and actuators is extended, this assumption is no longer valid, and an accurate understanding of the evolution of the material’s internal state is imperative. Hysteretic effects observed in multiferroic materials are usually modelled by means of internal variables. The internal variables can be, e.g., remanent magnetization or polarization, internal strains or phase fractions, and describe the microstructure at the macroscopic level of the material.
The main aim is to provide a comprehensive course teaching the fundamentals of hysteretic material behaviour. The course’s content includes the physics of ferroelectrics and ferromagnetics, phenomenological material models, thermodynamically consistent hysteresis models and their mathematical analysis, efficient numerical simulation schemes, and measurement set-ups for deriving the model parameters of real materials.
The course will start with an overview of scalar and vector hysteresis models followed by a detailed discussion of variational inequalities as the principal mathematical tool in hysteresis modelling, hysteresis energy balance, and continuous data dependence. Classical elasto-plasticity serves as an exemplary use-case, where thermodynamic potentials and dissipation functions are defined and their relation to commonly used yield conditions and associated flow rules is shown. The concepts developed there provide the basis for modeling ferroelectric material behavior appearing in piezoelectric ceramics. Next, the transition from microscopic to macroscopic level will be discussed for ferromagnetic materials, addressing also the origin of domain structures, domain wall motion and the rotation of magnetization. At this point, the identification of the material parameters based on measurements will be explained. Hysteresis modeling in materials undergoing large deformations, such as polarizable or magnetizable electro-active polymers, will conclude the theoretical part of the course. For all the above applications, theoretical models are complemented by efficient finite element strategies. In a practical session at the end, participants are encouraged to experiment on the behaviour of different hysteresis models in simple computational setups, which will support the understanding of the theories presented throughout the week.
The course will also include two poster sessions, in which the participants are invited to introduce themselves and to present their current research topics.