Modeling Collective Behavior of Dislocations in Crystalline Materials

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Varadhan, Satya N.

Contributors dc:contributor

• Beaudoin, Armand J.

• Engineering, Materials Science

Language dc:language

eng

Identifier

(MiAaPQ)AAI3301241

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/83901