Modeling Collective Behavior of Dislocations in Crystalline Materials
Varadhan, Satya N.
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https://hdl.handle.net/2142/83901
Description
Title
Modeling Collective Behavior of Dislocations in Crystalline Materials
Author(s)
Varadhan, Satya N.
Issue Date
2007
Doctoral Committee Chair(s)
Beaudoin, Armand J.
Department of Study
Mechanical Engineering
Discipline
Mechanical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Materials Science
Language
eng
Abstract
A part of this work deals with the kinematics of dislocation density evolution. An explicit Galerkin/least-squares formulation is introduced for the quasilinear evolution equation, which leads to a symmetric and well-conditioned system of equations with constant coefficients, making it attractive for large-scale problems. It is shown that the evolution equation simplifies to the Hamilton-Jacobi equations governing geometric optics and level set methods in the following physical contexts: annihilation of dislocations, expansion of a polygonal dislocation loop and operation of a Frank-Read source. The weak solutions to these equations are not unique, and the numerical method is able to capture solutions corresponding to shock as well as expansion fans.
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