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Title:Modeling Collective Behavior of Dislocations in Crystalline Materials
Author(s):Varadhan, Satya N.
Doctoral Committee Chair(s):Beaudoin, Armand J.
Department / Program:Mechanical Engineering
Discipline:Mechanical Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Engineering, Materials Science
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.
Issue Date:2007
Type:Text
Language:English
Description:89 p.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2007.
URI:http://hdl.handle.net/2142/83901
Other Identifier(s):(MiAaPQ)AAI3301241
Date Available in IDEALS:2015-09-25
Date Deposited:2007


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