Multiscale Modeling, Simulation, and Analysis of Microstructure Evolution in Polycrystalline Materials
Multiscale Modeling, Simulation, and Analysis of Microstructure Evolution in Polycrystalline Materials
In this talk, we will present recent perspectives on mathematical modeling, numerical simulation, and mathematical analysis of the evolution of the grain boundary network in polycrystalline microstructures. This evolution is a very complex, multiscale, and multiphysics process.
Our efforts support the solutions of the central problems in materials science, the design of technologies delivering an arrangement of grains that produces a desired set of material properties. Relevant recent experiments, along with current and future research, will be discussed as well.
Most technologically useful materials–spanning the length scale from meters to nanometers, from aircraft to microprocessors–are polycrystalline. Polycrystals are composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The changes in the grain and grain boundary structure of polycrystalline materials highly influence their properties, including, but not limited to, electrical, mechanical, optical, and thermal.
A method by which the grain structure can be engineered in polycrystalline materials is through grain growth (coarsening) of a starting structure. The evolution of the grain/grain boundary structure and associated grain growth involve, for example, the dynamics of grain boundaries, triple junctions in 2D (triple curves/lines and quadruple points in 3D), and the dynamics of lattice misorientations. Therefore, grain growth can be regarded as the anisotropic evolution of a large cellular network and can be described by a set of deterministic local evolution laws (nonlinear ODEs/PDEs) for the growth of individual grains combined with stochastic models for the interaction between them.
Part of this talk is based on the recent collaboration/work with Katayun Barmak (deceased), Batuhan Bayir, William M Feldman, David Kinderlehrer, Chang (Kamala) Liu, Chun Liu, Masashi Mizuno, Thuong Nguyen, Matthew Patrick, and Jeffrey Rickman, and is partially supported by the DMREF program under DMS-2118172 Award and the Simons Foundation Fellowship Award SFI-MPS-SFM-00010667.
The talk is dedicated to the memory of Katayun Barmak and Robert V. Kohn.
SPEAKER BIO: Yekaterina Epshteyn is a Professor of Mathematics at the University of Utah and is currently a 2025 Simons Fellow in Mathematics. She finished her undergraduate degree in Applied Mathematics and Physics at the Moscow Institute of Physics and Technology, Russia in 2000, was an undergraduate/post-undergraduate research assistant/fellow at the Keldysh Institute for Applied Mathematics of Russian Academy of Sciences, Moscow, Russia, 1999 – 2001 and obtained her Ph.D. in Mathematics from the University of Pittsburgh in 2007. She completed a 3-year NSF-RTG postdoctoral position at the Department of Mathematical Sciences and the Center for Nonlinear Analysis at Carnegie Mellon University. She joined the University of Utah in 2010.
Yekaterina Epshteyn’s research interests are in Numerical Analysis, Scientific Computing, Applied Analysis and Mathematical Modeling with applications to problems from Materials Science, Fluid Dynamics, and Biology.