MS07 - Advances in Phase Field Modeling: Theory, Algorithms and Applications

Keywords: Phase-field modelling; coupled problems; fracture; microstructure evolution; multiphase flow; numerical methods; topology optimization; crystal growth

Organizers:
Martha Kalina (1) – martha.kalina@tu-dresden.de
Jonas Heinzmann (2) – jheinzmann@ethz.ch
Marco ten Eikelder (3) – marco.eikelder@tu-darmstadt.de

Affiliations:
(1) Chair for Computational and Experimental Solid Mechanics, TU Dresden, Germany
(2) Computational Mechanics Group, ETH Zürich, Switzerland
(3) Institute for Mechanics, TU Darmstadt, Germany

Abstract:
The phase-field method is a well-established approach for modeling a wide range of problems involving evolving boundaries and interfaces. In a continuum approach, the sharp transition between phases is regularized by smooth scalar order parameters. This approach has been successfully applied to various areas, including multi-phase flows with moving boundaries, reaction-diffusion processes, and crystal growth or solidification.  It has also been effectively utilized in the variational formulation of fracture, where the phase-field naturally describes crack initiation and growth. Additionally, phase-field models have demonstrated their versatility in areas such as topology optimization, membrane behavior, and other numerous applications across engineering, materials science, biology, and medicine.

Despite their broad range of applications, phase-field models share key advantages - such as a rigorous mathematical structure and an accurate physical representation of interfaces - as well as common challenges. These challenges include amongst others the temporal and spatial discretization - the latter caused by large gradients of the phase-field at interfaces - as well as stable solution algorithms. In this minisymposium, we aim to explore phase-field modeling approaches across various application domains, with talks addressing theoretical and numerical challenges alike.