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Phase fields, contraints, and the Cahn - Hilliard equation

Event Type
Seminar/Symposium
Sponsor
Department of Mechanical Science and Engineering
Location
2005 Mechanical Engineering Lab (Deere)
Date
Sep 11, 2019   3:00 pm  
Speaker
Professor Eliot Fried, Mathematics, Mechanics, and Materials Unit, Okinawa Institute of Technology, Japan
Contact
Lindsey Henson
E-Mail
lrh@illinois.edu
Phone
217-300-8238
Views
196
Originating Calendar
MechSE Seminars

Abstract

We develop a constrained theory for species migration in bodies with microstructure described by a scalar phase eld. The distinguishing features of the theory stem from a systematic treatment and characterization of the reactions needed to maintain the internal constraint expressing the coincidence of the concentration and phase eld. We also develop boundary conditions for situations in which the interface between the body and its environment is structureless and cannot support species transport. In addition to providing a new derivation of the Cahn{Hilliard equation, the theory aords an interpretation of that equation as a limiting variant of an Allen{ Cahn type diusion system arising from the unconstrained theory obtained by considering the concentration and phase eld as independent quantities. We corroborate that interpretation with three-dimensional numerical simulations of a recently proposed benchmark problem. This work is joint with Fernando Duda and Adel Sarmiento.


Biographical sketch
The speaker obtained his Ph.D. in Applied Mechanics from the California Institute of Technology in 1991. He received a National Science Foundation Mathematical Sciences Postdoctoral Fellowship, a Japan Society for the Promotion of Science Postdoctoral Research Fellowship, and a National Science Foundation Research Initiation Award. Currently he is a tenured professor at the Okinawa Institute of Science and Technology, where he leads the Mathematics, Mechanics, and Materials Unit. Previously, at McGill University, he was a Professor of Mechanical Engineering and the Tier 1 Canada Research Chair in Interfacial and Defect Mechanics. Before that he held tenured positions in the Department of Theoretical and Applied Mechanics at the University of Illinois at Urbana-Champaign and the Department of Mechanical Engineering & Materials Science at Washington University in St. Louis. At Illinois, he was a Fellow of the Center of Advanced Study and was awarded a Critical Research Initiative Grant. In his research, he uses statistical and continuum mechanics and thermodynamics, geometry, asymptotic analysis, bifurcation theory, and large-scale scientic computing to study both fundamental and applied problems involving novel material systems and processes.

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