Benchmark for the Coupled Magneto-Mechanical Boundary Value Problem in Magneto-Active Elastomers.

Within this contribution, a novel benchmark problem for the coupled magneto-mechanical boundary value problem in magneto-active elastomers is presented. Being derived from an experimental analysis of magnetically induced interactions in these materials, the problem under investigation allows us to validate different modeling strategies by means of a simple setup with only a few influencing factors. Here, results of a sharp-interface Lagrangian finite element framework and a diffuse-interface Eulerian approach based on the application of a spectral solver on a fixed grid are compared for the simplified two-dimensional as well as the general three-dimensional case. After influences of different boundary conditions and the sample size are analyzed, the results of both strategies are examined: for the material models under consideration, a good agreement of them is found, while all discrepancies can be ascribed to well-known effects described in the literature. Thus, the benchmark problem can be seen as a basis for future comparisons with both other modeling strategies and more elaborate material models.

Interplay of domain structure and phase transitions: theory, experiment and functionality.

Domain walls and phase boundaries are fundamental ingredients of ferroelectrics and strongly influence their functional properties. Although both interfaces have been studied for decades, often only a phenomenological macroscopic understanding has been established. The recent developments in experiments and theory allow to address the relevant time and length scales and revisit nucleation, phase propagation and the coupling of domains and phase transitions. This review attempts to specify regularities of domain formation and evolution at ferroelectric transitions and give an overview on unusual polar topological structures that appear as transient states and at the nanoscale. We survey the benefits, validity, and limitations of experimental tools as well as simulation methods to study phase and domain interfaces. We focus on the recent success of these tools in joint scale-bridging studies to solve long lasting puzzles in the field and give an outlook on recent trends in superlattices.

Multi-phase-field model for surface and phase-boundary diffusion.

The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase boundaries, i.e., the boundaries between a condensed phase and its vapor and the boundaries between two or multiple condensed phases. The effect of capillarity is modeled via curvature dependence of the chemical potential whose gradient gives rise to diffusion. The model is used to study thermal grooving on the surface of a polycrystalline body. Decaying oscillations of the surface profile during thermal grooving, postulated by Hillert long ago but reported only in few studies so far, are observed and discussed. Furthermore, annealing of multi-nanoclusters on a deformable free surface is investigated using the proposed model. Results of these simulations suggest that the characteristic craterlike structure with an elevated perimeter, observed in recent experiments, is a transient nonequilibrium state during the annealing process.