Conference Agenda

Phase field modeling has been widely applied to model the evolution of domain patterns in various phase transformation problems. Existing phase-field models for the evolution of domain structures in ferroelectrics are based on an Allen-Cahn-type evolution law. This evolution law successfully captures equilibrium domain structures. However, it fails to capture rate effects due to its assumption of a linear kinetic relation between the thermodynamic driving force acting on a domain wall and the domain wall velocity. To overcome this limitation, we propose a new phase field model for ferroelectrics (Guin and Kochmann, 2022), one that incorporates nonlinearities in the kinetics of domain walls and fully accounts for electro-mechanical coupling. As a multi-phase-field generalization of the model of Alber and Zhu (2013), it is based on the domain volume fraction of each variant as the primary phase field and incorporates the anisotropic dielectric, elastic, and piezoelectric properties of the different variants. This multi-phase field generalization further allows imposing different kinetic relations in different types of domain walls. This new phase field model is validated through a comparison with the target sharp-interface model embedding nonlinear kinetics. With the ability to easily modify these different material properties, we investigate multiphysical effects to the growth of the ferroelectric embryo, and show the open challenge (in common with all ferroelectric phase field models) of the magnitude of the interfacial energy of the regularized domain wall.

Ferroelectrics exhibit many interesting effects, both linear and nonlinear, which is why these materials are widely used in science and industry. Recently, the nonlinear effects have also been employed in the field of energy harvesting [1, 2, 3], while for a long time only linear effects were exploited. Moreover, nonlinear effects are irreversible and are accompanied by energy dissipation, which generally leads to a temperature rise of the material. For modeling the characteristic nonlinear effects of ferroelectric materials, there are various possibilities, in particular microphysical and, phenomenological models.

For describing mutually coupled dissipative processes in ferroelectrics, in particular ferroelectric domain switching and viscoelasticity, a hybrid micromechanical - rheological constitutive model is developed and embedded in the framework of a multiscale modeling approach. The mathematical theory is consistent against the background of rational thermodynamics and deals with two types of internal variables. The advanced modeling approach is applied to identify novel energy harvesting cycles exploiting dissipative effects, resulting in a major electric work output.

REFERENCES

[1] W. Kang, L. Chang and J. E. Huber, Nano Energy 93 (2022), p. 106862.

[2] L. Behlen, A. Warkentin and A. Ricoeur, Smart Mater. Struct. 30 035031 (2021).

[3] A. Warkentin, L. Behlen and A. Ricoeur, Smart Mater. Struct. 10.1088/1361-665X/acafba (2023).

Magneto-active elastomers (MAE) are one of many emerging functional materials. Research applications span mechanical, civil, and biomedical engineering as actuators, sensors, vibration absorbers and vibration isolators. MAE consist of a soft elastomeric matrix filled with small, relatively rigid magnetizable inclusions. Set in a magnetic field, the inclusions deform the microstructure and, at the macro-scale, either stiffen by up to three orders of magnitude or bend to large strains.

Most MAE models focus on magneto-mechanical constitutive relations. This contribution showcases other physical phenomena and their coupled interactions. These phenomena include thermo-mechanical coupling and viscous dissipation leading to heat generation within the material. The model is capable of capturing dynamic effects, particularly when MAE are used as vibration absorbers. Formulated for three-dimensional finite deformations, this model handles incompressible material behavior through a Q1P0 finite element framework.

This study explores the relationship between magnetic fields and deformation in Ferromagnetic Shape Memory Alloys (FSMA), which are materials capable of sensing and actuation. These alloys can exhibit high strains of up to 6% when subjected to a magnetic field. To achieve this goal, a finite deformation formulation approach is proposed based on the multiplicative decomposition of the deformation gradient. In addition, a magneto-thermo-mechanical constitutive model for FSMA is discussed, which is based on a specific Helmholtz free energy function. The evolution equations of the internal magnetic and mechanical state variables are determined using a transformation function, and the model parameters are calibrated under different loading conditions. Finally, the model predictions for FSMA are compared against experimental results.

The renewable energy supply, the independence of fossil resources, as well as the change in mobility act as a driving force on technological innovation. To meet these challenges of our time, new and particularly powerful highperformance magnets are necessary [1], relying on new earth abundant materials and resource efficient processes. It has been shown that composite materials consisting of ferromagnetic grains separated by paramagnetic interphases can contribute to significant improvements in coercivity, when these interphases decouple the magnetic exchange between the individual grains, compare [2]. Novel processing routes based on severe plastic deformations (SPD) or additive manufacturing (AM) can be an option to tailor such magnetic composites. Here, the micromagnetic theory can be applied to numerically predict the magnetization distributions on fine scales. Due to their flexibility, finite elements are well suited to discretize and analyze strongly heterogeneous microstructures [3]. The evolution of the magnetization vectors is described by the Landau-Lifshitz-Gilbert equation, which requires the numerically challenging preservation of the Euclidean norm of the magnetization vectors, see [4,5]. With the aim to correctly reproduce the behavior of magnetic materials, competing energy contributions are considered within the energy functional, which are also responsible for the formation of magnetic domains. Also, grain boundaries, defect layers and misoriented grains can have a huge impact on the macroscopic hysteresis behavior of magnetic materials. Especially magnets formed by SPD are exposed to the potential stress-induced defects that might outweigh their

production benefits. Hence, micromagnetics analyses are performed to estimate the risks and challenges of these novelties.

[1] O. Gutfleisch, et al.: Magnetic Materials and Devices for the 21st Century: Stronger, Lighter, and More Energy Efficient. Advanced Materials, 23, 821–842, (2011).

[2] M. Soderznick, et al.: Magnetization reversal of exchange-coupled and exchange-decoupled Nd-Fe-B magnets observed by magneto-optical Kerr effect microscopy. Acta Materialia, 135, 68–76, (2017).

[3] A. Vansteenkiste, et al.: The design and verification of MuMax3. AIP Advances, 4, 107133, (2014).

[4] A. Prohl: Computational Micromagnetism. Springer, (2001).

[5] M. Reichel, B.-X. Xu and J. Schröder: A comparative study of finite element schemes for micromagnetic mechanically coupled simulation. Journal of Applied Physics, 132, 183903, (2022).